A Quantitative Evaluation of UAV Flight Parameters for SfM-Based 3D Reconstruction of Buildings

Abstract

This study aims to address the critical lack of standardized guidelines for unmanned aerial vehicle (UAV) image acquisition strategies utilizing structure-from-motion (SfM) by focusing on 3D building exterior modeling. A comprehensive experimental analysis was conducted to systematically investigate and quantitatively evaluate the effects of various shooting patterns and parameters on SfM reconstruction quality and processing efficiency. This study implemented a systematic experimental framework to test various UAV flight patterns, including circular, surface, and aerial configurations. Under controlled environmental conditions on representative building structures, key variables were manipulated, and all collected data were processed through a consistent SfM pipeline based on the SIFT algorithm. Quantitative evaluation results using various analytical methodologies (multiple regression analysis, Kruskal–Wallis test, random forest feature importance, principal component analysis including K-means clustering, response surface methodology (RSM), preference ranking technique based on similarity to the ideal solution (TOPSIS), and Pareto optimization) revealed that the basic shooting pattern ‘type’ has a significant and statistically significant influence on all major SfM performance metrics (reprojection error, final point count, computation time, reconstruction completeness; Kruskal–Wallis p < 0.001). Additionally, within the patterns, clear parameter sensitivity and complex nonlinear relationships were identified (e.g., overlapping variables play a decisive role in determining the point count and completeness of surface patterns, with an adjusted R² ≈ 0.70; the results of circular patterns are strongly influenced by the interaction between radius and tilt angle on reprojection error and point count, with an adjusted R² ≈ 0.80). Furthermore, composite pattern analysis using TOPSIS identified excellent combinations that balanced multiple criteria, and Pareto optimization explicitly quantified the inherent trade-offs between conflicting objectives (e.g., time vs. accuracy, number of points vs. completeness). In conclusion, this study clearly demonstrates that hierarchical strategic approaches are essential for optimizing UAV-SfM data collection. Additionally, it provides important empirical data, a validated methodological framework, and specific quantitative guidelines for standardizing UAV data collection workflows, thereby improving existing empirical or case-specific approaches.

1. Introduction

Inspecting and maintaining the exterior walls of buildings on a regular basis is essential for ensuring structural safety, increasing energy efficiency, and maintaining aesthetics [1]. There are a growing number of aging buildings worldwide, and with increasing social demands for building safety and stricter regulations, the need for reliable exterior inspections is becoming even more critical [2]. In addition, these diagnostic and related maintenance activities form a significant economic scale, with related costs showing a continuous upward trend [3]. These strong economic and social demands highlight the need for alternative methods that can overcome the potential risks and inefficiencies of traditional manual methods. As a result, the sustained growth of the building exterior wall inspection market is serving as a key driver for the adoption of new technologies in this field [4].

The introduction of automated technologies for efficiently and objectively collecting information on the condition of building exteriors is actively underway, with particular attention being paid to 3D data acquisition methods [5]. Traditional exterior wall inspection methods require workers to physically access the exterior walls, resulting in significant time and cost expenditures, as well as safety hazards during high-rise operations and subjective results [6]. As an alternative to address these issues, among various automated technologies being explored, those focusing on non-contact 3D data acquisition methods such as laser scanning and photogrammetry are emerging [7]. Notably, photogrammetry using unmanned aerial vehicles (UAVs) enables rapid imaging of large areas and facilitates data acquisition in hard-to-reach high-rise or complex structures, leading to a rapid increase in their application [8].

In this technological transition, the Structure from Motion (SfM) method provides the core component of the process for generating 3D models from UAV images [9]. This computer vision algorithm automatically extracts and matches feature points in image sequences captured from multiple angles to simultaneously estimate the camera’s external appearance features and the target’s 3D structure [10]. Generally, the camera information and sparse point cloud estimated with high precision through SfM are used as input for subsequent Multi-View Stereo (MVS) algorithms, directly enabling more accurate and complete dense point cloud generation and thus contributing to the final generation of a dense 3D model [11]. Therefore, SfM can be defined as an essential method element responsible for initial data processing and geometric information restoration in UAV image-based 3D modeling pipelines.

However, there is currently a lack of quantified standards or specific guidelines for image capture procedures and related parameter settings for SfM-based 3D building modeling using UAVs. The absence of standardized procedures or quantitative guidelines can exacerbate various practical problems during UAV photogrammetry work on large-scale buildings or structures with complex shapes. First, it is difficult to select the most appropriate shooting strategy based on objective evidence, considering the project objectives and the characteristics of the target building, thereby hindering rational decision-making. Second, inconsistently collected data increase the likelihood of errors in subsequent processing and reduce the reliability of key quality indicators such as the accuracy and completeness of the final 3D model. Third, it impairs the reproducibility of the data collection and processing processes, which manifests as issues such as failed alignment between upper and lower viewpoints of high-rise buildings [7], the necessity of a control system when operating multiple drones [12], and difficulties in establishing flight paths suitable for complex shapes [13]. These practical challenges act as constraints in ensuring the practical applicability and scientific rigor of UAV photogrammetry. Therefore, the establishment of systematic and standardized data collection methodologies is urgently required to enhance the reliability and utility of UAV photogrammetry.

This study aims to address the lack of standardized guidelines in the process of collecting image data using UAVs and applying SfM for diagnosing building exteriors. It systematically experiments with and quantitatively verifies the effects of various UAV shooting patterns (Circular, Close-up, Aerial, etc.), key variables (Distance, Overlap Rate, Camera Angle, etc.), and their combinations on the quality and processing efficiency of SfM results. Specifically, image data of actual buildings were collected for various shooting scenarios according to the designed experimental framework, and all collected data were processed using a specified and consistent SfM pipeline (e.g., utilizing the SIFT algorithm). Quantitative indicators such as reprojection error, final point count, computation time, and reconstruction completeness were calculated from the processing results, and the obtained data were analyzed using multiple regression analysis, nonparametric statistical tests, variable importance analysis, dimension reduction, clustering, response surface analysis, multi-criteria decision-making, and Pareto optimization. While this study focuses on common facade types under typical daylight conditions using standard commercial UAVs, its findings require careful consideration for highly reflective surfaces or extreme weather. The optimal data acquisition strategy derived from this study will provide concrete and reliable quantitative evidence that supports rational decision-making by balancing the quality of results required in practice with practical constraints (time, budget, etc.), surpassing the limitations of existing empirical methods.

2. Literature Review

2.1. Acquisition of Building Shape Information

Building geometry information is used as core data throughout the entire building lifecycle management process, including structural stability checks, material deterioration assessments, identification of exterior damage and defects, and maintenance plan development [14]. In particular, damage frequently occurs due to long-term use, environmental changes, and material deterioration, and accurate shape information is essential for effective management [11]. Traditional surveying methods include high-altitude work, photography, and aerial photography. These methods have issues such as difficulty in accessing high-rise exterior walls, safety concerns in operating equipment, and reduced economic efficiency due to long working hours [15].

Various 3D surveying and restoration technologies can be applied to collect building shape information. These include 3D scanning, photogrammetry, and 360-degree camera photography, each with its own advantages and limitations. First, 3D scanning is a technology that uses sensors such as laser scanners (LiDAR) or structured light to acquire high-precision, high-density point cloud data [16]. It is widely used in cultural heritage restoration, industrial plant measurement, and precise architectural structure measurement [17]. This method ensures high precision but requires expensive equipment, installation, and operation personnel, and faces measurement constraints in accessing high-rise exteriors [18]. Photogrammetry is a technology that analyzes multiple overlapping photographs to restore 3D information [19]. It uses general cameras, resulting in low equipment costs and flexibility for various scales and shapes of objects. Photogrammetry has already been applied in pilot studies for small-scale buildings or civil engineering structures, and it is able to easily obtain images even in locations difficult to access using UAVs [20,21]. However, when applied to large-scale structures, issues such as securing shooting points and blind spots arise, and image quality management is crucial for obtaining high-precision and high-density point clouds. Additionally, a well-planned shooting path is necessary to cover complex shapes. In this context, 360-degree cameras can record the entire surrounding environment in a single shot, making them useful for virtual tours and real estate presentations [22]. However, due to resolution limitations, they often lack sufficient detail and struggle to reproduce high-precision 3D data, making them unsuitable for precise structural analysis or defect detection [23].

An approach that simultaneously achieves measurement accuracy, efficiency, and minimization of blind spots by comparing and integrating these individual methodologies is necessary for rapid and precise modeling of building exteriors. Considering the significant cost and access limitations of 3D scanning for frequent, large-scale assessments and the precision drawbacks of 360-degree cameras for detailed analysis, photogrammetry emerges as a promising candidate. Therefore, when photogrammetry, which offers cost-effectiveness and ease of use, is combined with UAV-based image acquisition, significantly improved accessibility and data collection capabilities compared to existing methods can be expected.

2.2. Structure from Motion (SfM)

Three-dimensional reconstruction is essential in a wide range of fields, including computer vision, robotics, and cultural heritage preservation [24]. Structure from Motion (SfM) and Multi-View Stereo (MVS) are core image-based approaches that complement each other. SfM estimates the camera pose and sparse 3D structure of a scene from multiple 2D images, based on the principles of motion parallax and projection geometry [25]. This process typically involves stable feature detection and matching (e.g., SIFT, ORB), camera relative/absolute pose estimation using epipolar geometry and PnP algorithms, 3D point location calculation via triangulation, and global optimization through bundle adjustment [26]. SfM ultimately generates a sparse point cloud but inherently suffers from scale ambiguity and assumes static scenes, relying on robust geometric verification procedures such as RANSAC for outlier removal [27]. As a result, SfM serves the role of providing camera parameters and an initial geometric skeleton essential for subsequent dense reconstruction stages [28]. The quality and completeness of the results produced in the SfM stage directly influence the performance of the MVS stage, which aims to achieve detailed surface reconstruction of the scene [11].

SfM implementation strategies are broadly categorized into incremental and global approaches, each with distinct advantages and disadvantages in terms of accuracy, robustness, and scalability. These two primary strategies, incremental and global SfM, present distinct trade-offs as summarized in

Table 1. SfM Approach Comparison.

Feature	Incremental SfM	Global SfM	Latest Trends
Accuracy	Generally high	Initially low, improving	Aims for incremental SfM level or higher
Robustness	High (Iterative RANSAC/BA)	Low (Outlier sensitive, Weak translation averaging)	Aims for incremental SfM robustness
Scalability	Low (Sequential, Iterative BA)	High (Parallelizable)	Maintains high scalability
Cost	High (Repeated BA)	Low (Fewer BA)	Maintains low cost (Faster than incremental)
Error Accum.	Possible (Drift)	Relatively low	Suppressed by global approach
Challenges	Cost, Drift	Translation avg. instability, Outlier sensitivity	Solving translation avg., Ensuring robustness
Implement.	COLMAP	Theia, OpenMVG	GLOMAP

. Meanwhile, MVS leverages the principle of photometric consistency based on SfM results. Incremental SfM starts with a small number of images, sequentially adds views, and pursues high accuracy through iterative local optimization (bundle adjustment), but it has issues such as error drift and increased computational costs when processing large datasets [29]. On the other hand, global SfM simultaneously estimates all camera poses, offering superior computational efficiency and scalability, but it is sensitive to initial relative pose estimation errors and outliers, and ensuring stability in the translation averaging stage remains a technical challenge [30]. MVS utilizes precisely estimated camera parameters from SfM to estimate dense geometric information by evaluating pixel value similarity across multiple views based on specific depth or surface location assumptions [31]. It primarily estimates 3D coordinates by searching for corresponding points based on photometric consistency between features within a scene. Stathopoulou and Remondino [32] emphasized that this principle of photometric consistency forms the foundation of MVS methodologies. Therefore, MVS goes beyond sparse feature-based Structure from Motion (SfM) results to enable detailed 3D shape reconstruction of surfaces. The following discussion will examine the actual performance evaluation and technical limitations of the SfM-MVS pipeline in detail. Therefore, the choice of the SfM strategy determines the quality of the input information for MVS, and MVS itself fundamentally relies on the assumption that corresponding surface points appear similar across different views [33]. However, this core assumption of MVS is often violated in real-world environments, particularly with common building materials featuring reflective surfaces or large areas of uniform, textureless appearance necessitating advanced algorithms to handle such complexities during the dense reconstruction process [34].

One of the important limitations inherent in many MVS approaches is the difficulty of accurately restoring so-called weakly supported surfaces, which lack texture or have high reflectance. These types of surfaces do not provide sufficient photogrammetric information for reliable correspondence matching at multiple points, causing difficulties in the restoration process. This issue significantly impacts the reconstruction of planar structures commonly found in artificial environments, potentially resulting in incomplete or inaccurate models. Yan et al. [35] proposed a method to improve the completeness of reconstruction in such cases by interpolating points within the detected 3D plane boundaries. However, this solution is limited to planar geometric structures and often requires manual intervention for object plane identification, thereby limiting its generalizability and automation potential. Therefore, developing methods to robustly and automatically restore various types of weakly supported surfaces remains an important research challenge.

Previous research on SfM-MVS methodology has driven significant algorithmic advancements aimed at improving the quality and robustness of 3D reconstruction. These advancements are evident across various domains, ranging from feature detection and matching strategies to dense reconstruction algorithms that incorporate both traditional and learning-based paradigms. Algorithm improvements and comparative evaluations have been continuously conducted to optimize various stages of the reconstruction pipeline [32,36]. Nevertheless, challenges such as handling surfaces with insufficient texture or high reflectivity, ensuring scalability and preserving fine details remain ongoing challenges that highlight the difficulties still present [32,35]. While algorithmic advancements have mitigated some of the limitations from the past, consistently obtaining precise and complete 3D geometric information across diverse real-world environments remains a challenge, highlighting the need for novel approaches, potentially integrating learning-based priors or advanced data fusion techniques, to overcome these persistent limitations, especially in the context of building modeling.

2.3. Previous Research on SfM-Based 3D Reconstruction

Previous studies have extensively demonstrated the usefulness of combining unmanned aerial vehicle (UAV) platforms and the SfM-MVS pipeline for 3D reconstruction in various fields, particularly in the areas of cultural heritage preservation and building modeling. These studies have explored various platform types, onboard sensors, and data processing workflows, recognizing that careful planning is crucial for successful reconstruction [37]. Additionally, efforts have been made to improve specific algorithm components, such as enhancing the robustness of the MVS stage through learning-based approaches or developing multiple drone systems to increase the efficiency of large-scale data acquisition [12,20]. However, many studies have primarily focused on the application of the technology itself or algorithm improvements after data acquisition and often use flight paths that are manually designed or limited to specific situations without undergoing rigorous optimization processes. As a result, there is a significant gap in systematic verification and optimization studies on the impact of data acquisition strategies, particularly the influence of various flight patterns and parameters on the reconstruction quality of complex structures. To address these issues, it is necessary to shift the focus of research toward quantitatively evaluating the impact of flight design on the entire SfM-MVS workflow.

The absence of a systematic flight planning and quantitative evaluation framework is hindering the establishment of reliable and optimized UAV data acquisition protocols for SfM-MVS-based 3D reconstruction. Some studies have attempted model-based path planning methods that consider surface coverage or “reconstructability” metrics, but these methods do not necessarily guarantee globally optimal solutions, and thorough quantitative evaluation of the resulting SfM-MVS outputs is often lacking [13]. Other studies point out issues arising from inappropriate viewpoint distributions, such as registration failures due to large viewpoint differences or performance degradation of new viewpoint image synthesis algorithms, indirectly emphasizing the need for well-designed data acquisition patterns [38]. Crucially, the existing literature generally lacks comprehensive and comparative analyses of quantitative metrics such as feature point density distribution, reprojection error statistics, model completeness, processing time, and memory usage across various flight scenarios (e.g., grid-based, spiral, oblique angle capture patterns, overlap ratio, and flight altitude changes). The absence of such a systematic and metric-driven validation process makes it challenging to generalize research results or establish standardized best practices for acquiring high-quality data tailored to the complexity and reconstruction objectives associated with specific objects.

Therefore, this study aims to establish standardized guidelines for image data collection using UAV and the application of SfM for building exterior diagnosis. To achieve this, we will systematically experiment and quantitatively verify the effects of various UAV shooting patterns, key variables (distance, overlap rate, camera angle, etc.), and their combinations on the quality and processing efficiency of SfM results.

3. Methodology

This section describes in detail the research methodology designed to address the lack of standardized guidelines for the collection of building exterior image data using UAVs and the application of SfM. To systematically conduct the research, an analysis framework was established, UAV shooting patterns and variables were defined based on this framework, and a specific implementation environment was set up to ensure consistent experimentation. This methodology covers the entire process from data collection to result analysis, with a focus on ensuring the reliability and reproducibility of the research results. This study was conducted based on a systematic analysis framework to quantitatively clarify the relationship between UAV shooting variables and SfM processing results.

This framework consists of sequential steps: data collection planning, actual data acquisition, SfM processing, and result indicator evaluation (Figure 1). At each stage, core variables were defined, a consistent data processing pipeline was applied, and objective performance evaluation metrics were selected to achieve the research objectives. For example, in the data collection stage, scenarios were designed by combining various shooting paths, separation distances, overlap rates, and camera tilts, and all collected images were processed using the same SfM algorithm (SIFT-based) and parameter settings. This framework provides a systematic basis for comparing and analyzing the impact of various shooting conditions on the accuracy, completeness, and efficiency of SfM results. In this context, ‘Reconstruction Completeness’ is quantitatively defined as the percentage of the facade’s surface area that is successfully represented in the final 3D point cloud, measured against a high-density ground truth model.

Next, to effectively collect 3D shape information of building envelopes, a combination of various drone shooting patterns and key variables was systematically designed and tested. The main variables considered included shooting path type, distance from the target (A-offset, B-Radius), image overlap rate (forward and lateral overlap), and camera tilt angle. The imaging patterns applied in the experiments were defined into three main types: Circular, Surface, and Aerial (Figure 2,

Table 2. Defined shooting patterns and parameters.

Pattern Type	Key Variables	Parameter Range/Values	Notes
Circular	Altitude (AGL)	20~80 m (relative to rooftop)	Tilt angle oriented towards building center
	Radius (B-Rad)	10~50 m (from center point)
	Tilt Angle	adjusted to face center
Surface	Distance (A-Offset)	10~30 m	Designed for facade scanning
	Forward Overlap	1 m, 2 m, 4 m
	Side Overlap	1 m, 2 m, 4 m
	Tilt Angle	0°, 15°, 30°, 45°
Aerial	Altitude (AGL)	20 m, 40 m	Nadir/Oblique grid pattern
	Overlap (Forward/Side)	Fixed at 80%
	Tilt Angle	60°~75°
All Patterns	Positioning Accuracy (GNSS-RTK)	Horizontal and Vertical < 2~3 cm	Verified via pre-flight simulation

). Specifically, the circular shooting method was performed by adjusting the tilt angle toward the center of the building within a height range of 20 to 80 m from the building roof and a radius range of 10 to 50 m from the center point. The frontal shooting method was performed by setting the distance from the target to 10 to 30 m, the forward and lateral overlap distances to 1, 2, and 4 m, and the tilt angle to 0°, 15°, 30°, 45°, and the aerial photography method was conducted at altitudes of 20 and 40 m above the rooftop with an overlap rate of 80% and a tilt angle of 60–75°. Additionally, to ensure precise location information for each shooting point, GNSS-RTK was utilized to manage horizontal and vertical position errors within 2–3 cm. Prior to actual flight, simulations were conducted to verify the safety and appropriateness of the planned flight path. This comprehensively defined combination of capture patterns and variables enables data collection under various conditions, serving as a foundation for enhancing the reliability of subsequent analyses. In addition to analyzing these single patterns individually, this study also investigated composite shooting strategies, where data from two different patterns were combined. This was done to evaluate whether hybrid approaches could leverage the strengths of each pattern to produce a more comprehensive 3D model.

To ensure consistency and data quality in collecting building envelopes using UAVs, the experimental implementation environment was specifically defined and controlled (

Table 3. Implementation Environment Definition.

Category	Parameter	Specification/Value	Purpose/Note
Hardware	UAV Model	DJI Mavic 3 Enterprise	Commercial-grade drone
	Sensor Resolution	5280 × 3956 pixels (~20.9 MP)	High-resolution imaging
	Focal Length	12.3 mm (24 mm equiv.)	Wide-angle lens suitable for facade mapping
	Aperture	F/2.8 (fixed)	Balance light intake and depth of field
Camera Settings	Shutter Speed	1/2000 s	Minimize motion blur during flight
	ISO	400	Fixed to maintain consistent noise levels
	Color Space	sRGB	Standard color representation
	White Balance	Manual	Ensure color consistency
	Exposure Mode	Manual	Consistent exposure across images
	Exposure Compensation	0 EV	No automatic brightness adjustment
Environmental Conditions	Lighting	Overcast sky, <20,000 lux	Minimize shadows and harsh lighting variations
	Weather	No direct sunlight, cloudy	Consistent ambient lighting
Data Acquisition Summary	Target Building	Similar characteristics to apartment buildings	Representative structure
	Total Flight Paths	126	Covering diverse scenarios
	Avg. Flight Time per Path	~10 min
	Total Images Collected	13,416	Sufficient data for analysis
	Image Format	JPEG	Common image format
	Average File Size	~7.8 MB per image
	Metadata Recorded	Timestamp, GPS Coordinates, Camera Model, Exposure Info, etc.	Essential for processing and analysis reproducibility

). In this study, a commercial UAV model, DJI Mavic 3 Enterprise (DJI, Shenzhen, China), was used, and the camera mounted on it had the following specifications: effective pixel count of 5280 × 3956 (~20.9 MP), 35 mm equivalent focal length of 24 mm (original focal length of 12.3 mm), and a fixed aperture value of F/2.8. To minimize image blur during shooting, the shutter speed was set to 1/2000 s, the ISO sensitivity was fixed at 400 to manage noise levels, and the color space was set to sRGB to ensure consistent color reproduction. White balance was set to manual, exposure mode was set to manual, and exposure compensation was maintained at 0. In addition, to minimize data bias caused by changes in light conditions, all shots were taken on a cloudy day with no direct sunlight (measured illuminance of 20,000 lux or less). Buildings with architectural features similar to those of apartment complexes were selected as the experimental subjects, and a total of 13,416 images were collected through 126 different flight path designs with an average flight time of 10 min (number of images per path: circular 30–41, front 18–411, aerial 40–125) (Figure 3). All collected images were saved in JPEG format with an average size of 7.8 MB, and each image was accompanied by detailed metadata, including the shooting time, GPS coordinates, and camera and lens information.

4. Validation

Following the research flowchart (Figure 1), multifaceted analysis of single and multiple UAV shooting pattern data was conducted to quantitatively verify the influence of shooting variables on Structure from Motion (SfM) result indicators (

Table A1. SfM results for single flight pattern.

Pattern	Offset Distance	Radian	Forward Overlap (m)	Side Overlap (m)	Tilt Angle	Reprojection Error	Final Points	Registered Images	Mean Track Length	Point Density	Reconstruction Completeness	Computation Time (min)	Total Features
Circular	20	10	-	1	63.4	124.3939	33,210	35	90.32	0.1267	0.9459	3.63	666
Circular	20	20	-	1	45	132.685	27,280	34	−1	7.6351	0.9444	4.16	618
Circular	40	10	-	1	76	126.6485	35,120	36	−1	0.1714	0.9474	4.53	703
Circular	40	20	-	1	63.4	126.058	30,303	34	−1	1.3026	0.9444	4.47	630
Circular	40	30	-	1	53.1	136.3338	29,454	34	−1	5.2306	0.9444	4.31	630
Circular	40	40	-	1	45	136.3338	29,454	34	−1	5.2306	0.9444	4.31	630
Circular	40	50	-	1	38.7	156.2284	25,039	34	−1	5.0211	0.9444	8.32	549
Circular	60	10	-	1	80.5	132.8113	34,030	34	53.72	0.0571	0.9444	6.93	630
Circular	60	20	-	1	71.6	129.7001	34,584	34	728.14	0.8784	0.9444	6.31	630
Circular	60	30	-	1	63.4	129.7001	34,584	34	728.14	0.8784	0.9444	6.31	630
Circular	60	40	-	1	56.3	143.3672	33,524	34	−1	6.9719	0.9444	5.08	630
Circular	60	50	-	1	50.2	152.4983	31,645	34	−1	4.5198	0.9444	4.78	622
Circular	80	20	-	1	76	130.3469	36,155	34	144.44	0.5553	0.9444	7.7	630
Circular	80	30	-	1	69.4	135.738	37,659	34	568.94	1.3056	0.9444	5.54	630
Circular	80	40	-	1	63.4	145.7929	35,092	34	−1	4.1629	0.9444	4.78	630
Circular	80	50	-	1	58	145.7929	35,092	34	−1	4.1629	0.9444	4.78	630
Surface	10	-	1	1	0	126.2504	244,956	386	11459.98	0.0266	0.9948	30.12	47,431
Surface	10	-	1	1	15	126.2504	244,956	386	11,459.98	0.0266	0.9948	30.12	47,431
Surface	10	-	1	1	30	116.0709	260,805	385	10,790.98	0.0258	0.9948	32.95	49,122
Surface	10	-	1	1	45	103.7865	250,460	381	6348.13	0.024	0.9948	23.62	53,334
Surface	10	-	1	2	0	136.0838	136,274	205	7161.62	0.0479	0.9903	25.58	13,152
Surface	10	-	1	2	15	132.4321	130,594	200	4092.17	0.0211	0.9901	29.47	12,335
Surface	10	-	1	2	30	122.4061	139,154	199	3241.23	0.0278	0.99	33.62	12,739
Surface	10	-	1	2	45	108.9702	142,087	197	2155.59	0.0266	0.99	24.24	14,054
Surface	10	-	1	4	0	139.8755	70,166	109	2547.65	0.0336	0.982	25.25	3696
Surface	10	-	1	4	15	138.2702	64,126	106	1702.08	0.0134	0.9815	29.53	3441
Surface	10	-	1	4	30	138.2702	64,126	106	1702.08	0.0134	0.9815	29.53	3441
Surface	10	-	1	4	45	112.5045	80,870	109	210.86	0.0403	0.982	26.6	4193
Surface	10	-	2	1	0	134.116	119,438	192	2777.12	0.0187	0.9897	30.15	11,767
Surface	10	-	2	1	15	134.116	119,438	192	2777.12	0.0187	0.9897	30.15	11,767
Surface	10	-	2	1	30	122.886	129,485	192	1215.99	0.0219	0.9897	33.61	12,224
Surface	10	-	2	1	45	108.5725	134,300	190	1124.01	0.0449	0.9896	24.91	13,288
Surface	10	-	2	2	0	143.9869	56,231	102	1204.69	0.0249	0.9808	26.84	3251
Surface	10	-	2	2	15	142.6184	50,242	97	1016.29	0.0074	0.9798	30.62	2939
Surface	10	-	2	2	30	129.0874	55,608	99	437.28	0.0121	0.9802	35.09	3188
Surface	10	-	2	2	45	112.254	65,824	98	393.11	0.0138	0.98	25.18	3479
Surface	10	-	2	4	0	148.5389	23,576	54	313.27	0.0263	0.9643	26.57	923
Surface	10	-	2	4	15	150.365	18,565	52	325.12	0.0052	0.9811	30.89	804
Surface	10	-	2	4	30	188.2078	332	65	−1	1.2115	0.9811	24.01	918
Surface	10	-	2	4	45	114.8124	28,820	54	−1	0.0325	0.9643	27.65	1016
Surface	10	-	4	1	0	145.3158	57,307	101	1974.9	0.0486	0.9806	25.25	3185
Surface	10	-	4	1	15	141.8635	50,919	95	242.25	0.0085	0.9794	31.21	2910
Surface	10	-	4	1	30	128.4746	55,605	95	−1	0.0147	0.9794	34.81	3044
Surface	10	-	4	1	45	112.2702	64,456	94	−1	0.0522	0.9792	25.68	3322
Surface	10	-	4	2	0	151.6473	17,177	46	−1	0.0119	0.9388	33.56	720
Surface	10	-	4	2	15	151.6473	17,177	46	−1	0.0119	0.9388	33.56	720
Surface	10	-	4	2	30	136.0137	18,479	47	−1	0.0102	0.94	38.04	778
Surface	10	-	4	2	45	113.4647	26,665	50	−1	0.0172	0.9615	26.38	907
Surface	10	-	4	4	0	157.4342	6518	24	−1	0.0079	0.8889	33.18	199
Surface	10	-	4	4	15	158.6881	4880	24	−1	0.0047	0.8889	37.25	204
Surface	10	-	4	4	30	164.5591	279	30	−1	0.2522	0.8889	26.62	216
Surface	10	-	4	4	45	114.8897	9687	27	−1	0.1767	0.931	28.06	261
Surface	20	-	1	1	0	117.4807	215,946	370	37,253.42	0.0477	0.9946	8.71	62,637
Surface	20	-	1	1	15	110.8154	230,876	369	35,045.16	0.0523	0.9946	13.14	61,923
Surface	20	-	1	1	30	91.6698	228,508	372	26,412.67	0.0347	0.9947	21.69	58,153
Surface	20	-	1	1	45	76.4481	205,333	370	12,493.58	0.0579	0.9946	13.54	59,541
Surface	20	-	1	2	0	122.3159	136,409	192	19,439.12	0.0409	0.9897	9.34	16,750
Surface	20	-	1	2	15	116.0804	145,108	194	17,347.84	0.0382	0.9898	13.98	17,057
Surface	20	-	1	2	30	96.3049	143,972	194	18,102.06	0.0754	0.9898	22.33	15,841
Surface	20	-	1	2	45	81.1682	128,709	192	5803.54	0.1279	0.9897	13.69	16,014
Surface	20	-	1	4	0	126.8276	82,441	104	8368.59	0.0483	0.9811	10.37	4833
Surface	20	-	1	4	15	119.8551	88,141	106	7969.87	0.0305	0.9815	14.7	5044
Surface	20	-	1	4	30	100.445	88,680	104	7972.34	0.0315	0.9811	23.04	4495
Surface	20	-	1	4	45	85.6205	79,142	103	1971.81	0.0634	0.981	14.11	4619
Surface	20	-	2	1	0	122.6949	12,4828	184	15,036.38	0.031	0.9892	9.13	15,618
Surface	20	-	2	1	15	122.6949	12,4828	184	15,036.38	0.031	0.9892	9.13	15,618
Surface	20	-	2	1	30	96.2432	13,4237	185	6888.16	0.0652	0.9893	21.78	14,467
Surface	20	-	2	1	45	96.2432	13,4237	185	6888.16	0.0652	0.9893	21.78	14,467
Surface	20	-	2	2	0	128.8887	72,343	95	5084.25	0.0244	0.9794	10	4155
Surface	20	-	2	2	15	122.0118	74,507	96	2119.56	0.0214	0.9796	14.06	4251
Surface	20	-	2	2	30	109.8035	3679	159	−1	1.5683	0.9796	8.19	3907
Surface	20	-	2	2	45	85.1361	72,991	95	−1	0.0514	0.9794	14.24	3967
Surface	20	-	2	4	0	136.5335	36,370	52	3465.17	0.0112	0.963	11.53	1229
Surface	20	-	2	4	15	128.4041	38,392	52	1159.09	0.0525	0.963	15.38	1247
Surface	20	-	2	4	30	110.1034	3558	114	−1	1.6157	0.963	4.94	1101
Surface	20	-	2	4	45	89.1996	39,466	51	−1	0.0253	0.9623	15.25	1155
Surface	20	-	4	1	0	130.3841	69,471	91	4512.23	0.0787	0.9785	9.49	3859
Surface	20	-	4	1	15	122.3447	70,516	91	4758.61	0.0285	0.9785	13.88	3848
Surface	20	-	4	1	30	100.5156	77,388	92	1705.85	0.0636	0.9787	22.62	3613
Surface	20	-	4	1	45	84.5974	70,656	91	−1	0.0534	0.9785	14.6	3690
Surface	20	-	4	2	0	136.5941	35,242	47	714.78	0.0711	0.9592	10.63	1041
Surface	20	-	4	2	15	128.3716	33,188	46	−1	0.031	0.9583	14.94	997
Surface	20	-	4	2	30	128.3716	33,188	46	−1	0.031	0.9583	14.94	997
Surface	20	-	4	2	45	88.1287	39,462	48	−1	0.0935	0.96	15.4	1026
Surface	20	-	4	4	0	147.6474	12,580	25	14.04	0.0349	0.9259	14.69	297
Surface	20	-	4	4	15	139.5202	12,650	25	−1	0.0108	0.9259	19.01	303
Surface	20	-	4	4	30	111.5926	13,406	24	544.54	0.0399	0.9231	27.23	256
Surface	20	-	4	4	45	111.5926	13,406	24	544.54	0.0399	0.9231	27.23	256
Surface	30	-	1	1	0	99.8357	140,081	229	14,082.35	0.0318	0.9913	3.08	26,561
Surface	30	-	1	1	15	99.5791	133,387	229	18,462.12	0.0218	0.9913	4.64	26,454
Surface	30	-	1	1	30	95.0395	135,652	229	9239.27	0.0454	0.9913	10.87	24,852
Surface	30	-	1	1	45	91.6557	123,570	228	13,476.39	0.1231	0.9913	5.82	24,920
Surface	30	-	1	2	0	103.9715	88,734	119	7106.93	0.0118	0.9835	3.2	7260
Surface	30	-	1	2	15	104.1194	85,163	119	14,956.72	0.0212	0.9835	4.84	7231
Surface	30	-	1	2	30	104.1194	85,163	119	14,956.72	0.0212	0.9835	4.84	7231
Surface	30	-	1	2	45	104.1194	85,163	119	14,956.72	0.0212	0.9835	4.84	7231
Surface	30	-	1	4	0	108.0496	51,259	64	19.77	0.0236	0.9697	3.73	2145
Surface	30	-	1	4	15	109.498	49,515	64	7069.7	0.0138	0.9697	5.79	2126
Surface	30	-	1	4	30	109.498	49,515	64	7069.7	0.0138	0.9697	5.79	2126
Surface	30	-	1	4	45	100.0733	44,627	63	1800.06	0.085	0.9692	6.72	1929
Surface	30	-	2	1	0	103.3338	83,067	114	5171.95	0.0283	0.9828	3.19	6670
Surface	30	-	2	1	15	103.6918	79,677	114	5787.55	0.0381	0.9828	4.82	6644
Surface	30	-	2	1	30	98.3177	80,441	114	2173.11	0.1169	0.9828	11.35	6229
Surface	30	-	2	1	45	95.1229	72,872	113	3914.18	0.0355	0.9826	6.06	6184
Surface	30	-	2	2	0	107.1248	56,041	64	869.59	0.044	0.9697	3.9	2145
Surface	30	-	2	2	15	107.5477	54,533	64	4926.83	0.0808	0.9697	5.96	2129
Surface	30	-	2	2	30	101.0973	53,221	64	564.33	0.0852	0.9697	13.67	1936
Surface	30	-	2	2	45	98.0697	42,136	55	2619.23	0.0993	0.9649	6.23	1502
Surface	30	-	2	4	0	112.9791	27,057	34	813.64	0.0393	0.9444	5.08	630
Surface	30	-	2	4	15	112.9791	27,057	34	813.64	0.0393	0.9444	5.08	630
Surface	30	-	2	4	30	107.305	25,475	34	36.11	0.0934	0.9444	13.86	565
Surface	30	-	2	4	45	101.7301	21,249	29	743.06	0.045	0.9355	8.09	433
Surface	30	-	4	1	0	109.4827	42,376	56	3125.72	0.0301	0.9655	3.93	1653
Surface	30	-	4	1	15	109.7895	42,050	56	1420.88	0.0842	0.9655	5.67	1641
Surface	30	-	4	1	30	102.0954	41,935	56	1342.17	0.0246	0.9655	12.34	1541
Surface	30	-	4	1	45	98.4708	39,761	56	1560.79	0.0126	0.9655	6.68	1557
Surface	30	-	4	2	0	113.9939	23,814	31	793.3	0.0378	0.9394	5.57	528
Surface	30	-	4	2	15	113.9939	23,814	31	793.3	0.0378	0.9394	5.57	528
Surface	30	-	4	2	30	106.3159	23,281	31	−1	0.0415	0.9394	14.87	473
Surface	30	-	4	2	45	100.9601	19,539	27	725.38	0.0712	0.931	8.12	383
Surface	30	-	4	4	0	117.2254	11,803	16	−1	0.016	0.8889	11.52	153
Surface	30	-	4	4	15	120.2272	11,648	16	−1	0.0345	0.8889	16.56	152
Surface	30	-	4	4	30	110.2882	12,756	16	−1	0.0205	0.8889	24.48	138
Surface	30	-	4	4	45	102.0131	12,644	16	−1	0.0763	0.8889	18.72	139
Aerial	20	-	1	1	60	95.2114	80,012	118	632.21	0.2456	0.9752	10.19	4108
Aerial	40	-	1	1	75	95.6289	31,755	44	−1	3.0771	0.9565	4.57	904

). Initially, the Kruskal–Wallis test was applied to establish the overall statistical significance of the basic shooting pattern ‘type’. Subsequently, the influence of individual parameters within each pattern was quantified; Multiple Regression was used to model linear trends, while Random Forest Feature Importance assessed non-linear contributions. The interactive effects between key variable pairs were then visualized using Response Surface Methodology (RSM). To further characterize the performance space, Principal Component Analysis (PCA) and K-Means Clustering were employed to identify distinct outcome profiles. Finally, to identify the most efficient shooting strategies amidst conflicting objectives, TOPSIS was used to rank composite patterns, and Pareto Optimization was applied to delineate the optimal trade-off frontiers. The key findings and implications derived from the analysis are presented for each analytical methodology, and the study concluded by synthesizing these findings to discuss the contributions and limitations of the research.

4.1. Single Shooting Pattern

4.1.1. Multiple Regression

Multiple Regression analysis assumes a linear relationship between each shooting variable and SfM result indicators (final number of points, reconstruction completeness, reprojection error, calculation time, etc.), and aims to determine the magnitude of the influence of individual variables on changes in result indicators (regression coefficients), statistical significance (p-value), and the explanatory power of the model as a whole (adjusted R-squared).

The results of the surface capture pattern analysis showed that the variables related to the overlap between images, Forward Overlap and Side Overlap, exhibited a close linear relationship with the quality indicators of SfM results (

Table 4. Summary of multiple regression analysis of the effect of shooting variables on SfM result metrics.

Shooting Pattern	Surface				Circular
Dependent Variable	Final Points	Reconstruction Completeness	Reprojection Error	Computation Time	Final Points	Reconstruction Completeness	Reprojection Error	Computation Time
Adj R-squared	0.6960	0.7620	0.3780	0.0150	0.7750	0.4930	0.7520	−0.0400
Prob	0.0000	0.0000	0.0000	0.2110	0.0001	0.0105	0.0002	0.5140
Coef Intercept	211,300	1	112	12	14,250	1	112	7
Prob Intercept	0.000	0.000	0.000	0.000	0.104	0.000	0.000	0.353
Coef Forward Overlap	−30,560	−0.0150	3.8176	1.2686	0.4770	−0.0001	−0.0589	0.0471
Prob Forward Overlap	0.0000	0.0000	0.0020	0.1070	50.637	0.0070	0.7570	0.4010
Coef Side Overlap	−27,830	−0.0126	4.2159	0.5805	0.6550	0.0001	0.6943	−0.0399
Prob Side Overlap	0.0000	0.0000	0.0010	0.4580	236.21	0.0420	0.0520	0.6770
Coef Tilt angle	−11.886	0.0000	−0.6057	0.0683	0.1020	0.0001	0.1200	−0.0429
Prob Tilt angle	0.9520	0.7320	0.0000	0.2420	47.058	0.0110	0.7620	0.7100

). Specifically, these two variables showed statistically highly significant (p < 0.001) negative regression coefficients for both the number of points generated and the model reconstruction completeness. This quantitatively demonstrates that as the values of these variables decrease, i.e., as the physical overlapping between images increases, the number of points and reconstruction completeness increases linearly. These results align precisely with the fundamental principle of SfM that sufficient feature matching between multi-view images is essential for successful 3D reconstruction and statistically reaffirm that ensuring overlap is a critical factor for quality improvement. Data analysis results show that the Forward Overlap and Side Overlap variables accounted for approximately 70% (adjusted R² ≈ 0.70) of the variability in Final Points and approximately 68% (adjusted R² ≈ 0.68) of the variability in Reconstruction Completeness. Additionally, these variables had a significant negative impact on reducing projection errors; however, the model’s explanatory power was relatively low, at approximately 21% (adjusted R² ≈ 0.21). On the other hand, the camera tilt angle variable did not show statistically significant linear effects on most of the result indicators in this analysis model.

In the case of the Circular shooting pattern, the influence of variables different from those in the Surface pattern was prominent. An increase in the radius when shooting in a circular pattern around the subject suggested a significant (p ≈ 0.052) positive relationship with an increase in the reprojection error. This implies that as the shooting distance increases, the geometric accuracy of the final model may decrease due to changes in image scale and increased likelihood of feature point matching errors. The explanatory power of the model was high, at approximately 80% (adjusted R² ≈ 0.80). In contrast, an increase in the camera tilt angle showed a statistically significant (p ≈ 0.003) positive relationship with an increase in the final number of points (adjusted R² ≈ 0.69). This suggests that capturing objects from more diverse angles can reduce occlusion areas and enhance the model’s detail. However, high condition numbers were observed in some regression models used in the Circular pattern analysis, raising the possibility of multicollinearity. Multicollinearity implies strong correlations among independent variables, meaning that changes in one variable (e.g., Diameter) may be associated with changes in another variable (e.g., Tilt angle). Therefore, a cautious approach is required to interpret the independent pure effects of each variable on the outcome metric. Similarly to how specific tilt angle settings may impose constraints on the minimum shooting radius in real-world scenarios, these variables may be difficult to control independently.

In conclusion, multiple regression analysis clearly demonstrated that the key variables influencing SfM results can vary depending on the shooting pattern. In the Surface pattern, ensuring image overlap plays a decisive role in improving result quality, while in the Circular pattern, the shooting radius and camera tilt angle can have opposite effects on reprojection error and point count, respectively, and the potential for interaction between these variables must be considered. Furthermore, the relatively low adjusted R² values observed in some result metrics (e.g., Reprojection Error in the Surface pattern model) suggest that these result metrics cannot be perfectly explained by simple linear relationships with the shooting variables considered in this study.

4.1.2. Kruskal–Wallis Test

Next, considering the possibility that the distribution characteristics of SfM result data generated under various shooting conditions, particularly the assumptions of normality and homoscedasticity, may not be satisfied, we applied the Kruskal–Wallis test, a nonparametric statistical test. The purpose of this analysis was to rigorously verify whether there were statistically significant differences in the median distributions of the main SfM result indicators according to the three main shooting pattern types (‘Circular’, ‘Surface’, ‘Aerial’) as categorical variables.

The results of the Kruskal–Wallis test analysis confirmed that statistically significant differences existed in the median distributions of all major SfM result metrics investigated in this study, namely reprojection error, final number of points generated, total computation time, and reconstruction completeness, across shooting pattern types. This demonstrates that the Kruskal–Wallis test is less stringent in its assumptions about data distribution, making it flexible for application in real-world data analysis scenarios, and clearly shows that the ‘type’ of shooting pattern itself is an important factor explaining the variability in the result metrics in this dataset. The specific Kruskal–Wallis test results for each performance metric are summarized in

Table 5. Summary of Kruskal–Wallis test on the effect of shooting variables on SfM result metrics.

Dependent Variable	Kruskal–Wallis (H)	Kruskal–Wallis (p)
Reprojection Error	20.2338	0.0001
Final Points	7.4992	0.0235
Computation Time	25.8498	0.0001
Reconstruction Completeness	15.7081	0.0004

. For the reprojection error, the H statistic was 20.23 (p < 0.001), for the final number of points, H = 7.50 (p = 0.024), for computation time, H = 25.84 (p < 0.001), and for reconstruction completeness, H = 15.71 (p < 0.001). All p-values were significantly lower than the conventional significance level of 0.05, strongly supporting that the observed differences in the distribution of outcome metrics between shooting pattern types were not due to chance.

These results provide important insights beyond the parameter influences identified in the previous multiple regression analysis. Specifically, they provide strong experimental evidence that the choice of shooting ‘type’ itself has a decisive influence on the overall result quality (model accuracy and completeness) and processing efficiency (computation time) of SfM-based 3D modeling projects.

Therefore, when conducting actual 3D modeling projects, it is essential to comprehensively consider various factors such as the geometric shape of the target building or structure (e.g., vertically tall buildings, horizontally wide structures, presence of complex curved surfaces or corners, etc.), accessibility constraints during on-site photography, and the intended use of the final modeling results (e.g., focus on overall shape restoration or detailed diagnosis and precise analysis of specific parts) to select the most appropriate basic shooting pattern type (e.g., Surface pattern for wide area coverage, Circular pattern for specific objects or complex shapes) as a priority.

4.1.3. Random Forest Feature Importance

To address the inherent limitations of multiple regression analysis, which assumes linear relationships, and to more comprehensively understand the complex interactions and nonlinear relationships between shooting variables and their impact on SfM result metrics, we performed feature importance analysis using Random Forest, a machine learning technique. This analysis aims to evaluate the relative importance of each shooting variable in predicting specific SfM result metric values by quantifying their contribution as importance values (

Table 6. Random forest feature importance ranking and distribution by shooting type and result indicator.

Shooting Type	Dependent Variable	1st Feature (Importance≈)	2nd Feature (Importance≈)	3rd Feature (Importance≈)	Importance Distribution
Circular	Computation Time	Tilt angle (0.59)	Distance (0.30)	Radian (0.12)	High-Mid-Low
	Final Points	Tilt angle (0.71)	Distance (0.22)	Radian (0.07)	High-Mid-Low
	Reconstruction Completeness	Radian (0.60)	Distance (0.28)	Tilt angle (0.14)	High-Mid-Low
	Reprojection Error	Radian (0.82)	Tilt angle (0.12)	Distance (0.06)	Very High Dominance
Surface	Computation Time	Tilt angle (0.39)	Forward overlap (0.31)	Side overlap (0.30)	Similar High-Mid
	Final Points	Forward Overlap (0.52)	Side overlap (0.45)	Tilt angle (0.03)	Two High, One Low
	Reconstruction Completeness	Forward Overlap (0.50)	Side overlap (0.46)	Tilt angle (0.04)	Two High, One Low
	Reprojection Error	Tilt angle (0.59)	Side overlap (0.21)	Forward overlap (0.20)	High, Two Mid

Importance Scale: High (>0.40), Mid (0.10~0.40), Low (<0.10).

).

The results of the Random Forest analysis for surface capture patterns showed that the two variables related to image overlap, Forward overlap and Side overlap, had a combined importance of 0.9 or higher in predicting the Final Points and Reconstruction Completeness metrics, indicating that they exert an absolute influence. This trend aligns with the regression analysis results, reaffirming that ensuring overlap is the most critical factor for the number of points and completeness of the model. On the other hand, in the Computation Time prediction model, the three variables Forward overlap, Side overlap, and Tilt angle all showed relatively similar and high importance levels between 0.3 and 0.4, suggesting that computation time is influenced by a combination of multiple variables. Interestingly, in the Reprojection Error prediction, Tilt angle was found to be significantly more important than Forward overlap and Side overlap

In the case of the Circular shooting pattern, the importance of variables showed a distinct difference depending on the target result indicator. Camera tilt angle was the most important variable, with an importance of approximately 0.71 in the prediction of the final number of points and approximately 0.59 in the prediction of computation time. On the other hand, shooting radius showed the highest importance, with approximately 0.82 in reprojection error prediction and approximately 0.60 in reconstruction completeness prediction. The importance of camera height offset was evaluated as relatively low or moderate, ranging from 0.06 to 0.30, in most of the analyzed result indicators. It is particularly noteworthy that the Tilt angle variable of the Surface pattern, which did not show a statistically significant linear relationship with Reprojection Error and Computation Time in multiple regression analysis or had a small influence, was evaluated as an important variable in the random forest analysis. This strongly suggests that Tilt angle may influence the result indicators in a non-linear manner rather than a simple linear relationship, or that it may contribute to the prediction performance through interactions with other variables (e.g., overlap). This emphasizes that complex relationships between variables that are difficult to capture with linear models alone may exist.

In conclusion, Random Forest variable importance analysis partially confirms the results of multiple regression analysis (e.g., the importance of the overlap variable in the Surface pattern) while providing a clearer understanding of the relative importance of variables from a nonlinear model perspective. Additionally, it offers specific insights into how the influence of each shooting variable varies depending on the shooting pattern and the target outcome metric. For example, when applying the Circular pattern, if improving geometric accuracy or completeness of reconstruction is the top priority, controlling the shooting radius is essential, but if maximizing the model’s detail (number of points) or processing efficiency management is important, it is necessary to focus more on optimizing the camera tilt angle.

4.1.4. Principal Component Analysis and K-Means Clustering

To mitigate the complexity of the multidimensional performance space composed of multiple disparate SfM result metrics and effectively identify the intrinsic structure of the data, we sequentially applied principal component analysis (PCA) and k-means clustering techniques. First, PCA was used to reduce the multivariate performance data into a smaller set of core principal components (PCs), making visualization and interpretation easier. Subsequently, the k-means clustering algorithm was applied to group shooting settings (data points) with similar performance characteristics, aiming to classify overall performance patterns and identify the unique characteristics of each cluster. To ensure the robustness of the analysis, rows containing outliers defined based on missing values and the interquartile range (IQR) were preemptively removed from the original data before performing PCA and clustering (

Table 7. Explanation of top principal components.

Principal Component	Individual Explained Variance (%)	Cumulative Explained Variance (%)
PC1	43.5	43.5
PC2	22.6	66.1
PC3	16.8	≈82.8

).

For the analysis, we standardized six key performance metrics (Reprojection Error, Final Points, Mean Track Length, Point Density, Computation Time, Reconstruction Completeness) and then performed PCA. The results showed that the top three principal components (PC1, PC2, PC3) explained approximately 82.8% of the total data variance (individual explanatory power: PC1 43.5%, PC2 22.6%, PC3 16.8%). This indicates that a relatively small number of principal components effectively summarize a significant portion of the information in the original data without loss, successfully achieving dimension reduction.

PCA is useful for interpreting complex multivariate data, and by analyzing the correlations (loading values) between each principal component axis and the original variables, one can understand their meaning. For example, if the loading value analysis shows that PC1 has a high positive correlation with indicators related to ‘overall reconstruction quality and detail’ and a negative correlation with Reprojection Error, then the PC1 axis can be interpreted as a comprehensive indicator of model quality. Similarly, PC2 may show a high correlation with variables related to ‘computational efficiency’. Next, we applied the Elbow method to determine the optimal number of clusters (k) for cluster analysis. By observing the changes in the within-cluster sum of squares, the ‘elbow’ point where the slope of the graph curve becomes the most gradual was clearly identified when the number of clusters was 2, and the optimal number of clusters was finally determined to be 2.

Using the determined optimal number of clusters (k = 2), k-means clustering was performed, and the results were visualized in a two-dimensional space with PC1 and PC2 as axes (Figure 4). The visualization results showed that the two clusters (Cluster 0 and Cluster 1) tended to be relatively clearly distinguished based on the PC1 axis. Specifically, Cluster 0 was mainly distributed in the negative region of PC1, while Cluster 1 was primarily located in the positive region of PC1. However, some data points were observed to be mixed in the boundary region between the two clusters.

In conclusion, the unsupervised learning analysis combining PCA and k-means clustering strongly suggests that the extensive UAV-SfM shooting settings tested in this study do not simply form a continuous performance spectrum but naturally divide into two distinct performance profile groups when considering multiple performance metrics comprehensively.

4.1.5. Response Surface Methodology (RSM)

RSM approximates the relationship between selected independent variable pairs and the dependent variable using a quadratic polynomial regression model and presents the results as a visual response surface or contour plot. This technique is useful for intuitively identifying patterns of relationships between variables and local regions of optimal variable combinations that optimize specific outcome metrics. Therefore, to explore the combined effects of two shooting variables changing simultaneously on specific SfM outcome metrics and potential interactions beyond the influence of individual variables, this study employed RSM (

Table 8. Summary of Key RSM Results.

Analysis Combination	Adjusted R2	Key Feature of Response Surface/Contour	Key Implication
Circular: Final Points vs. (Offset, Tilt angle)	0.876	Gentle ridge shape, points tend to increase towards top-right (high values)	Tilt angle influence relatively large; optimum for max points found
Circular: Reprojection Error vs. (Radian, Tilt angle)	0.856	Elliptical valley shape, error minimum in specific zone (Brad ≈ 10–15 m, Tilt ≈ 55–65°)	Interaction effect is important; identifies ‘sweet spot’ for min error
Surface: Computation Time vs. (Forward Overlap, Side Overlap)	0.003	Parallel straight contours, time increases linearly as overlap decreases (overlap area increases)	Increased overlap causes more computation time; model fit very low
Surface: Final Points vs. (Forward Overlap, Tilt angle)	0.422	Nearly vertical contours, points increase sharply as Forward Overlap decreases	Forward Overlap is decisive for points; Tilt angle effect minimal
Surface: Reconstruction Completeness vs. (Side Overlap, Tilt angle)	0.286	Near-vertical contours, completeness increases as Side Overlap decreases	Side Overlap mainly affects completeness; Tilt angle effect negligible

).

For the analysis, a quadratic polynomial regression model was constructed for five predefined combinations of (independent variable pairs × dependent variable), and the explanatory power (Adjusted R²) of each model varied from approximately 0.42 to 0.80 depending on the analyzed combination, confirming that the model’s suitability varies depending on the case. For example, in the Circular pattern, the model predicting Reprojection Error using Radian and Tilt angle as variables showed an adjusted R² value of approximately 0.80, indicating relatively high explanatory power and suggesting that the quadratic relationship between the variable combination and the result indicator is well explained.

The prediction results of each RSM model were visualized as contour plots showing the trend of changes in the predicted values of the dependent variable according to changes in the two independent variables. The analysis of the Circular pattern showed that Final Points increased as both offset and Tilt angle increased, with the contour lines forming a gentle ridge shape where the influence of Tilt angle appeared to be greater (Figure 5). The optimal region that maximizes the number of points in this model is interpreted as being in the upper right of the plot, i.e., the region where both variables are high. On the other hand, Reprojection Error exhibited a distinct elliptical valley-shaped response surface, minimizing when both Radian and Tilt angle were within specific ranges (as described in the text, Radian ≈ 10–15 m, Tilt ≈ 55–65°). When the optimal region is exceeded, the reprojection error increases, and a tendency for the error to increase more prominently as the shooting radius increases was observed.

The results of the surface pattern analysis showed a different pattern (Figure 6). Computation Time increased linearly as Forward overlap and Side overlap decreased (i.e., as the overlapping area between images increased), and the contour lines appeared as straight lines that were almost parallel. Final Points depended mainly on Forward overlap, increasing sharply as this value decreased (i.e., as the overlap increased), while the influence of Tilt angle was negligible, with contour lines appearing almost vertical. Similarly, Reconstruction Completeness also primarily depends on Side overlap, showing an increasing trend as the overlap increases, while the influence of Tilt angle is negligible, resulting in contour lines that are nearly vertical.

4.1.6. Pareto Optimization of Single Shooting Patterns

Based on previous analyses, it is common for various performance goals pursued in UAV-SfM-based 3D modeling tasks, such as reducing computation time, minimizing reprojection error, maximizing the number of points, and maximizing reconstruction completeness, to be in conflict with each other (trade-offs). In this section, a Pareto optimization analysis was performed by pairing the main performance objectives (e.g., computational time–reprojection error, computational time–number of points, reprojection error–number of points, computational time–reconstruction completeness). Pareto optimization is a multi-objective optimization methodology that aims to identify a set of “non-dominated” solutions, where improving one specific objective necessarily results in a loss in one or more other objectives, thereby forming the Pareto Frontier. Among the entire set of shooting configurations (data points) analyzed for each goal combination, different configurations were identified as Pareto optimal solutions, and

Table 9. Summary of Pareto Optimization Analysis for Key Objective Pairs.

Objective Pair Analyzed	N Points on Frontier	Key Frontier Characteristics and Implication
Time vs. Error	4	Weakly concave shape (bottom-left); diminishing returns for error reduction over time
Time vs. Points	5	Concave rising shape; diminishing returns for point increase over time
Error vs. Points	4	Concave shape (top-left); clear trade-off exists, optimal balance selection needed
Time vs. Completeness	4	Nearly horizontal shape (top-left); diminishing returns for completeness improvement over time

summarizes the analysis results for each goal combination.

Visualizing the Pareto frontier for each goal combination clearly revealed the trade-off characteristics between goals (Figure 7). The frontier for the ‘Error_vs._Points’ combination exhibited a concave shape toward the upper left, indicating low error and high point count simultaneously. This suggests that there is an efficient range where the number of points can be significantly increased by slightly allowing (increasing) the error, while there is a range where the number of points must be significantly sacrificed to reduce the error below a certain level. On the other hand, the frontier for the ‘Time-vs-Completeness’ combination is in the upper left corner, indicating short computation time and high reconstruction completeness, and exhibits a nearly horizontal shape. This indicates a ‘diminishing returns’ phenomenon, meaning that even with significantly more time invested beyond a certain point, the improvement in completeness is minimal, while it is possible to achieve a fairly high level of reconstruction completeness (0.985 or higher) within a very short computation time (e.g., 3–8 min). The frontier of the ‘Time_vs._Error’ combination is located in the lower left (short time, low error) and exhibits a slightly convex shape, indicating that investing a little more time initially (e.g., 3–6 min) can significantly reduce errors, but the error reduction effect gradually diminishes with further time investment. Finally, the frontier of the ‘Time_vs._Points’ combination shows a convex upward trend from the lower left to the upper right, indicating that initial time investment (e.g., 3–14 min) is highly effective in increasing the number of points, but additional time investment beyond that point contributes significantly less to further increases in the number of points.

Considering specific requirements or constraints unique to each project (e.g., limited total working time, required minimum accuracy level, required model detail), this study provides quantitative grounds for reasonably selecting the most efficient shooting strategy (parameter combination) from among multiple alternatives on the Pareto frontier that best fits the given conditions. For example, in a project with a very tight deadline, the solution located farthest to the left on the time-related axis among the analyzed frontiers (the fastest time) can be prioritized. Conversely, if the final model’s detail is the top priority, the optimal balance point can be sought around the solutions with the highest number of points on the ‘Time_vs._Points’ or ‘Error_vs._Points’ frontier.

4.2. Analysis of Multiple Shooting Patterns

The effects of individual shooting variables on SfM result metrics were analyzed from various angles within different single shooting patterns (Surface, Circular, Aerial), and the importance of multifaceted performance evaluation beyond single target optimization was confirmed. However, single shooting patterns alone may not be sufficient for complete 3D modeling of complex structures, and a composite shooting strategy combining shooting patterns with different characteristics may be required. Therefore, in this section, we comprehensively evaluate the performance of such composite shooting patterns and analyze their characteristics.

4.2.1. Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS)

Composite shooting pattern strategies offer the potential to leverage the advantages of various individual patterns, but at the same time, the performance criteria that need to be evaluated become more complex. In this study, we applied the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), one of the multi-criteria decision-making (MCDM) techniques, to comprehensively consider multiple performance criteria and evaluate the overall effectiveness or preference of various composite shooting pattern combinations, thereby determining their relative rankings. The analysis considered a total of seven performance criteria, including input-related indicators such as computation time, number of images used, and reprojection error, as well as output-related indicators such as final point count, reconstruction completeness, point density, and average track length.

In this analysis, equal weights were assigned to all performance criteria to calculate the comprehensive performance score for each composite shooting pattern combination (

Table 10. Performance indicators of composite shooting patterns ranked by TOPSIS.

Topsis Rank	Pattern1	Pattern2	Topsis DistIdeal	Topsis DistNegIdeal	Topsis Score
1	C_O40	L_O30	0.039644	0.088516	0.69067
2	C_O20	L_O30	0.041811	0.091929	0.687373
3	L_O30	P_O40	0.041934	0.09167	0.68613
4	C_O40	P_O20	0.046117	0.099455	0.683203
5	P_O20	P_O40	0.046888	0.099512	0.679727
6	L_O30	P_O20	0.039896	0.084661	0.679699
7	C_O20	P_O20	0.047719	0.099743	0.6764
8	C_O20	C_O40	0.051008	0.104072	0.671084
9	C_O40	P_O40	0.050765	0.103508	0.670941
10	C_O20	P_O40	0.052928	0.103664	0.661999
11	C_O20	L_O10	0.041451	0.080858	0.661095
12	C_O40	L_O10	0.041381	0.080343	0.660041
13	L_O10	P_O40	0.041964	0.080544	0.657458
14	L_O10	P_O20	0.046425	0.077117	0.624216
15	C_O20	L_O20	0.048799	0.070943	0.592463
16	L_O20	P_O40	0.048934	0.070758	0.591167
17	C_O40	L_O20	0.0494	0.069785	0.585517
18	L_O20	P_O20	0.053078	0.066345	0.555547
19	L_O10	L_O30	0.062454	0.064512	0.508104
20	L_O20	L_O30	0.074386	0.052379	0.413198
21	L_O10	L_O20	0.104304	0.051267	0.329539

). The naming convention for each analysis is “[Shooting Type]_O[Distance Value (m)]” (e.g., C_O20: Circular pattern offset distance 20 m). According to the TOPSIS analysis results, the composite shooting pattern named C_O40_S_O30 (Circular pattern offset distance 40 m and Surface pattern offset distance 30 m) achieved the highest overall efficiency score (TOPSIS Score: 0.691) and was selected as the top-ranked combination with the best performance under the evaluated criteria.

Following closely behind were C_O20_S_O30 (Score: 0.687), S_O30_A_O40 (Score: 0.686), and C_O40_A_O20 (Score: 0.683), which formed the top ranks with minimal score differences, demonstrating high overall performance. On the other hand, the S_O10_S_O20 combination recorded the lowest score (Score: 0.330) and was evaluated as the least efficient composite shooting pattern under the same weighting conditions as the criteria considered in this analysis. In summary, this result indicates that a complex shooting path plan that maximizes the estimation of architectural features is more beneficial for 3D reconstruction than a method that collects as many detailed images as possible from nearby shooting points.

In conclusion, by applying the TOPSIS method, we were able to integrate multiple conflicting performance criteria into a single quantitative score, enabling an objective comparison of the ‘overall performance’ of various composite shooting patterns and assigning relative priorities. The composite shooting pattern combinations ranked at the top in this analysis (C_O40_S_O30, C_O20_S_O30, etc.) can be considered as promising candidate strategies for achieving overall effective 3D modeling results under resource-constrained environments (e.g., time, cost).

4.2.2. Pareto Optimization of Multiple Shooting Patterns

The TOPSIS analysis comprehensively considered multiple performance criteria with equal weights to rank the overall efficiency of composite shooting patterns. This confirmed that combinations such as C_O40_L_O30 are excellent strategies that satisfy multiple criteria in a balanced manner. However, certain objectives (e.g., fast processing time or highest accuracy) may be more important than others. Therefore, in addition to the overall ranking from TOPSIS, it is important to identify which composite shooting strategies are the most efficient alternatives for performance goal pairs with significant trade-offs (e.g., time vs. error). To this end, we performed a Pareto optimization analysis on the composite shooting pattern data, similarly to the single pattern analysis, to identify the Pareto frontier.

The analysis was conducted using composite pattern data targeting the same key goal combinations considered in the single pattern analysis, and the sets of Pareto optimal solutions and frontier forms for each combination are shown below (Figure 8). The analysis results show that different composite shooting pattern combinations form a Pareto optimal frontier for each goal combination, indicating an efficient trade-off between the goals. As a specific example, only three composite pattern combinations were identified as Pareto optimal solutions for the ‘Time_vs._Error’ objective combination. These combinations are located in the efficient region in the lower left corner of the visualization results, achieving relatively short computation times (estimated to be in the range of 0–35 min) and low reprojection errors (approximately 1.08–1.09) simultaneously. Additionally, for the ‘Time_vs._Points’ combination, a total of 13 composite pattern combinations formed the Pareto frontier. This frontier exhibited a convex upward trend from the lower left (short time, few points) to the upper right (long time, many points), indicating that the initial time investment (estimated to be in the range of 0–70 min) is highly effective for increasing the number of points, but the efficiency of additional time investment decreases sharply thereafter, demonstrating the ‘diminishing returns’ trend in composite pattern analysis. Similar Pareto optimal sets were identified for other key goal combinations such as ‘Error_vs._Points’ and ‘Time_vs._Completeness’, with each frontier presenting the most efficient trade-offs between the respective goals.

In conclusion, even when using composite shooting patterns, non-dominated strategies exist that demonstrate superior or at least equivalent efficiency compared to other combination strategies under specific performance goal combinations. Therefore, when selecting the final composite shooting strategy, it is reasonable to prioritize the comprehensive performance rankings derived from the TOPSIS analysis (Table 10) while selecting the solution that provides the most appropriate balance on the Pareto frontier (Figure 7) for the relevant goal combinations based on the specific requirements of the project (e.g., time constraints, quality goals).

4.3. Discussion

The individual variable effects on analyzed single and composite shooting patterns, performance comparisons between pattern types, and multi-criteria and multi-objective optimization evaluations clearly demonstrated that the UAV-based SfM 3D reconstruction process is a multifaceted optimization problem that goes beyond a simple input–output relationship. From the fundamental selection of capture patterns to the fine-tuning of individual parameters and the inevitable trade-offs between different performance metrics (e.g., accuracy, completeness, efficiency), the quantitative results emphasize the necessity of a systematic and data-driven strategic approach to maximize the efficiency and quality of SfM-based 3D modeling.

Most importantly, the fundamental and significant influence of the basic shooting pattern “type” (e.g., Circular, Surface, Aerial) on the quality and efficiency of subsequent results was statistically clarified through Kruskal–Wallis tests. The results of this non-parametric test proved that the median distributions of key SfM result metrics, such as reprojection error, final point count, computation time, and reconstruction completeness, differ statistically significantly (p < 0.05) depending on the shooting pattern type (Table 5). This suggests that determining the most appropriate macro-level shooting approach that aligns with the project’s objectives (e.g., geometric characteristics of the subject, required model precision, available resources) is a prerequisite before optimizing individual variables. In other words, the pattern type itself acts as a critical design factor that primarily constrains or defines the result space, serving as the foundation for determining the direction and effectiveness of subsequent parameter optimization.

Within a specific selected shooting pattern type, detailed parameters such as overlap, shooting distance/radius, and camera tilt function as key variables that control the result metrics. The results of the multiple regression analysis, Random Forest variable importance evaluation, and response surface analysis (RSM) in this study consistently demonstrated that the influence of these variables varies depending on the target performance metric and the selected pattern type, and includes not only simple linear relationships but also complex nonlinear relationships and interactions between variables. In the Surface pattern, the overlap degree variable exerted a dominant influence on the number of points and reconstruction completeness (regression analysis R² ≈ 0.70, RF importance sum ≈ 0.9), In the Circular pattern, the shooting radius and tilt angle each played distinct yet important roles in the projection error and number of points (regression analysis R² ≈ 0.80 and 0.69, RF importance ≈ 0.82 and 0.71, respectively). Notably, some variables (e.g., Tilt angle in the Surface pattern) were not significant in the linear model but showed high importance in the nonlinear model, warning of the risk of bias that may arise when relying on a single analysis method for evaluating variable effects. The RSM results visually confirm these interaction effects and suggest the possibility of a ‘sweet spot’ where optimal performance is achieved under specific variable combinations (Figure 4 and Figure 5). This suggests that SfM optimization cannot be achieved through independent adjustments of individual variables alone, and that a multivariate optimization approach is required to understand and consider the complex functional relationships between variables depending on the target metrics and pattern types.

Finally, the potential of composite shooting patterns was confirmed as an alternative to overcome the inherent limitations of single shooting patterns and improve performance. According to the TOPSIS analysis, a multi-criteria decision-making technique, a specific composite pattern combination (e.g., C_O40_L_O30) demonstrated the highest overall efficiency (TOPSIS Score: 0.691) when considering multiple performance metrics comprehensively (Table 10). This suggests that the complementary nature of information provided by different shooting paths can contribute to improving overall model quality. Additionally, Pareto optimization analysis of composite pattern data identified efficient alternative sets for key conflicting goal pairs, such as time-error and time-point count, providing useful information for finding optimal trade-offs under specific constraints (Figure 7 and Figure 9).

It is also important to contextualize our findings. The quantitative guidelines presented herein were derived from a specific, controlled experimental setup: a mid-rise, concrete-facade building and a single commercial UAV under consistent overcast lighting. This controlled environment, while necessary for isolating variable effects, means that the direct applicability of our numerical results—such as specific optimal overlap ratios or ‘sweet spot’ coordinates from RSM—may be limited in more challenging, real-world scenarios involving, for instance, high-rise glass facades or variable lighting. Therefore, our findings should be regarded as a foundational baseline that requires calibration and validation when applied to projects with significantly different characteristics.

5. Conclusions

This study was initiated to address the lack of standardized guidelines for UAV-based image data collection and the application of Structure from Motion (SfM) techniques for diagnosing building exteriors. Previous studies have primarily focused on specific cases or algorithm improvements, resulting in a lack of systematic and quantitative evidence for establishing a shooting strategy applicable to various field conditions. Therefore, this study aimed to derive an optimal methodology for collecting shape information by comprehensively analyzing the influence of UAV shooting patterns, shooting variables, and their complex combinations on SfM result metrics. To this end, an experimental framework was designed, and actual data were collected according to various single and composite shooting pattern scenarios. The collected data were processed using an SfM pipeline (based on the SIFT algorithm), and quantitative evaluations of the results were conducted using multiple regression analysis, nonparametric tests (Kruskal–Wallis), random forest variable importance analysis, principal component analysis (PCA) and K-means clustering, response surface analysis (RSM), multi-criteria decision-making (TOPSIS), and Pareto optimization. The analysis yielded the following key conclusions.

The analysis results provided strong experimental evidence that the selection of the basic shooting pattern “type” has a primary and decisive influence on the quality and efficiency of SfM results. Second, within the selected patterns, the influence of detailed shooting variables such as overlap ratio, shooting radius, and camera tilt varied depending on the target performance metrics, and this relationship exhibited a complex pattern that included nonlinearity and interactions between variables rather than a simple linear relationship. Third, we confirmed that composite shooting patterns, which complement the limitations of single patterns, have the potential to achieve multiple performance goals in a balanced manner under specific conditions. Finally, through Pareto optimization analysis, we quantitatively identified the inevitable trade-offs between key performance objectives and demonstrated that it is possible to support rational decision-making by identifying the set of most efficient shooting strategy alternatives (Pareto frontier) under given constraints.

This study contributes as follows. We conducted a systematic and quantitative comparison and verification study of shooting patterns and variables, which were lacking in the field of UAV-SfM-based 3D data collection of building exteriors, and provided empirical data. We also demonstrated the possibility of multifaceted interpretation of complex data through the integrated application of various analytical methodologies. Furthermore, the study provides specific quantitative grounds for selecting the optimal shooting pattern type (e.g., overlap rate management in the Surface pattern, consideration of radius/tilt combination in the Circular pattern) and detailed parameters tailored to practical conditions. The Pareto optimization results clearly present the most efficient set of shooting strategy alternatives amid various conflicting relationships, providing a practical tool to support rational decision-making. These results can be utilized as basic data for input data quality management and optimization module design in the future development of UAV-based automatic building exterior wall diagnosis systems.

However, this study was conducted on a specific building typology (a mid-rise apartment-like structure) using a particular hardware and software configuration (a DJI Mavic 3 Enterprise and a SIFT-based SfM pipeline), so caution is required when generalizing the results. Additionally, statistical verification of the interaction effects of complex patterns is insufficient, and the analysis primarily focused on result indicators at the SfM stage. Therefore, future studies should expand verification research under a wider variety of conditions including different building types (e.g., high-rise, industrial plants), facade materials (e.g., reflective glass), and sensor technologies, conduct experimental designs including repeated measurements to quantitatively clarify the interaction effects of complex patterns, and perform integrated research on optimizing shooting strategies that consider the quality of the final MVS results. Through such follow-up studies, it is anticipated that the achievements of this study will be further developed and generalized, contributing to enhancing the reliability and applicability of UAV-SfM technology.