3D Reconstruction and Printing of Small, Morphometrically Complex Food Replicas and Comparison with Real Objects by Digital Image Analysis: The Case of Popcorn Flakes

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Three-dimensional reconstruction and printing of popcorn flakes provide an innovative tool for generating physical replicas of small and morphometrically complex foods. Digital image analysis (DIA) of popcorn replicas and original flakes enables the precise assessment of printing fidelity and morphometric accuracy, supporting a better understanding of the relationship between structure, size, and texture, and aiding the assessment of functionality. The use of polylactic acid (PLA) as a printing material ensures dimensional stability and the preservation of structural details, enhancing the reliability of the models obtained and allowing their use in applications such as thermal and mass transfer simulations, sensory training, food science education, and product structural design, and will influence real food printing. Altogether, this approach strengthens food digitization and opens new opportunities for innovation in food engineering.

Abstract

Popcorn maize (Zea mays everta) exhibits complex morphologies that challenge structural analysis. This study assessed the fidelity of the three-dimensional (3D) reconstruction and printing of four popcorn morphologies, unilateral, bilateral, multilateral, and mushroom, by integrating structured-light 3D scanning and (DIA), which can support the construction of food replicas. Morphometric parameters (projected area, perimeter, Feret diameter, circularity, and roundness) and fractal descriptors (fractal dimension, lacunarity, and entropy) were quantified as the relative ratios of printed/real parameters (P/R) to compare real flakes with their 3D-printed counterparts. Results revealed the lowest mean errors for Feret diameter (6%) and projected area (10%), while deviations in circularity and roundness were more pronounced in mushroom flakes. With respect to the actual mean values of the morphological parameters, real flakes showed slightly larger perimeter values (86 mm for real and 82 mm for printed objects) and a higher fractal dimension (1.36 for real and 1.33 for printed), indicating greater texture irregularity, whereas the projected area remained highly comparable (225 mm² in real/229 mm² in printed). These parameters reinforced that the overall morphological fidelity remained high (P/R = 0.9–1.0), despite localized deviations in circularity and fractal descriptors. Less complex morphologies (unilateral and bilateral) demonstrated higher structural fidelity (P/R = 0.95), whereas multilateral and mushroom types showed greater variability due to surface irregularity. Fractal dimension and lacunarity effectively described textural complexity, highlighting the role of flake geometry and moisture in determining expansion patterns and printing accuracy. Principal Component Analysis confirmed that circularity and fractal indicators are critical descriptors for distinguishing morphological fidelity. Overall, the findings demonstrated that 3D scanning and printing provided reliable physical replicas of irregular food structures as popcorn flakes supporting their application in food engineering.

1. Introduction

Food models or food replicas are duplicates of real food objects made of inert materials and play an important role in food technology and engineering, as they allow the evaluation of structural performance during production, quality control, and research and development tasks [1]. Likewise, three-dimensional food models have been used as teaching tools in education, sensory analysis, industrial simulations, and in the assessment of food choices and nutritional knowledge [2]. However, their usefulness largely depends on morphometric fidelity, i.e., the structural similarity between the replica and the original food, which underpins reliable technological and research applications. Recent advances in 3D computer vision of food systems notably apply structured-light scanning, laser triangulation, and photogrammetry to enhance the ability to capture the geometry and texture of irregular food surfaces with high precision. Xiang et al. [3] stated that such imaging systems provide high-resolution digital meshes suitable for reconstructing complex food morphologies, enabling quantitative modeling of shape, curvature, and volume essential for digital analysis and process simulation.

From the manufacturing perspective, 3D food printing integrates mechanical, rheological, and thermal controls to transform digital reconstructions into physical replicas. Waseem et al. [4] emphasized that extrusion flow dynamics, viscosity, surface tension, and heat transfer strongly influence printing accuracy, determining the degree of shape preservation and layer adhesion during deposition. Similarly, Derossi et al. [5] pointed out that the digital chain from reconstruction to printing requires precise geometric calibration, material compatibility, and process parameter optimization to achieve functional replicas. These technologies, combined with the potential of structured-light scanning proposed by Uyar et al. [6], provide the foundation for assessing 3D reconstruction and printing fidelity by means of DIA of small and morphometrically complex foods such as popcorn flakes.

However, their usefulness largely depends on morphometric fidelity, that is, the degree of structural similarity between the model and the original food, which ensures reliable representations for technological and research applications [2]. Pereira et al. [1] highlighted that texture design, multi-material printing, and internal structural geometries are critical to improving morphological accuracy. Likewise, Ma et al. [5] demonstrated that extrusion parameters (layer height, printing speed, and material flow rate) significantly influence the structural fidelity of printed food models. Previous studies have emphasized that material rheology and heat transfer control are crucial towards printing fidelity [7], while emerging applications point to the relevance of shape accuracy for functional food development and personalized nutrition [8].

In this respect, Goñi et al. [2] developed a 3D reconstruction method for irregularly shaped foods using reverse engineering. They applied the finite element method to estimate volume and surface area that was validated with apples and meat cuts and reporting volume errors under 2%. They also proposed predictive equations for estimating surface area based on weight and volume.

Three-dimensional (3D) scanning has proved useful for simulating thermal processes in foods with complex geometries. Using realistic 3D models of products such as pears, strawberries, and bananas, Uyar et al. [6] demonstrated that scanned geometries can be directly incorporated into computational fluid dynamics (CFD) environments to model cooling behavior with high accuracy, showing strong agreement between simulated and experimental temperature profiles. Their findings highlighted the broader potential of 3D scanning to enhance geometry-based modeling in food engineering, improving the prediction of heat and mass transfer phenomena in irregular foods. Also, Zhang et al. [9] scanned vegetables with irregular shapes to obtain geometric models used in radiofrequency heating simulations via COMSOL Multiphysics 6.0 software. Results showed improvement in temperature distribution predictions in relation to results obtained when using real shapes. The 3D reconstructions allowed for a better identification of overheating and cooling zones and proved effective in enhancing the reliability of thermal models for foods with complex morphologies.

Three-dimensional (3D) printing, also known as additive manufacturing, is a layer-by-layer fabrication technique that enables the controlled deposition of food materials according to digital models, allowing the creation of customized shapes and internal structures. Most published works focus on mechanical objects for industrial or laboratory purposes, while relatively large food replicas such as chicken pieces and fruits have been successfully reconstructed and applied in preservation studies, thermal simulations, and structural modeling [9,10]. In contrast, reproducing small foods with irregular and intricate geometries involves greater challenges. Popcorn is a paradigmatic case, as upon popping, kernels can develop four main morphologies, unilateral, bilateral, multilateral, and mushroom, which largely determine product quality, affect flavoring and packaging, and ultimately influence market value [11]. In particular, 3D reconstruction and printing to produce replicas of small, complex food objects as popcorn flakes is rather challenging owing to the possibility that a given scanner and printer may not reproduce morphometric details of the original object [12]. Novel tools such as digital image analysis (DIA) have been used to obtain information on the structure of the material and to understand the relationships among structure, process, and functionality [13].

Developing reliable 3D replicas of popcorn flakes is relevant not only for visualization and marketing purposes but also for engineering studies, particularly those related to external heat and mass transfer parameters [14]. Printed models also provide the opportunity to analyze food structure without compromising chemical integrity, supporting further studies [12,14]. Therefore, this study aimed to evaluate the accuracy of 3D reconstruction and printing of popcorn flakes by comparing real and hot-air-popped with their corresponding scanned and printed models. Printing fidelity was assessed through digital image analysis using non-fractal (projected area, perimeter, Feret diameter, circularity, and roundness) and fractal (fractal dimension, lacunarity, and image entropy) descriptors to quantify morphological differences.

2. Materials and Methods

2.1. Preparation and Popping of Popcorn Kernels

For popping experiments, samples of 50 Zea mays var. everta kernels (Valle Verde^®, Mexico City, Mexico) obtained from three commercial bags acquired in a local supermarket in Mexico City were selected for each run, ensuring uniform size prior to the popping process. Popping was conducted by using a hot-air propulsion device, with an inverted conical popping chamber as shown in Figure 1, preheated for 5 min to ensure uniform thermal distribution [15]. Popping temperature was set at 180 ± 5 °C with an airflow of 1 m/s, obtaining the four main flake morphologies: unilateral, bilateral, multilateral, and mushroom type [13].

2.2. Three-Dimensional Scanning Reconstruction and Printing of Models

The entire scanning, reconstruction, and-printing process is illustrated in Figure 2. Scanning (Figure 2a) was carried out by using a Creality 3D-S01 optical scanner (Shenzhen Creality 3D Technology Co., Ltd., Shenzhen, China) with structured white light. The equipment was mounted on a tripod, used in conjunction with a rotating platform, and situated inside a scanning box with the inner walls painted matte black. Scanning was carried out as reported by Kim et al. [16] by applying two 50 s 360° sequences; the adjusted frame rate was 10 FPS (frames per second), and a scanning area of 536 × 378 mm was selected with an accuracy of 0.1 mm, mm [17]. A scanning range 0.3–0.5 mm and a scanning distance of 60 cm were also used. The reconstruction (Figure 2b) process was carried out by means of the CR Studio 2.7.0 software [16], generating models based on four digital parameters: point cloud, mesh, 3D surface, and surface with mesh. Then, the image was reconstructed and processed for subsequent analyses [10,13,18]. The effective scan resolution was estimated as the point-to-point (nearest-neighbor) distance in the point cloud [19]. The models obtained with the Creality S01 scanner were exported in .obj format and analyzed by the CloudCompare software (https://cloudcompare.org/) [20]. For each cloud, the distance to the nearest neighbor was calculated, reporting the mean ± SD. This parameter reflects the separation between captured points and, therefore, the spatial resolution of the scan [19]. This parameter reflects the spatial separation between captured points and the amount of information per reconstructed surface [21].

Printing was carried out by means of a Creality Ender 3D printer (Figure 2c) by using a polylactic acid (PLA, density 1.24 g/cm³) filament, which is commonly used for constructing models of varying size [21]. Printing conditions included a nozzle temperature of 220 °C as reported by Rivera-López et al. [22] as to maximizing the mechanical performance of FDM-printed PLA. The 3D-printed flake models (Figure 2d) were then digital image analyzed as described in Section 2.4.

2.3. Popcorn Image Capture

Images of real and printed popcorn flakes were captured inside a box with matte-black painted inner walls by using a digital camera (Nikon D7000, Tokyo, Japan) positioned 20 cm above the flake inside the box using white LED lighting (12 W) to eliminate shadows and reflections. Flakes were positioned by considering their natural fall orientation and then rotated in 90° increments to obtain six standardized views (front, right, rear, left, top, and bottom) of each object (Figure 3) [19]. This procedure enabled the one-to-one comparison of morphometric descriptors across morphologies and minimized orientation-induced bias [10]. The imaging setup (Figure 4a) provided a scale of 0.03 mm/pixel and a resolution of 2120 × 2064 pixels [23,24].

2.4. Digital Image Analysis (DIA) of Real and Printed Popcorn Flakes

This procedure involved semi-automatic segmentation of the original RGB image, conversion to 8-bit grayscale, contrast adjustment, and thresholding at 44/255 automatic to obtain a binarized image as illustrated in Figure 4b [13].

The following morphometric parameters were evaluated for each face of the popcorn flakes: projected area (mm²), Feret diameter (mm), perimeter (mm), circularity, and roundness by using ImageJ software v.1.50f (National Institutes of Health, Bethesda, USA) [13]. The average actual values for each morphometric parameter, considering the six different sides (Figure 3) for both printed and real flakes, as well as the rate (P/R) of the morphometric parameters for each side of the printed (P) and real (R) flakes, were reported.

Circularity is based on the area and perimeter of each particle and provides a dimensionless value ranging from 0 to 1, where values close to 1 indicate more circular geometries, while values close to 0 represent irregular or elongated shapes as given by Equation (1) [25].

$$Circularity=4\pi \times {\displaystyle \frac{Area}{{Perimeter}^2}}$$

(1)

Roundness is calculated by means of Equation (2) by considering the relationship between the particle area and its major axis and describes the degree of similarity of the shape to a circle. Values close to 1 indicate more rounded shapes, while lower ones reflect elongated or irregular geometries [26].

$$Roundness=4\times {\displaystyle \frac{Area}{\pi \times {Major axis}^2}}$$

(2)

Also, the morphometric fractal image parameters, namely the fractal dimension of contour, quantify scale-dependent roughness and contour irregularity and are particularly suitable for irregular biological geometries such as popcorn flakes, as well as being sensitive to moisture-induced structural changes and fracture patterns in food matrices [27,28]. This parameter is determined by using the FracLac plugin (version 1.5b) of the Image J software through the box-counting and the lacunarity analysis methods [28].The field of view (FOV) was divided into N boxes, and the fractal dimension of the perimeter of the object (FDP) was calculated (box counting) according to Equation (3) as a function of the pixel density in grayscale within each box. FDP has a dimension index (q = 0), and µ is the density of the grayscale pixels located in each frame [27,28]. The face of each object corresponding to the natural fall position was considered as face or side one [29]

$$FDP={\displaystyle \frac{1}{1-q}}\underset{\mathrm{\varepsilon }-0}{\lim }{\displaystyle \frac{{\sum }_{i=1}^N\mathrm{\mu }\raisebox{1ex}{$q$}\!\left/ \!\raisebox{-1ex}{$i$}\right.}{\log \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{\varepsilon }$}\right.}}$$

(3)

Lacunarity describes spatial heterogeneity and the distribution of voids/patches, complementing FD to characterize morphological organization and porosity [30,31], which enables the analysis of mass distribution within a deterministic or random set, was evaluated from the standard deviation (σ) and the mean (η) of the pixels per box of a selected size (r), considering box counts in any direction (g), according to Equation (4) [28].

$${Lacunarity=\left({\displaystyle \frac{\sigma }{\eta }}\right)}_{r,g}^2$$

(4)

Image entropy as descriptor summarizes the degree of disorder and gray-level variability; hence, it directly reflects texture, and detail preservation [31] is an indicator of the randomness in pixel intensity distribution, using the probability (pi) of each gray level (i) in the image, according to Equation (5) [32].

$$Entropy=-{\sum }_{i=1}^{n}pi {\mathrm{l}\mathrm{o}\mathrm{g}}_2\left(pi\right)$$

(5)

The above descriptors enhance the evaluation of printing fidelity by incorporating a textural dimension into the geometric comparison.

Additionally, the fractal dimension of surface texture, which is an indicator of the irregularity of surface images and illustrated as the fractal texture map of the image, was evaluated over the face corresponding to the initial position (natural fall) of the flake [32]. In Equation (6), the fractal dimension of texture (FDS_DBS) was calculated by the Shifting Differential Box-Counting method, where N is the number of occupied boxes and ɼ is the box size [32].

$${FDS}_{DBC}{\displaystyle \frac{\log \left(N\right)}{{log}^{{(r}^{-1)}}}}$$

(6)

Additionally, the relative printing error (P_error) in relation to the real object were calculated as reported by Maldonado-Rosas et al. [33] by means of Equation (7).

$$P_{error}={\displaystyle \frac{P_{printed}-P_{real}}{P_{real}}}\times 100$$

(7)

In which $P_{printed}$ represents the value of the geometric parameter determined from the printed model, and $P_{real}$ is the value obtained from the real flake.

2.5. Statistical Analysis the Popcorn Morphology and 3D Reconstruction

All tests were carried out in triplicate, and results were expressed as mean value ± SD. Statistical analysis included an ANOVA to evaluate the influence of morphology of real versus 3D-printed model parameters as a P/R rate, as described above, with a significance level α = 0.05. A Principal Component Analysis (PCA) was also performed to reduce data dimensionality and to identify the main variables contributing to the differentiation of the morphometric parameters.

3. Results and Discussion

3.1. Three-Dimensional Scanning Reconstruction and 3D Printing

Table 1. Three-dimensional scanning and reconstruction parameters of popcorn flakes.

Morphology	FPS	Faces	Vertices
Unilateral	306.4 ± 0.5	6673.8 ± 4.1	9465 ± 3.4 *
Bilateral	306.8 ± 0.8	6086.2 ± 3.7	6278 ± 6.3
Multilateral	309.1 ± 0.7 *	10,718.8 ± 5.6 *	5432 ± 4.3
Mushroom	305.8 ± 0.8	9442.2 ± 4.5	4704 ± 3.2

* Significant differences (p ≤ 0.05) with respect to other values in column, FPS (photograms per second).

presents the 3D scanning and reconstruction parameters for the four popcorn morphologies. Each scanning took about the same number of FPS and produced reconstructed 3D images with a higher number of faces for multilateral and mushroom morphologies than for unilateral and bilateral flakes. Multilateral and mushroom morphologies are the most complex ones concerning structural complexity [13], and it was noticeable that these flakes had a significantly (p ≤ 0.05) higher value (37%) of faces with respect to uni- and bilateral flakes, reflecting greater surface irregularity. Vertices and points were similar amongst the four morphologies, given the scan resolution parameters [6]. In contrast, bilateral models depicted the least face structuring (6086 ± 13), associated with less complex surfaces. For the vertices, unilateral morphology recorded the highest number of these features (9465 ± 13), while the multilateral and mushroom morphologies presented lower values (p ≤ 0.05) of this parameter. These results are higher (thus accusing improved resolution levels) than those reported by Ma et al. [34], who reduced volume errors by developing the MFP3D model (Monocular Food Portion Estimation Leveraging 3D Point Clouds), a reconstruction and portion estimation approach based on a single image (1024 points). By integrating point cloud data with RGB information, this method decreased energy estimation errors by more than 50%.

Recent advances in computer vision demonstrated the potential of 3D reconstruction towards food characterization. Dehais et al. [35] proposed a dense, two-view reconstruction system using images acquired with mobile devices, achieving an average error of less than 10% in food volume estimation with fully automated processing, thus demonstrating the feasibility of accurate and efficient dietary assessment. More recently, Masoudi et al. [36] applied a particle film coating to tomatoes to overcome the limitations of conventional photogrammetry on glossy surfaces, reporting that using Structure from Motion (SFM) software significantly enhanced point cloud quality and reduced volume and surface area estimation errors to below 5%. These results highlighted the importance of combining various geometric features for a more accurate characterization of foods, particularly when applied to portion size estimation and nutritional assessment.

3.2. Digital Image Analysis

Digital image analysis was performed to images of Figure 5, Figure 6 and Figure 7, which depict the original popcorn samples, followed by their digital reconstructions obtained through 3D scanning, and finally the corresponding 3D-printed models in six rotational views at 90°. Figure 5 presents the images of the four evaluated popcorn morphologies. Additionally, Figure 6 shows the digital reconstructions of the unilateral flake generated from point cloud data and mesh processing. Point cloud models demonstrated the accuracy of the 3D scanning procedure in preserving the surface geometry and structural complexity of the original kernels [15], and Figure 7 illustrates the 3D-printed models corresponding to each morphology. These printed objects enabled a tangible validation of the digital workflow and facilitated a direct comparison between the reconstructed data and their physical representation [35].

Morphological characterization of foods through digitization and three-dimensional modeling has been explored in popcorn, where computer tomography (CT) scanning and voxel-based reconstruction have been used to generate digital models and simulate the packing behavior of different morphologies [37]. In this respect, 3D printing of maize and legume-based formulations were used to evaluate structural fidelity, shape stability, and textural characteristics after printing [38]. Three-dimensional food printing has proven to be an innovative tool to customize shapes, structures, as well as nutritional and sensory profiles of foods, while simultaneously facing challenges related to texture control, consumer acceptance, and process standardization [19,38].

In

Table 2. Morphometric parameters of real and 3D-printed popcorn flakes by morphology.

Parameters	Popcorn Real (R)	3D-Printed Flake (P)
Unilateral
Area (mm2)	232.0 ± 4.01 *	219 ± 1.97
Perimeter (mm)	71.4 ± 0.39	67.40 ± 0.77 *
Feret diameter (mm)	22.72 ± 0.04	23.5 ± 1.01
Fractal dimension	1.23 ± 0.02 *	1.16 ± 0.01
Lacunarity	9.67 ± 0.19 *	5.75 ± 0.58
Image entropy	5.56 ± 0.11	5.14± 0.03
Circularity	0.58 ± 0.01	0.62 ± 0.01 *
Roundness	0.62 ± 0.01	0.61± 0.02
Bilateral
Area (mm2)	226 ± 3.40 *	205 ± 2.77
Perimeter (mm)	86.3 ± 1.47 *	73.7 ± 2.10
Feret diameter (mm)	24.5 ± 0.33 *	22.6 ± 0.74
Fractal dimension	1.39 ± 0.02	1.21 ± 0.01
Lacunarity	6.23 ± 0.08 *	4.27 ± 0.35
Image entropy	5.55 ± 0.13 *	4.84 ± 0.01
Circularity	0.75 ± 1.30	0.53± 0.01
Roundness	0.58 ± 0.01	0.64 ± 0.03
Multilateral
Area (mm2)	189 ± 2.09	244 ± 1.56 *
Perimeter (mm)	73.5 ± 1.84 *	70.8 ± 1.10
Feret diameter (mm)	20.67± 0.22 *	5.21 ± 0.56
Fractal dimension	1.24 ± 0.05	1.26 ± 0.41
Lacunarity	21.6 ± 0.04 *	6.01 ± 0.46
Image entropy	5.53 ± 0.05	5.12 ± 0.06
Circularity	0.51 ± 0.01	0.66 ± 0.01 *
Roundness	0.80 ± 0.04 *	0.75 ± 0.04
Mushroom
Area (mm2)	225 ± 2.57	299 ± 1.01 *
Perimeter (mm)	86.11 ± 0.92 *	81.44 ± 1.14
Feret diameter (mm)	21.98 ± 0.19 *	4.26 ± 1.11
Fractal dimension	1.19 ± 0.03	1.23 ± 0.01
Lacunarity	3.63 ± 0.42	5.72 ±1.04 *
Image entropy	5.78 ± 0.15	5.41 ± 0.78
Circularity	0.45 ± 0.02	0.63 ± 0.77 *
Roundness	0.78 ± 0.07	0.77 ± 0.15

* Significant differences (p ≤ 0.05) to values.

, the mean morphometric parameters of real and 3D-printed popcorn flakes are presented according to their morphological classification. Shape-related parameters revealed that printing fidelity was strongly influenced by morphological complexity.

For unilateral and bilateral flakes, the 3D-printed models exhibited significantly lower (p ≤ 0.05) values of area, perimeter, and Feret diameter compared to real samples, whereas circularity and roundness showed no significant differences. In contrast, multilateral and mushroom morphologies displayed more pronounced differences (p ≤ 0.05) across all geometric descriptors, confirming that irregular and highly expanded structures are more difficult to replicate. The reduction in perimeter and Feret values in printed samples reflects the challenge of reproducing overlapping surfaces and deep concavities typical of complex morphologies.

Fractal and texture-related descriptors also exhibited significant differences (p ≤ 0.05) between real and printed flakes. Lower values of fractal dimension, lacunarity, and image entropy in printed models demonstrate a reduction in microstructural irregularity and a smoother surface texture [23]. These effects were particularly noticeable in multilateral and mushroom flakes, where void distribution and fine surface roughness were not completely captured. Nevertheless, circularity and roundness remained statistically similar (p > 0.05), confirming that the global flake geometry was effectively retained.

Overall, the results confirm that PLA printing maintains high geometric fidelity in simple morphologies but partially attenuates fine surface irregularities in complex ones. The combination of geometric and fractal descriptors provides a comprehensive framework to assess multi-scale fidelity in 3D food models, underscoring the balance between dimensional accuracy and surface realism achieved in the reconstruction and printing of expanded foods such as popcorn [21].

Table 3. Relative parameters (size and shape) of original popcorn morphologies compared to 3D-printed models and actual average values.

Parameter (P/R)	Sides
	Side 1	Side 2	Side 3	Side 4	Side 5	Side 6
Unilateral
Area	0.91 ± 0.31	0.92 ± 0.14	0.92± 0.52	0.92 ± 0.22	1.31 ± 0.21 *	1.02 ± 0.52
Perimeter	0.71 ± 0.22	0.82 ± 0.64	0.81 ± 0.22	0.96 ± 2.12	1.01 ± 0.82	1.35 ± 0.71 *
Feret diameter	0.82 ± 0.12	1.0 1± 0.75	1.01 ± 0.13	0.92 ± 0.43	1.35 ± 0.54 *	1.03 ± 0.73
Fractal dimension	0.81 ± 0.06	0.87 ± 0.27	1.02 ± 0.12	0.95 ± 0.23	1.13 ± 0.12 *	1.15 ± 0.11
Lacunarity	1.02 ± 0.83 *	0.74 ± 0.11	0.71 ± 0.67	0.43 ± 0.22	0.35 ± 0.59	0.87 ± 0.78
Image entropy	0.91 ± 0.15	0.71 ± 0.72	0.81 ± 0.17	0.82 ± 0.94	1.08 ± 0.93 *	0.91 ± 0.34
Circularity	1.61 ± 0.41	1.12 ± 0.13	1.32 ± 0.42	1.11 ± 0.14	1.04 ± 0.57	2.61 ± 0.22 *
Roundness	0.91 ± 0.62	0.92 ± 0.14	0.94 ± 0.17	1.22 ± 0.41 *	0.91 ± 0.21	1.62 ± 0.48
Bilateral
Area	0.98 ± 2.51 *	0.83 ± 8.11	0.93 ± 3.64	0.92 ± 1.21	0.97 ± 1.78	0.86 ± 1.34
Perimeter	0.74 ± 3.32	0.93 ± 1.92	0.71 ± 1.67	1.07 ± 1.72 *	0.86 ± 2.38	0.98 ± 1.38
Feret diameter	0.97 ± 0.54	0.84 ± 0.24	0.96 ± 1.33	0.98 ± 0.56	1.18 ± 0.78 *	1.13 ± 1.17
Fractal dimension	0.94 ± 0.11	0.81 ± 0.75	1.07 ± 0.27	1.07 ± 0.10 *	0.98 ± 0.18	0.87 ± 0.57
Lacunarity	7.81 ± 0.82 *	4.01 ± 0.54	0.68 ± 0.78	0.34 ± 0.24	4.67 ± 0.57	4.07 ± 0.21
Image entropy	0.88 ± 0.11	0.92± 0.14	0.97 ± 0.34	0.77± 0.46	0.93 ± 0.47 *	0.77 ± 0.42
Circularity	1.01 ± 0.54	0.91 ± 0.97	0.82 ± 0.52	0.87 ± 0.16	1.07 ± 0.68	2.67 ± 0.25 *
Roundness	0.93 ± 0.11	1.22 ± 0.37	0.97 ± 0.18	1.47 ± 0.47 *	1.36 ± 0.57	1.35 ± 0.57
Multilateral
Area	1.60 ± 1.14	1.07 ± 0.37	1.33 ± 0.66	1.05 ± 0.52	1.19 ± 7.85	1.67 ± 0.17 *
Perimeter	0.83 ± 4.64	0.90 ± 3.33	0.96 ± 2.78	0.81 ± 0.87	1.21 ± 1.07	1.21 ± 1.08 *
Feret diameter	1.09 ± 0.41	1.09 ± 0.88	1.03 ± 1.18	1.09 ± 0.99	1.23 ± 0.52 *	1.20 ± 0.53
Fractal dimension	0.97 ± 0.03	0.95 ± 0.08	1.00 ± 0.02	1.01 ± 0.01	1.12 ± 0.12 *	0.99 ± 0.10
Lacunarity	3.05 ± 0.20	2.28 ± 1.44	1.21 ± 1.80	1.15 ± 4.20	0.59 ± 0.13	9.83 ± 0.70 *
Image entropy	0.91 ± 0.16	0.91 ± 0.10	0.97 ± 0.11	0.91 ± 0.18	0.87 ± 0.19	0.94 ± 0.06
Circularity	2.22 ± 0.04 *	1.45 ± 0.02	1.41 ± 0.01	1.76 ± 0.05	0.98 ± 0.01	0.82 ± 0.03
Roundness	1.07 ± 0.02	0.89 ± 0.02	1.10 ± 0.03 *	0.86 ± 0.04	0.91 ± 0.06	0.76 ± 0.01
Mushroom
Area	1.07 ± 0.30	1.38 ± 0.02	1.07 ± 0.88	1.37 ± 0.03	1.60 ± 0.57	1.7 ± 0.27 *
Perimeter	0.78 ± 0.71	0.83 ± 0.30	1.19 ± 0.16	0.87 ± 1.41	0.91 ± 1.90	1.2 ± 0.44 *
Feret diameter	1.08 ± 0.60	1.11 ± 0.45	1.13 ± 1.40	1.11 ± 1.02	1.15 ± 1.10	1.3 ± 0.31 *
Fractal dimension	0.86 ± 0.02	0.88 ± 0.03	0.86 ± 0.06	0.81 ± 0.09	0.98 ± 0.04	0.9 ± 0.5 *
Lacunarity	4.17 ± 1.50	5.22 ± 2.18	4.93 ± 0.77	5.26 ± 1.77	7.43 ± 1.9	6.0 ± 0.5 *
Image entropy	0.95 ± 0.87	1.02 ± 0.17 *	0.22 ± 0.69	0.98 ± 0.12	0.96 ± 0.57	1.02 ± 0.88
Circularity	1.81 ± 0.17	2.94 ± 0.92 *	0.85 ± 0.57	2.28 ± 0.27	1.42 ± 0.12	1.78 ± 0.61
Roundness	0.81 ± 0.66	1.18 ± 0.17 *	0.93 ± 0.12	1.56 ± 0.58	1.07 ± 0.13	1.07 ± 0.33

* Significant differences (p ≤ 0.05) within the same rows. P/R are relative values of the morphometric parameters.

presents the relative digital parameters of size and shape obtained through image analysis in ImageJ, comparing real popcorn flakes with their 3D-printed models. Data were organized by morphology (unilateral, bilateral, multilateral, and mushroom), displaying the corresponding values for each observation side (1 to 6) to identify directional variations within each sample. Additionally, key parameters such as area, perimeter, Feret diameter, fractal dimension, lacunarity, image entropy, circularity, and roundness are reported as average values throughout the six faces of the objects to provide a comprehensive characterization of geometry and surface texture.

To facilitate the interpretation of the results, P/R ratios (printed/real) were included for each parameter and flake morphology, allowing a direct comparison of the relative magnitude between printed and original flakes. This provided a clear perspective on the printing fidelity of the replicas, regardless of the actual value of the individual morphometric parameters (Table 3).

The comparative analysis revealed consistent trends and several statistically significant differences (p ≤ 0.05), confirming that while 3D printing can reproduce the size and shape of popcorn kernels, certain geometric and textural features were systematically altered. Specifically, the printed models tend to display smooth contours, increased regularity, and occasionally, overestimate surface areas, whereas real flakes displayed higher edge complexity, irregularity, and heterogeneity. These findings emphasize that printing morphological fidelity cannot be evaluated solely in terms of size preservation but must also account for shape complexity and surface texture.

Within this context, a parameter-by-parameter analysis provides clearer insights into the strengths and limitations of the replication process. Regarding area, significant differences were found in unilateral and multilateral morphologies, where printed models showed higher values than real flakes at specific sides (p ≤ 0.05). This indicated that although the overall scale is preserved, 3D printing tends to overestimate surface areas in multilateral and mushroom objects. Values of perimeter for real flakes consistently displayed higher values with respect to printed ones, with significant differences in bilateral and multilateral morphologies, reflecting greater edge irregularity in real samples compared to the smoothing of contours in printed models.

Additionally, multilateral and mushroom morphologies exhibited significant differences (p ≤ 0.05) of P/R in relative area, perimeter, Feret diameter, and circularity, indicating their suitability for describing these morphologies. In particular, mushroom kernels, which are preferred in industrial coating and packaging due to their uniform expansion [6], depicted the highest geometric local complexity during production, due to the presence of eyes or expanded endosperm fractures, which are complicated to print. Fractal parameters further illustrated these findings; unilateral and bilateral flakes showed relative values of fractal dimension lower to one (0.98 and 0.94), confirming that in printed flakes, the equipment filled voids, thus giving place to smoother surfaces. Multilateral and mushroom flakes presented the closest P/R values to one for fractal dimension in spite of their irregular surfaces, which indicated high values of printing accuracy based on this parameter [39].

Lacunarity figures provided complementary insights. Mushroom flakes showed significantly higher lacunarity (p ≤ 0.05), reflecting heterogeneous void distribution and irregular contours, possibly due to the presence of eyes, while unilateral and bilateral flakes exhibited lower values, consistent with compact and more homogeneous geometries. These findings emphasized lacunarity as a robust descriptor for heterogeneity and a complement to FD in food structure analysis [31].

Image entropy also reflected differences in surface complexity between morphologies. Multilateral flakes showed higher entropy relative values compared to mushroom objects. This supports the view that image entropy is a sensitive parameter for evaluating detail preservation and visual complexity in 3D-printed models. In this study, image entropy was complemented with morphometric parameters such as area and perimeter, which reinforced the discrimination among morphologies and confirmed that morphometric parameters can be effectively used to assess surface complexity [13]. Similar approaches have been applied in the fractal analysis of food microstructures of popcorn external surfaces [27]. These approaches have also been applied in the fractal analysis of food microstructures, such as instant coffee and starch, where entropy and FD effectively detected spatial organization changes [34,35].

Overall, the combined results confirm that simpler morphologies (unilateral, bilateral) are reproduced with higher fidelity, while complex geometries (multilateral, mushroom) exhibited greater deviations, primarily due to their inherent irregularity. The integration of fractal dimension, lacunarity, and entropy proves effective for quantifying morphological complexity and validating the accuracy of 3D printing in food systems [13,23].

3.3. Error in Reconstruction and 3D Printing of Morphologies

Feret diameter (Figure 8) showed the lowest relative printing error (6%), reflecting consistent reproduction comparative morphology. Projected area and circularity followed with average errors of 10–15%, while roundness exhibited the highest variability (up to 22%) in mushroom-type flakes, confirming the difficulty of reproducing highly irregular surface curvatures. These results indicated that the scanning–printing pipeline achieved overall structural fidelities within tolerance limits commonly reported for 3D food printing (<10% error depending on geometry). Accurate replication of food morphology not only validates the workflow but also enables the creation of durable educational and experimental models without relying on perishable specimens. Techniques such as high-resolution photogrammetry and laser scanning have proven effective in capturing fine structural details of irregularly shaped food products [2].

To assess the morphological differentiation between real popcorn samples and their corresponding 3D-printed models, a Principal Component Analysis (PCA) was conducted (Figure 9). Figure 9a depicts projected area, perimeter, and Feret diameter, with 84% of the variance explained; projected area (0.764) and perimeter (0.796) were the dominant contributors. Unilateral kernels clustered in compact regions, while bilateral and multilateral types aligned with higher perimeter and Feret values, reflecting elongated shapes. Figure 9b shows the PCA of circularity, roundness, fractal dimension and lacunarity, which explained 91.4% of the variance, separating regularity from complexity: unilateral kernels grouped with high circularity and low fractal dimension, whereas mushroom and multilateral kernels showed greater dispersion, indicating higher variability and reduced symmetry. Overall, the analysis confirms that simpler geometries are more reproducible by 3D printing, while having complex morphologies with high lacunarity and fractality displayed greater challenges.

3.4. Contribution of DIA Parameters Towards Describing Morphometry of Popcorn Flakes as Estimated by Principal Component Analysis (PCA)

Similar conclusions have been reported in food 3D printing studies, where PCA was employed to classify samples and identify key parameters affecting print fidelity. For example, Pan et al. [7] used PCA to optimize shrimp surimi formulations by distinguishing treatments based on rheological and textural indicators, thereby improving structural stability during printing. De Salvo et al. [8] applied PCA to tapioca starch protein inks, demonstrating its utility in grouping formulations by printability and guiding composition adjustments [1]. Likewise, Johansson et al. [40] employed PCA to evaluate protein- and fiber-rich bean fractions, showing that compositional differences determined the clustering patterns of printed samples and their stability.

In line with these works, the PCA of popcorn morphologies confirms that morphological descriptors, particularly circularity, fractal dimension, and lacunarity, are critical indicators of structural fidelity, reinforcing their relevance for both evaluating and optimizing 3D printing of complex food geometries [41].

3.5. Three-Dimensional Texture Analysis of Popcorn Flakes

To ensure comparability of texture metrics, we restricted the analysis to a single standardized face: the surface in the initial pose. The same view was applied to both real and 3D-printed specimens to preserve geometric correspondence and reduce orientation-induced bias [29].

The 3D texture maps and pixel-intensity histograms of real and 3D-printed shown in Figure 10A indicate that real unilateral flakes samples exhibited a central peak with low dispersion, reflecting smoother and more homogeneous topography. Bilateral kernels exhibited bimodal distributions of gray-level intensities linked to cavities and protrusions, multilateral kernels displayed the broadest gray-scale histograms indicative of high surface heterogeneity, and mushroom kernels presented narrow peaks consistent with compact, semi-spherical expansion [7,42]. In Figure 10B, the 3D-printed popcorn kernel models show gray-scale histograms in which kernels with cavities and protrusions exhibited higher dispersion values, reflecting greater surface heterogeneity. A similar trend was reported by Acosta-Ramírez et al. [23], who observed that irregular structures produced broader and less defined multifractal acoustic spectra, with amplitude and frequency peaks directly influenced by surface complexity. This parallel supports the interpretation that pixel-intensity distribution in 3D maps can serve as a quantitative proxy for irregularity, in line with acoustic-based findings.

The histograms of printed models showed narrower peaks and reduced shorter tails compared to real flakes, indicating a loss of fine structural irregularities associated with the smallest and largest intensities. This smoothing effect is attributed to the resolution and deposition parameters of extrusion-based printing, as reported in polymer studies [43,44]. Fractal dimension (FD) and lacunarity values supported these observations. FD captured roughness across scales, while lacunarity quantified void heterogeneity, in line with previous findings [8,37].

Table 4. Comparison of texture fractal dimension (FDt) and model lacunarity texture (real and 3D-printed models) and morphology type.

Morphology	Model	Fractal Dimension Texture	Lacunarity Texture
Mushroom	Real	2.64 ± 0.01 Aa	0.14 ± 0.00 Ba
	3D Print	2.65 ± 0.01 Aa	0.146 ± 0.01 Ba
Unilateral	Real	2.60 ± 0.01 Ba	0.27 ± 0.02 a
	3D Print	2.60 ± 0.01 Ba	0.271 ± 0.02 a
Multilateral	Real	2.59 ± 0.01 Ba	0.25 ± 0.02 Ba
	3D Print	2.59 ± 0.01 a	0.26 ± 0.02 Ba
Bilateral	Real	2.56 ± 0.01 a	0.34 ± 0.02 Aa
	3D Print	2.56 ± 0.01 a	0.35 ± 0.02 Aa

Significant differences (p ≤ 0.05) were determined by ANOVA and Tukey’s test comparison. Different uppercase letters in the same lines depict significant differences between morphologies. Different lowercase letters within the same column correspond to significant differences between models.

reveals no significant differences between real and printed flakes within each morphology (p > 0.05), confirming the accurate reproduction of void/patch distribution. However, the effect of morphology was significant (p ≤ 0.05); bilateral flakes had the highest lacunarity, reflecting heterogeneous lobes and cavities, while unilateral and mushroom flakes showed the lowest, consistent with compact geometries. Similar relationships were observed between histogram asymmetry and surface roughness [8].

Overall, the combined evidence from histograms, FD, and lacunarity indicates that morphological complexity rather than the printing process itself drives surface heterogeneity. Three-dimensional printing mainly smooths high-frequency irregularities but retains the global organization of surface voids, confirming its reliability for replicating complex food morphologies.

The accuracy of the 3D reconstruction of popcorn morphologies was influenced by the intrinsic geometric complexity of each type. This study demonstrates that three-dimensional reconstruction and printing of popcorn flakes is a robust strategy to evaluate the morphometric fidelity of small morphometrically complex foods.

The results confirmed that printed accuracy is closely linked to the intrinsic structural complexity of each morphology. Unilateral and bilateral flakes, considered less complex, showed higher fidelity (P/R ≈ 0.95), while multilateral and mushroom types exhibited larger deviations, reflecting the inherent variability and irregularity of their expanded structures [13,37]. These findings reinforced the idea that replication of structural food geometries cannot be detached from the physics of expansion, particularly the role of kernel moisture and surface heterogeneity. Elevated lacunarity and entropy values in mushroom flakes evidenced the difficulty of preserving void distribution and fine surface irregularities, confirming that complex foods challenge even high-resolution scanning and 3D printing systems. Nevertheless, the errors achieved remained within tolerance limits (<10–15%) commonly reported for 3D food printing [8,45].

The use of digital image analysis DIA was particularly valuable in this context, as it enabled systematic comparison between real and printed objects across multiple descriptors [13,15,31].

PLA ensures dimensional stability and high geometric accuracy. Its mechanical surface properties differ from those of real food matrices, as they tend to smoothen surface imperfections. However, its ability to replicate overall texture details is not hindered. Studies have shown that the layer-by-layer deposition process upon using PLA sufficiently mimic various surface irregularities and does not compromise the morphometric replication of the original objects [46,47]. Future works will explore the alternative use of other biopolymeric materials including edible ones.

3D food models can serve as fake foods or replicas, demonstration tools for nutritional education, sensory analysis, and industrial simulations, as well as supports for evaluating food choices and nutritional knowledge [14]. These studies demonstrated the effectiveness of fake food replicas for promoting healthy meal selection based on composition and dietary recommendations [48].

Although the reproduction of highly irregular morphologies still presents limitations, the workflow combining structured light scanning, DIA, and 3D printing with PLA demonstrated high potential for capturing the essential features of small and structurally complex foods. The findings validate the robustness of DIA as a methodological standard and confirm that accurate reconstruction of popcorn flakes is feasible within acceptable error ranges, thereby reinforcing the significance of this approach for both research and industrial applications [6,16].

In the present study, the proposed methodology advances the integration of structured-light 3D scanning and printing coupled to digital image analysis as a unified workflow directed to small, morphometrically complex food such as popcorn flakes. This approach goes beyond previous replica-based studies by quantitatively linking fractal and non-fractal morphometric descriptors with printing fidelity, thus enabling a reproducible metric for morphological validation [49]. Although this work focused on structural fidelity rather than consumer or sensory assessment, the obtained replicas possess sufficient geometric precision to support practical applications such as in heat and mass transfer modeling, educational visualization, and sensory training, and constitute the first steps towards experimental validations in applied technological and engineering contexts.

4. Conclusions

Three-dimensional reconstruction and printing of popcorn flakes enabled accurate morphological characterization across different structural types. Morphology of flakes was shown to directly influence printing fidelity. Complex shapes, such as multilateral and mushroom objects, presented higher deviations compared to unilateral and bilateral ones. The PLA proved to be appropriate as printing material, provided dimensional stability, and reduced tolerances, thus favoring the preservation of small and complex morphometric details, which contributed to maintaining the structural fidelity of the printed models. The incorporation of global mean values across all sides and morphologies offered an integrative view of morphological fidelity, confirming that while real flakes retained greater perimeter irregularity and slightly higher fractal dimension, projected area was consistently reproduced in the printed counterparts. This synthesis reinforced the robustness of the scanning–printing workflow and validated its capacity to capture structural features beyond flakes specific variations due to rotation. Overall, findings highlighted the potential of combining scanning, DIA, and 3D printing as a reliable strategy for assessment of printing fidelity and structural evaluation of small and morphometrically complex foods. Applications may include simulations, education, sensory analysis, and food engineering research, validating the relevance of this approach in both academic and industrial contexts.