Cartographic Generalization of Islands Using Remote Sensing Images for Multiscale Representation

Abstract

The multi-scale representation of remote sensing images provides various levels of image information crucial for decision-making in GIS applications and plays a significant role in information processing, data analysis, and geographic modeling. Traditional methods for multi-scale representation of remote sensing images often struggle to simplify local details of individual targets while preserving the overall characteristics of target groups. These methods also encounter issues such as transitional texture distortion and rough final boundaries. This paper proposes a novel multi-scale representation method for remote sensing images based on computer vision techniques, which effectively maintains the overall characteristics of target groups. Initially, the K-means algorithm is employed to distinguish between islands and oceans. Subsequently, a superpixel segmentation algorithm is used to aggregate island groups and simplify the generated boundaries. Finally, texture synthesis and transfer are applied based on the original image to produce the aggregated island images. Evaluation metrics demonstrate that this method can generate multi-scale aggregated images of islands, effectively eliminate redundant information, and produce smooth boundaries.

1. Introduction

As a crucial carrier of geographic information, remote sensing imagery’s multi-scale representation has been a key focus in geographic information science research. Multi-scale representation refers to providing data processing results at various scales according to different user requirements for features, locations, attributes, and relationships of geographic information. Currently, the main methods for multi-scale representation include image pyramids and filtering transformations. Image pyramids achieve multi-resolution representation by continuously downsampling to obtain images with varying levels of detail [1]. Specifically, images at different levels are derived from the original image by reducing its resolution. Due to their simple structure, significant enhancement of computational efficiency, and noise removal capabilities, image pyramids are widely used in fields such as feature extraction [2], optical flow tracking, and image enhancement [3].

Image filtering is one of the core operations in the field of computer vision. As another technique for multi-scale image representation, its primary function is to preserve the overall characteristics of target groups while removing unnecessary local details and other redundant information. Due to its similarity to the core objectives of cartographic generalization, image filtering will be utilized as an experimental method in this study. Its effects will be compared with other techniques such as multi-scale aggregation and simplification. Image filtering is widely used in areas such as noise reduction, edge detection, and image sharpening. Buades et al. (2005) [4] proposed a non-local means filtering method, which effectively achieves noise reduction while preserving the original features of the image by associating the similarity between pixels with weights. Additionally, there are mean filtering techniques (linear filtering) and median filtering techniques (non-linear filtering). Although these methods can smooth boundaries, they also tend to blur the image content, resulting in a loss of information.

Islands constitute the primary focus of this study. In geological terms, islands are defined as landmasses surrounded by water, typically with an area of no less than 500 square meters. They play significant roles in natural ecosystems by contributing to the formation of features such as atolls, coastlines, and volcanic island chains, while also serving as abundant resources for local fisheries. Moreover, islands are essential components in both cartographic mapping and remote sensing applications. Given their distinctive characteristics compared to mainland features, islands necessitate specialized treatment in cartographic generalization processes. For instance, in the cartographic generalization of sparsely distributed islands, the large disparity in area between the sea and islands means that islands displayed at the same scale can appear overly detailed. Therefore, it is necessary to employ the principle of variable scaling to separately determine the comprehensive scales for islands and marine areas [5].

The aggregation of planar elements is a fundamental aspect of cartographic generalization. With the development of GIS and the continuous accumulation of geographic spatial data, conflicts between different targets inevitably arise at the same mapping scale. Therefore, a series of operations are required to remove redundant local information while maintaining overall characteristics. Traditional vector-based methods, such as boundary extraction in ArcGIS, aggregate planar features but often lose original textures, resulting in geospatial information loss and lack of scale diversity. Raster-based aggregating methods, like filtering, cannot eliminate gaps between islands, failing to achieve global simplification. To address these challenges, this paper proposes a new approach for the multi-scale representation of remote sensing imagery, aiming to achieve a balance between simplification efficiency and visualization efficacy. This method ensures the preservation of overall target group characteristics while generating aggregated outputs at varying scales through the adjustment of parameters.

The structure of this paper is as follows: The first section provides a comprehensive review of relevant research on aggregation and simplification algorithms. The second section details the procedural steps of the proposed method, illustrated using small island samples: Firstly, the Kmeans algorithm from computer vision theory is used to separate islands and seawater based on color. Secondly, superpixel segmentation is employed to aggregate discrete islands and smooth the generated boundaries. Finally, texture synthesis and migration are conducted using the original image. The third section presents selected experimental data, experimental methodologies, results, and evaluation of metrics. The fourth section concludes with a summary of the experiment’s findings and a discussion of its limitations.

2. Related Works

The process of cartographic generalization involves the abstraction and generalization of geospatial information in accordance with specific conditions, thereby reflecting geographical laws. The objective of cartographic generalization is to reconcile the disparity between map models and complex realities, facilitating the conversion of data map content into novel representations.

With the advancement of computer technology, automatic cartographic generalization technology is also progressing rapidly. This progress is attributed to the collaborative efforts of numerous cartographic generalization operators specialized in different tasks. The subprocess of complex cartographic generalization, known as the cartographic generalization operator, independently describes the transformation process of map elements. Various models for generalization operators have been developed in cartographic generalization, including the seven-operator generalization model [6] and nine-operator generalization model [7], among others. These models encompass essential algorithmic operations such as simplification, selection, shifting, merging and smoothing that form the foundation for cartographic generalization algorithms. In this paper, two specific types of cartographic generalization operators are comprehensively described.

2.1. Aggregation

Due to the ongoing decrease in map scale, both the dimensions of the depicted targets and the gaps between these illustrations are progressively shrinking. As the spacing between these graphics becomes excessively congested, rendering them indistinguishable, there arises a necessity to substitute the smaller graphics with a singular, enlarged representation. This process is referred to as aggregation.

Elements that are physically adjacent and have similar properties are perceived as a whole [8]. During the merging process, the target element loses some or even most of its typical characteristics [9]. Therefore, it is important to preserve the global characteristics of objects before and after merging.

The target elements of aggregation operators are typically categorized into artificial architectural elements and natural planar elements. Research on the aggregation of artificial planar elements primarily relies on raster data and vector data, with vector data being the predominant one. Delaunay triangulation skeletons are extensively employed for merging vector data. Ai and Zhang (2007) [10] present a cluster distribution analysis model based on the Delaunay triangulation skeleton, which utilizes a specialized geometric structure resembling a Voronoi diagram to calculate the structure variables of each partition while considering conflict detection, displacement, and the geometry’s impact on merging. Guo et al. (2016) [11] present an approach to automatically identify right angles and aggregate buildings based on six parameters in Delaunay triangulation. Zhang et al. (2023) [12] introduced a polygonal building aggregation method based on the bridging modes and minimum loop search, which retains the characteristic of right angles while demonstrating improved visual clarity in results through validation advantages. Considering urban architecture’s orthogonality, Guo and Ai (2000) [13] proposed a novel method for aggregating polygons with shared arcs using clipped and extended links that overcome drawbacks associated with organizing arc link sequences in traditional aggregation methods without necessitating unnecessary detection of polygon islands. He et al. (2018) [14] introduced a progressive aggregation method for residential areas based on scale subgroups, which effectively maintains orthogonal characteristics and ensures area balance while also considering cartographic bundle reduction.

To address the issue of the aggregation of natural planar elements, an iterative approach is commonly employed to select an object from the target group and merge it with neighboring objects. Li et al. (2018) [15] proposed an automated processing method for agglomeration areas based on parameters such as the distributed pattern index (DPI). This method effectively resolves the problem of subjective judgment dependency in previous agglomeration methods, enabling intelligent computer processing. Subsequently, Li et al. (2021) [9] introduced a novel approach for merging structured geographic objects by classifying and identifying them according to seven spatial structure parameters, while utilizing miter buffer transform to extract their complete boundaries. Compared to traditional methods, this technique ensures balanced area changes across different land cover categories.

However, the current aggregation methods still have notable drawbacks. During the aggregation process, detailed geographic information can be overly simplified or omitted, which can impact the accuracy of geographic analysis. The aggregated data might distort the true situation, leading to misleading representations [16].

2.2. Simplification

Simplification is a crucial operator extensively employed in cartographic generalization. Simplification typically refers to the process of eliminating intricate details from external contours and internal structures of geographical elements while retaining their main features.

Based on shape characteristics, simplification targets can be categorized into two groups: linear elements and planar elements. As a map contains the most abundant elements, linear elements have garnered significant attention from researchers. The challenge lies in removing unnecessary bends while preserving local bending features, domain features, and global features of linear elements.

Vector data-based simplification methods were initially applied to the simplification of linear elements. Douglas and Peucker (1973) [17] proposed a recursive approach that effectively reduces the number of points required for drawing lines during automatic generalization. Ai et al. (2013) [18] proposed a coastline simplification method based on Delaunay triangulation that considers estuarine tree modeling to capture dendrite patterns along with specific morphology and domain constraints related to coastlines. Subsequently, Ai et al. (2016) [19] present a polyline simplification algorithm based on the ε-circle rolling method, which utilizes Delaunay triangulation for detecting bending characteristics, constructing an envelope structure around a polyline, and generating abstract results accordingly. This method inherits Perkal’s algorithm’s scale-specificity while maintaining the primary shape of polylines amidst large-scale changes and effectively avoiding self-intersection issues after linear element simplifications occur. Visvalingam and Whyatt (1993) [20] proposed a progressive linear element simplification method based on calculating “effective area”.

The representation of polygonal boundaries is an approximation method used to simplify linear elements in raster data, but its applicability for cartographic generalization is limited due to the constraints imposed by the raster data type, resulting in a scarcity of related research.

In the field of simplification, planar elements can be categorized into natural and artificial types. Simplifying natural surface elements is relatively straightforward as the curvature of their boundaries allows the application of linear element simplification methods. However, simplifying settlement areas poses additional complexities due to their unique orthogonality. Zhang et al. (2006) [21] proposed a least square adjustment-based method for residential area simplification, while Chen et al. (2011) [22] introduced a constrained Delaunay triangulation nets approach to identify local concave–convex structures within residential areas.

In addition to vector data, scholars have extensively investigated simplification methods based on raster data. The techniques for simplifying residential land primarily encompass mathematical morphology [23,24] and neural network technology. Cheng et al. (2013) [25] proposed a simplified method for locating residents using a backpropagation neural network (BPNN) model. Yang et al. (2022) [26] introduced a hybrid approach to simplify all buildings by employing a backpropagation neural network to construct an evaluator through supervised learning that measures building parameters. This method demonstrates superior performance in terms of corner squareness and preservation of regional architectural characteristics compared to traditional approaches.

However, existing simplification methods still have certain limitations. During the simplification process, errors can be introduced and subsequently propagate through further analyses, potentially leading to inaccurate results [27]. And if the algorithm is not precise enough, it may lead to topological errors, such as line crossings or overlaps, which can undermine the integrity and reliability of the map data [16].

3. Methods

The aggregation of planar elements primarily encompasses object grouping and geometric form integration [10]. Elements adjacent in physical space and possessing similar attributes are perceived as cohesive wholes [8], with target elements often forfeiting a portion or even the majority of their distinctive traits during the aggregation process. Natural planar element aggregation, a subset of planar element aggregation methods, constitutes the principal focus of this study. Initially, islands are delineated, followed by classification and comprehensive simplification through superpixel algorithms to emphasize the boundary-smoothing characteristics essential for the aggregation of natural planar elements. Subsequently, texture synthesis and migration are employed using the Efros-Leung algorithm [28]. The schematic diagram depicting the methodology of this study is presented in Figure 1 below.

3.1. Island-Cover Extraction

The initial step involves utilizing the K-means clustering algorithm for color segmentation to classify islands and water bodies. The K-means algorithm stands as one of the most renowned and commonly employed clustering methodologies. However, it is crucial to note that its utilization entails an initialization phase where the number of clusters must be predetermined, thus rendering it not strictly an unsupervised clustering approach [29]. The fundamental aim of the K-means algorithm is to partition a dataset into K distinct clusters, striving to maximize the intra-cluster similarity while minimizing the inter-cluster similarity. As depicted in Figure 2a, the original image has dimensions of 205 × 190 pixels. By setting the cluster parameter to a value of 2, the classification outcome is illustrated in Figure 2b. Increasing the cluster value leads to a greater variety of features in the classification results. The original image is segmented based on color, resulting in two mask images, as shown in Figure 2c,d.

3.2. Islands Aggregation

The purpose of the superpixel algorithm is to find an over-segmented set of images [30]. Superpixel segmentation is an image segmentation method designed to partition an image into regions with homogeneous characteristics. After the segmentation of planar elements, typically six types of superpixels are generated [31], as depicted in Figure 3.

The recognition rules of six types of superpixels are as follows:

Type 1 These superpixels represent the original island planar elements, displayed in light green. They are treated as baseline pixels;

Type 2 These superpixels, which are solely connected to a single polygon and are first-order neighbors to Type 1 superpixels, are indicated in dark green and treated as type 2;

Type 3 These superpixels, which are linked to two or more polygons and are first-order neighbors to Type 1 superpixels, are shown in yellow and treated as type 3;

Type 4 These superpixels denote internal superpixels, first-order neighbors to Type 1 superpixels, and are connected to only one polygon, depicted in light blue. They are treated as type 4;

Type 5 These superpixels signify internal superpixels distinct from Type 4 superpixels, presented in dark blue. They are treated as type 5;

Type 6 These superpixels encompass all superpixels other than the aforementioned types, represented in white. They are treated as type 6;

Next, we conducted superpixel segmentation on the island planar elements depicted in the sample image and subsequently performed global simplification on the results. Figure 4a,b display the globally simplified images for superpixel counts of N = 1500 and N = 500, respectively. Generally, the complexity of texture and structure within an image correlates with the required number of superpixels. Additionally, median filtering is utilized to process the simplified images. As demonstrated in Figure 4c,d, median filtering effectively smooths the boundaries of aggregated polygons, ensuring a favorable merging effect while preserving the global characteristics of the planar elements and simplifying local details. This highlights the influence of different parameter settings on the aggregating effects of planar elements within the image.

3.3. Texture Migration

Firstly, extract the T-boundary from the aggregated image. Secondly, traverse the image to identify all enclosed white pixels bounded by the T-boundary, forming closed regions. Apply color assignments to these regions, as demonstrated in Figure 5b. Subtract the T-boundary fill image from the classified image yields, as shown in Figure 5c. Overlaying the blue pixels onto the original image, with their RGB values set to white, produces Figure 5d. The white areas are designated for texture filling.

It is apparent that further issues remain to be resolved: the excessive width between the original island boundary and the aggregated boundary due to the superpixel size setting results in overly rough texture filling post-filling. To address this, we employ morphological erosion operations to diminish the boundary width.

As erosion operations are exclusively applicable to binary images, we first undertake color transformation on the T-boundary fill image, as illustrated in Figure 6a. Subsequently, employing experimentation, we ascertain that setting the erosion iterations to 6 yields the most favorable outcome, as evidenced in Figure 6b. The superimposition of the eroded boundary onto the original image, as illustrated in Figure 6c, reveals a noticeable inward contraction of the white area post-erosion, closely aligning with the island edge.

The next task involves filling the vacant areas, necessitating the utilization of texture from the original island planar elements. Here, we employ the Efros–Leung algorithm for texture synthesis: leveraging statistical properties of local regions within the texture, new texture is generated by identifying the most similar local region from the original island planar elements to the area awaiting synthesis. The computational complexity of this method can be expressed as O(n × w² × h² × k), where n represents the total number of image pixels, w represents the filter kernel size, h represents the number of times the filter kernel slides, and k represents the number of channels. A small segment of island planar elements near the white area is extracted as a sample, as depicted in Figure 7a; texture synthesis based on the sample image using the Efros–Leung algorithm yields the result shown in Figure 7b; segments representing the aggregated island shape are excavated from the synthesized texture image, as illustrated in Figure 7c; finally, the synthesized texture is applied to the blank areas, resulting in the effect depicted in Figure 7d. It is evident that the filled texture closely resembles that of the original island planar elements, facilitating a smooth transition.

The following illustration, Figure 8, exemplifies the application of this methodology to other island planar elements:

4. Experiments

4.1. Dataset

The original experimental image data are sourced from Google Maps and organized into RGB map tiles using an image pyramid structure. On the server, the tiling strategy manages and loads large-scale geospatial data by dividing it into smaller, manageable chunks [32]. Each map tile is uniquely identified by its level, row number, and column number. Different resolution tiles are retrieved as users browse and zoom the map. In this study, 300 map tiles at level 8 with a scale of 1:611.5 were downloaded and mosaicked to form two regions containing different quantities of polygonal islands, as shown in Figure 9.

The Philippines and Sulawesi, located in Southeast Asia, exhibit a tropical maritime climate with consistently high temperatures, humidity, and significant rainfall. These regions experience distinct wet and dry seasons, influenced by monsoons, and are frequently affected by typhoons. The geography includes mountainous terrain and numerous archipelagic formations.

4.2. Experimental Procedure

Utilizing MATLAB 9.12.0.1927505 (R2022a) for data classification, we implement the K-means clustering algorithm to segment colors, effectively separating the islands and water bodies, as shown in Figure 10a,b. Following this segmentation process, island masks are individually extracted (Figure 10c,d), with the islands distinguished in blue against a white background.

Nonetheless, two outstanding issues remain unaddressed: Firstly, there are voids within the interior of the classified island segments, stemming from the misclassification of shadows by the K-means clustering segmentation algorithm. Secondly, certain small islands from the original dataset persist in the classification output. These scattered islands are predominantly located far from major islands, which could potentially impede subsequent aggregating procedures, resulting in aesthetically and practically compromised mapping outcomes.

For the first issue, no intervention may be necessary as these interior voids will be filled by the synthetic textures during the aggregation process, thereby not affecting the experimental results.

Concerning the second issue, we mitigate it by employing a method involving setting area thresholds to eliminate fragmented islands. Initially, the blue connected components representing islands are labeled, and the area of each connected component is computed. Subsequently, a threshold is established, and connected components with areas smaller than the threshold are deleted.

Then, we recorded the positions of removed connected components, excavated tiny islands on the original image, and filled the resulting holes with a texture resembling seawater.

The figure below, Figure 11, illustrates the aggregation effects of the experimental method at three different scales. This study is capable of producing results at various scales by controlling the number of superpixels. From the figure, it can be observed that this method effectively aggregates multiple polygonal islands while preserving the overall characteristics of the entire area.

Although certain aggregated results effectively preserve the overall characteristics, the resulting boundaries are not smooth and exhibit noticeable jaggedness. Consequently, filtering is introduced to smooth these boundaries. The comparative effects before and after smoothing are shown in Figure 12a,b, respectively. Subsequently, the closed regions enclosed by the T boundaries are filled, as depicted in Figure 12d. The comparison of the final effects of aggregation at different scales is shown in Figure 13.

To better illustrate the characteristics of the aggregating method utilized in this experiment, we employed the ArcGIS aggregating algorithm to process island planar features and conduct a comparative analysis. In Figure 14, the top three images display the aggregated results obtained from ArcGIS, whereas the bottom three present the results produced by our experimental method. It is evident that our method effectively maintains the overall characteristics of the aggregated surface features while simplifying local details and generating smooth aggregation boundaries. Conversely, the ArcGIS results demonstrate insufficient simplification of local details, leading to notably rough aggregation boundaries.

Following this, the filled image is subjected to a binary operation, followed by a suitable erosion process to inwardly contract the aggregated boundary. The resultant image is then superimposed onto the original image, yielding the effect illustrated in Figure 15.

Subsequently, we employ the Efros–Leung algorithm for texture synthesis. Initially, a small patch of island planar elements is sampled from the vicinity of the white areas to be filled. Texture expansion and generation are then conducted based on this sample image. Finally, the synthesized texture is applied to the regions aggregated at different scales, resulting in the observed effect shown in Figure 16 and Figure 17.

4.3. Experimental Results and Evaluation of Metrics

Figure 18 illustrates the aggregated outcomes of island planar elements under varied parameter configurations. The ultimate shape of the aggregated island is governed by two parameters: the count of superpixels, denoted as N, and the filter kernel size, denoted as len. Specifically, the superpixel count predominantly impacts the resultant island’s area, while the filter kernel size modulates the degree of boundary smoothness in the aggregated outcome.

Next, a similarity assessment will be conducted. Median filtering and mean filtering techniques, as classic grid-based data methods, will be applied to the raw images. The processed results will then be compared with those obtained from the proposed method. The fast adaptive bilateral filtering was originally proposed for sharpening and noise removal, now it can also be used for other applications, such as artifact removal and texture filtering [33]. To simulate smooth texture transitions, we employ a combination of deep neural network filtering (CNN filtering) with robust denoising capabilities [34] and Gaussian blur on the original images. These two advanced filters will also serve as comparative methods in our study. The computational complexities of the above four methods are O(n × w² log(w²)), O(n × w²), O(nlog(n)), and O(n × w² × k²), respectively, where n represents the total number of image pixels, w represents the filter kernel size, and k represents the number of channels. The results obtained from all methods are shown in Figure 19.

The evaluation of similarity between the processed result image and the original one will be based on five assessment metrics: Mean Squared Error (MSE), Peak Signal-to-Noise Ratio (PSNR), Normalized Mutual Information (NMI), Structural Similarity Index (SSIM), and Spatial Correlation Coefficient (SCC).

Mean Squared Error (MSE) computes the average of the squared pixel-wise differences between the two images, representing a fundamental metric for similarity evaluation. A lower MSE value signifies a higher degree of similarity between the images.

$$MSE={\displaystyle \frac{1}{MN}}{\displaystyle \sum _{i=1}^M{\displaystyle \sum _{j=1}^N{\left[x(i,j)-y(i,j)\right]}^2}}$$

(1)

The Peak Signal-to-Noise Ratio (PSNR) quantifies the similarity between two images by employing the maximum pixel value, denoted as MAX, and the Mean Squared Error (MSE). Here, ‘inf’ denotes infinity. A higher PSNR signifies that the quality of the processed image approaches that of the original image.

$$PSNR=10\log {\displaystyle \frac{MA{X}^2}{MSE}}$$

(2)

Normalized Mutual Information (NMI) is primarily employed for assessing the consistency of classification labels. Its computation incorporates mutual information and entropy from information theory, facilitating equitable comparisons across diverse datasets and varying numbers of clusters. A higher NMI value, approaching 1, indicates a greater similarity between two images.

$$NMI={\displaystyle \frac{2I(A;B)}{H(A)+H(B)}}$$

(3)

The Structural Similarity Index (SSIM) evaluates the similarity between different images by analyzing their brightness, contrast, and structure. A higher SSIM value, nearing 1, denotes a greater similarity between two images. The Spatial Correlation Coefficient (SCC) combines visual features and spatial features to measure the similarity between two images. It can also be used to describe whether the variation patterns of one dataset are correlated with those of another dataset.

The evaluation metrics for all processing results are shown in

Table 1. Evaluation metrics (1).

Sulawesi Island	MSE	PSNR	NMI	SSIM	SCC	Area (Pixels)
Original	0	inf	1	1	1	72,716
Mean Filtering	4.062966665	42.04	0.5853	0.970603887	0.9479
Median Filtering	3.374132156	42.85	0.6555	0.97418511	0.9501
Fast Adaptive Bilateral Filtering	11.610228856404623	37.48	0.4258	0.9068859377076354	0.9576
CNN + Gaussian Blur	19.700342814127605	35.19	0.2786	0.8411278436573086	0.8788
N = 2500, len = 17	8.240512848	38.97	0.837	0.921223914	0.8612	122,520
N = 1800, len = 40	10.82569504	37.79	0.7951	0.905779965	0.8605	136,301
N = 7000, len = 30	6.943405151	39.72	0.8582	0.926534499	0.8639	114,136

and

Table 2. Evaluation metrics (2).

Philippine Archipelago	MSE	PSNR	NMI	SSIM	SCC	Area (Pixels)
Original	0	inf	1	1	1	657,615
Mean Filtering	8.830849365	38.67	0.5484	0.945734931	0.9440
Median Filtering	7.667456009	39.28	0.6013	0.949695802	0.9487
Fast Adaptive Bilateral Filtering	17.1392986398493	35.79	0.4097	0.867839697459523	0.9533
CNN + Gaussian Blur	25.9185290249534	33.99	0.3245	0.7777573460086513	0.8912
N = 1800, len = 65	32.76713031	32.98	0.4788	0.794131297	0.8953	1,441,493
N = 6400, len = 75	24.0629642	34.32	0.5361	0.841412155	0.9062	1,224,822
N = 9000, len = 50	16.88695558	35.86	0.581	0.872360166	0.9231	1,055,782

.

From the table, it is evident that the performance of various metrics is closely linked to changes in island area. The two traditional filters, mean and median filters, result in relatively minor changes and do not introduce new island pixels, thus demonstrating strong performance across all metrics. In the results obtained through our experimental method, the greater the number of superpixels (N), the smaller the variation in island area, leading to superior performance across metrics. Using MSE as an example, the calculation formula clearly shows that MSE measures similarity between two images by calculating the point-by-point difference between corresponding pixels. This metric straightforwardly emphasizes visual similarity, indicating that the fewer the number of pixels modified in an image or the smaller the change in pixel values, the more closely the modified image resembles the original. The proposed method, however, involves the addition of numerous synthetic pixels during the aggregating process, resulting in significant deviations in overall pixel values from the original image and consequently poorer MSE performance.

NMI stands out as the most comprehensive metric among all, as it evaluates the average amount of information and the consistency of category distributions by considering mutual information and entropy [35], thereby enabling fair comparisons across datasets with varying cluster numbers. Thus, a higher NMI value reflects the reasonableness and effectiveness of our experimental method in aggregating islands. Moreover, a high and stable SCC indicates that the pattern of involving island pixels in our experimental method aligns well with the trend of aggregating planar features.

Image feature points and sharpness are also crucial factors influencing similarity. Fast adaptive filtering tends to lose edge details during the denoising process, resulting in a performance that is not as strong as that of traditional filtering. Moreover, incorporating Gaussian blur in CNNs leads to the loss of significant image details, resulting in the weakest performance across all metrics.

Since this experiment explores the multi-scale representation of islands, similarity serves only as a reference metric. Due to inherent algorithmic limitations, traditional filtering methods cannot fill the gaps between islands, which means they cannot achieve multi-scale representation. Our method, however, can produce aggregating effects at different scales and exhibits superior performance in similarity metrics compared to various filtering techniques.

5. Summary

In addressing issues of traditional aggregating methods such as the inability to maintain simplification efficiency while preserving overall characteristics, coarse overall boundaries after aggregating and difficulty meeting diverse scale requirements, this research proposes an integrative innovative approach based on computer vision theory. Initially, the K-means clustering analysis is applied to distinguish islands from seawater. Subsequently, superpixel segmentation is utilized to generate aggregated results at varying scales through parameter adjustments. Finally, the Efros–Leung algorithm is employed to synthesize island-like pixels and fill in gaps. The experiment employs four metrics—MSE, PSNR, NMI, and SSIM—to assess both visual similarity to the original image and structural consistency in category distribution.

Compared to traditional approaches in multi-scale representation of remote sensing imagery, the novel method proposed in this study exhibits several advantages:

• Traditional vector-based methods often lose original textures when aggregating planar features, and raster-based aggregation methods cannot eliminate gaps between islands. However, our proposed method can preserve the original textures while filling the gaps between islands during the aggregating process.
• In contrast to traditional aggregating techniques, our method achieves smoother boundaries and sharper textures, thereby enhancing visualization quality;
• Unlike traditional methods limited to a single scale, our approach allows for the generation of aggregated results at varying scales tailored to specific requirements.

However, this method still presents certain limitations in the multi-scale representation of remote sensing imagery. During texture synthesis, the approach utilizes only a small subset of pixels from the planar elements of islands in the original image. In cases when there is a significant difference in pixel values between the two ends of the area to be aggregated, it may result in non-smooth transitions in texture migration. And this section occupies the majority of the computational complexity of the entire algorithm. Therefore, there is a need for further research into a comprehensive method that considers all pixels while increasing computational efficiency. Moreover, in the classification step, the sharp edges at the junction between the island and the seawater will affect the boundary generation, which means the accuracy needs to be further improved.