Hybrid contour and geometric partitioning for accurate plantar foot region segmentation

Ethics approval

The experimental paradigm was approved by the Research Ethics Committee (REC) of New Engineering Industry College, Putian University (NO. 2023030206), in compliance with the Declaration of Helsinki. Written informed consent was waived by the REC.

Device for foot pressure scanning

Plantar pressure images were collected using a non-invasive foot pressure scanner (Footbird), equipped with flexible pressure sensors, as shown in Fig. 1A. The device comprises a self-designed motherboard and a high-precision flexible thin-film array piezoresistive pressure sensor. The sensor array consists of 14,400 sensing units arranged in a 120 × 120 grid, with each unit capable of detecting pressures ranging from 0 to 255 kPa. The total effective acquisition area is 42 × 42 cm², enabling real-time visualization of plantar pressure distribution on a display screen, as illustrated in Fig. 1B. Scanned images were stored for further analysis.

Participants and recruitment

The study participants consisted of 400 adult volunteers (228 males, 172 females; aged ≥18 years) who visited the Shuangchi Customized Factory shoe store for footwear customization services. Inclusion criteria required participants to be adults with no prior foot-related medical conditions, while exclusion criteria excluded individuals with recent foot injuries or surgeries. Recruitment was conducted via in-store announcements, and participants were verbally informed of the study’s purpose, with the option to decline participation. To prioritize privacy and focus on algorithmic evaluation, no personal identifiers (e.g., age, height, weight) were collected.

Data collection protocol

Before data collection, the Footbird system was calibrated to zero pressure. Participants removed their shoes, donned disposable socks, and stood motionless on the fixed foot area of the scanner for approximately 15 s until the plantar image appeared on the screen. The device captures 125 frames of grayscale pressure images, each measuring 700 × 700 pixels. These 125 images are then combined and processed into a single composite image, which is pseudo-colored according to the pressure values, as illustrated in Fig. 1B. Each volunteer contributed one footprint per foot, yielding a total of 800 plantar pressure foot samples from 400 participants.

Sample size determination

To balance sample quality and quantity, we selected 200 footprints from the initial 800 plantar pressure images. This selection constitutes 25% of the total dataset, which is a common practice in many studies. The initial dataset included complete (full footprint), basically complete (missing some toes), and incomplete (missing partial foot regions) images, as demonstrated in Fig. 2. To ensure representativeness, selected images prioritized completeness (excluding severely fragmented scans) and diversity in foot morphology, including normal, low arch, high arch, inward heel tilt, and outward heel tilt, as shown in Fig. 3. The definitions of the five foot types are as follows (Pinney, 2023):

• Normal foot: Slightly curved midfoot (approximately 50% midfoot contact, Fig. 3A).

• Low arch (flatfoot): Near-complete midfoot contact (Fig. 3B).

• High arch: Minimal midfoot contact (Fig. 3C).

• Inward heel tilt: Calcaneus deviation inward; the toe area may exclude the hallux (Fig. 3D).

• Outward heel tilt: Calcaneus deviation outward; the toe area may show only the hallux (Fig. 3E).

Plantar image segmentation algorithms

For the segmentation of plantar images, we evaluated three established algorithms: thresholding, region splitting and merging, and Canny edge detection. Each method has its advantages and disadvantages, and we focused on their effectiveness in segmenting the forefoot and heel regions.

Contour extraction, filtering, and foot assignment

After applying the three segmentation algorithms (Thresholding, Region Split & Merge, Canny), the binary outputs underwent the following post-processing steps to extract and refine contours and assign them to the respective foot (left or right).

Contour detection identifies closed object shapes by locating continuous points along their boundaries with the same color or intensity. This process retrieves boundary lines from a binary image generated through the aforementioned segmentation techniques. Filtering enhances contours by removing smaller, less relevant regions, leading to clearer identification of the forefoot, midfoot, and heel regions.

In this study, contour detection employs the border-following algorithm (Suzuki & Abe, 1985). Each detected contour is stored as a vector of points in an array. A minimum area criterion is applied to filter out unwanted contours, calculated using Eq. (2), and the coordinates of the contour boundaries for regions of interest are stored in the intersContour array, as shown in Eq. (3).

(2)${\displaystyle area\left[i\right]=\frac{1}{2}\sum _{j=0}^{n_i}{x}_j{y}_{j+1}-x_{j+1}{y}_j|\left(x_j,y_j\right)\in contour\left[i\right]}$ (3)${\displaystyle intersContour=intersContour+contour\left[i\right],ifarea\left[i\right]>minArea}$ where area[i] represents the area enclosed by the ith contour in the contour array; n_i denotes the number of boundary points contained in the ith contour array; minArea is set to 6000 in this study.

To analyze the left and right feet separately, we assign regions of interest extracted from the entire image to each foot. This involves determining the minimum bounding rectangle (boundingRect) for each contour based on the intersContour array, as defined in Eq. (4). The relevant region information is then stored in the regions list, as shown in Eq. (5). (4)${\displaystyle \begin{array}{c}\hfill x,y,w,h=boundingRect\left(intersContour\right)\hfill \\ \hfill topLeft=\left(x,y\right);bottomRight=\left(x+w,y+h\right)\hfill \\ \hfill side=\left\{\begin{array}{c}left,ifx<imgWidth/2\hfill \\ right,otherwise\hfill \end{array}.\right.\hfill \end{array}}$ (5)${\displaystyle regions=\left[\left(sid{e}_0,topLef{t}_0,bottomRigh{t}_0\right),\dots ,\left(sid{e}_m,topLef{t}_m,bottomRigh{t}_m\right)\right].}$

Here, x, y, w, and h represent the coordinates of the top-left corner (x, y) and the width and height of the contour’s bounding rectangle. The variable side indicates whether the contour belongs to the left or right foot, and imgWidth is the width of the entire image.

Combining contours and geometric segmentation for foot region analysis

To achieve precise segmentation of the forefoot, midfoot, and heel regions, we developed a hybrid approach that integrates the post-processed contour information with geometric partitioning techniques. This combined method proceeds as follows for the left foot (analogously for the right). Since abnormal feet may result in missing toe parts in plantar images, the proposed integrating algorithm uses an area threshold to exclude the toe region.

Initial calculations involve determining the minimum and maximum y-coordinate values for the left foot and the x-coordinate values for each region, as illustrated in Fig. 4. The foot length from forefoot to heel is determined based on the values in the contour regions, as shown in Eq. (6). This length is then divided into three regions: the forefoot, midfoot (arch), and heel, based on standard proportions (Pinney, 2023), as described in Eq. (7). The forefoot is further subdivided into outer and inner regions using Eqs. (8) and (9), while rectangular regions for the midfoot and heel are defined using Eqs. (10) and Eq. (11), respectively. Information about the four regions in the left foot is stored in the leftRegions list, as shown in Eq. (12). (6)${\displaystyle leftL=max\left(leftY\right)-min\left(leftY\right)+1}$ (7)${\displaystyle leftL\text{\_}fore,leftL\text{\_}arch,leftL\text{\_}heel=leftL\ast 0.3,leftL\ast 0.3,leftL\ast 0.4}$ (8)${\displaystyle outerFore=\left[\left(min{F}_x,min\left(leftY\right)\right),\left(minF\text{\_}x+int\left(\frac{max{F}_x-{\text{minF}}_{\mathrm{x}}}{2}\right),min\left(leftY\right)+leftL\text{\_}fore\right)\right]}$ (9)${\displaystyle innerFore=\left[\left(minF\text{\_}x+int\left(\frac{max{F}_x-{\text{minF}}_{\mathrm{x}}}{2}\right),min\left(leftY\right)\right),\left(maxF\text{\_}x,min\left(leftY\right)+leftL\text{\_}fore\right)\right]}$ (10)${\displaystyle arch=\left[\left(\text{minA}\text{\_}\mathrm{x},min\left(leftY\right)+leftL\text{\_}fore\right),\left(maxA\text{\_}x,min\left(leftY\right)+leftL\text{\_}fore+leftL\text{\_}arch\right)\right]}$ (11)${\displaystyle heel=\left[\left(min{H}_x,min\left(leftY\right)+leftL\text{\_}fore+leftL\text{\_}arch\right),\left(\text{maxH}\text{\_}\mathrm{x},max\left(leftY\right)\right)\right]}$ (12)${\displaystyle leftRegions=\left[ourerFore,innerFore,arch,heel\right]}$ where, min(leftY) represents the minimum y-coordinate of the left foot, and max(leftY) is the maximum y-coordinate of the left foot.

Comparison of image segmentation algorithms

Using this test dataset, we compared the performance of three widely used algorithms: thresholding, region split and merge, and Canny edge detection. Each algorithm was evaluated based on its effectiveness in segmenting the forefoot and heel regions.

Comparison of threshold segmentation methods

Three common threshold segmentation methods (Simple, Otsu’s binarization, and Adaptive) were applied to the same image, with results depicted in Fig. 5.

As illustrated in Fig. 5, the adaptive thresholding method captures more detailed small regions, while Otsu’s method results in fewer regions. Although the simple threshold method yields less detail than the adaptive method, it successfully outlines the overall contours of the forefoot and heel, which is essential for plantar pressure analysis. Therefore, simple thresholding is recommended as the threshold segmentation algorithm for plantar image segmentation.

Comparison of merging thresholds in split and merge algorithm

To identify suitable merging thresholds (minThresh, maxThresh), we tested three different pairs and compared their segmentation results using the region split and merge algorithm, as illustrated in Fig. 6.

The results indicate that lower threshold values (50, 100) yield more detailed regions, while higher values (200, 300) result in fewer merged regions. The pair (50, 100) was preferred for capturing clearer contours of the forefoot and heel.

Comparison of double thresholds in Canny edge detection

Three sets of double thresholds (minVal, maxVal) were evaluated for the Canny edge detection algorithm, with results shown in Fig. 7.

The comparison reveals that lower double threshold values (100, 200) produce more refined regions but may lead to discontinuous edges, while threshold values (200, 300) provide fewer segmented regions, with some broken edges. Higher thresholds (300, 600) capture only the outer contour edges, making it suitable for detecting the external contours of the foot.

Combining filtering contours with geometric method for foot structural segmentation

To enhance contour clarity, we initially applied a filtering approach to three tested algorithms: Simple Thresholding, Split & Merge (50, 100), and Canny (300, 600). The experimental results indicated that while filtering improved contour clarity by removing smaller, less relevant regions, none of the algorithms adequately captured the structural boundaries of the foot (forefoot, midfoot, heel) based solely on pixel connectivity. This limitation motivated the development of our hybrid algorithm.

This section evaluates the effectiveness of integrating geometric structural segmentation with the selected contour and edge detection algorithms. We utilized a test dataset of 200 images, representing a diverse range of normal and abnormal foot types, ensuring that our comparisons are based on a comprehensive dataset reflecting various foot conditions. The performance of the combined geometric method with the three algorithms was rigorously assessed using average Intersection over Union (IoU) and mean Average Precision (mAP) metrics. The IoU and mAP values were calculated in two steps: first, by averaging the results for normal and abnormal foot images to compare differences, and then by averaging these values for the final results.

The mAP is a comprehensive metric for evaluating object detection models, as it considers both precision and recall, allowing for a nuanced assessment of model performance. IoU measures the similarity between predicted and ground truth bounding boxes, calculated as the ratio of their intersection to their union, as expressed in Eq. (13). The ground truth was obtained manually using the Make Sense platform (https://www.makesense.ai/). (13)${\displaystyle IoU\left(A,B\right)=\frac{\left(A\cap B\right)}{\left(A\cup B\right)}}$ where A and B represent the predicted and ground truth bounding boxes, respectively. An IoU score of 1 indicates perfect overlap, while a score of 0 indicates no overlap. In this study, algorithm performance was classified as: poor (IoU <0.6), good (0.6 ≤ IoU <0.90), and excellent (IoU ≥ 0.90).

The performance evaluation results, measured by IoU and mAP, are summarized in Table 1. The hybrid Canny + Geometric method consistently outperformed the other algorithms, achieving IoU and mAP scores exceeding 0.90 for all regions (forefoot, midfoot, heel). In contrast, the other methods exhibited greater variability, particularly in the heel region. This discrepancy in performance can be attributed to the Threshold and Split & Merge algorithms, which focus on detecting contours within the foot’s interior, thereby compromising stable detection of the outer edge and leading to inconsistent segmentation. Overall, our findings indicate a positive correlation between higher IoU values and mAP scores, highlighting the effectiveness of the hybrid Canny + Geometric method for accurately segmenting the foot into forefoot, midfoot, and heel regions.

Furthermore, the results demonstrate that the performance of the proposed hybrid algorithm is comparable for both normal and abnormal foot types, with no significant differences observed. The segmentation results for the five foot types using the combined Canny and geometric structural method are illustrated in Fig. 8.