Overlapping Shoeprint Detection by Edge Detection and Deep Learning

1. Introduction

In the realm of 2-D image processing and computer vision, the task of object detection, particularly in scenarios with overlapping or obscured objects, poses a significant challenge. The intricacies and diversities in object shapes, textures, and overlapping patterns contribute to the complexity of accurately identifying and segmenting objects within images. This is in contrast to human perception, where the tendency to three-dimensionality helps to isolate objects foreground from objects in the background of the image.

Recent approaches, predominantly relying on Convolutional Neural Networks (CNN) for object detection, have shown a notable degree of success in various image analysis tasks [1,2,3]. However, when faced with overlapping objects in two dimensions, these models' performance drops, mainly due to the inability to accurately segment the overlapping areas and delineate the underlying object boundaries.

A shoeprint represents the textured image left behind when the sole of a shoe makes contact with a surface in the natural environment [4]. In forensic investigations involving shoeprints left behind at the scene of a crime, a clear and complete texture is important for accurate identification [5,6]. However, in reality, there are frequent instances where two or even multiple textures overlap, leading to a loss of information. Also, real shoeprint images contain non-shoeprint content in the background, such as grit and sand, which can be considered noise. While there has been previous work on images containing single shoeprints in the neural network literature, the task of handling multiple shoeprints against a noisy background in the same image remains a challenge. In an endeavour to achieve target recognition of overlapping shoeprints under intricate noise conditions, we employ contemporary neural network models to evaluate their performance. This study specifically focuses on overlapped shoeprint images, where the task is to separate these shoeprints into separate objects in the presence of noise for the purpose of subsequent identification.

Applications of computer vision to shoeprint images are relatively scarce. The unique, discontinuous texture of shoeprint images and their typical incompleteness pose challenges for research. The sensitivity of neural networks to images containing single shoeprints has been confirmed in a previous study [7]. In that research, a basic convolutional neural network was utilized, comprising three convolutional layers, three pooling layers, and a softmax layer for classification, totalling a seven-layer structure to determine the presence of shoeprints in images—a fundamental binary classification judgment required prior to identification of which shoe the shoeprint belongs to.

The most critical information for shoeprint detection lies in the boundaries between the shoeprint texture and the ground, which together form a complete shoeprint. Retaining only the edge information of the shoeprints as the sole basis for detection might seem like an extreme method of recognition. However, this approach can more clearly reflect the neural network's sensitivity when processing edge data. In particular, any detection model must be able to ignore the background noise against which the shoeprint image is taken, especially grit, sand and mud.

For the research described below, we deployed the YOLO (You Only Look Once) model to detect overlapping shoeprint locations. The model was trained using a dataset containing bounding boxes and subsequently used to delineate the position of shoeprints in new images. Additionally, visualization techniques were employed, offering insights into neuron activation patterns when processing overlapped images to identify possible reasons for the network’s behaviour.

This paper seeks to elucidate the potential synergies between edge detection and image segmentation in enhancing object detection within overlapping shoeprint images. This research not only aims at advancing the accuracy and efficiency of shoeprint analysis but also extends possible methods for the integration of various image processing techniques in tackling multiple overlapping object detection more broadly.

This research also establishes a promising benchmark for future applications in detecting overlapping shoeprints from images. It demonstrates that deep learning models possess sensitivity and precision in separating and identifying the presence of shoeprints. For images with minimal overlap, the confidence level exceeds 85%. For those that are almost entirely overlapped, the confidence remains above 70%.

2. Background and Related work

Shoeprints can provide invaluable clues in the detection of criminal cases [8,9]. Accurate discriminative features play a critical role in achieving effective performance in shoeprint recognition tasks. The effectiveness of shoeprint detection and identification methods is primarily dependent on the feature extraction technique used, which can exhibit significant variability [10]. A convolutional neural network (CNN) model typically consists of a series of layers that can be trained to recognize patterns in data without the need for prior feature extraction or selection [11].

Edge detection is a pivotal technique in image processing and computer vision, with the objective of identifying the boundaries of objects or regions. Edges typically occur where there is a change in image brightness or colour, signifying the contours of objects [12].

In executing edge detection, techniques such as the Sobel operator, Scharr operator, Prewitt operator, and the Canny edge detection algorithm are often employed to analyse the local structure of the image and determine which points constitute edges [13]. Through edge detection a binary image can be obtained, in which the white pixels represent the edges in the original image.

Edge detection finds extensive applications in many image-processing tasks such as object recognition [14], tracking [15], segmentation [16], and feature extraction [17], among others [18]. By enabling a better understanding of the structure and content of images, edge detection lays a solid foundation for subsequent image analysis and processing.

There have been many recent advancements in edge detection technology [19,20]. The application of deep learning and Convolutional Neural Networks (CNNs) has identified new directions for improving edge detection algorithms [21]. Deep learning, with a particular emphasis on Convolutional Neural Networks, has emerged as a new avenue in edge detection research [22]. By training on extensive image data, CNNs are capable of learning edge detection features without prior and separate feature extraction techniques, thereby achieving effective edge detection across a variety of scenarios [23]. The incorporation of attention mechanisms in edge detection models can assist the model in focusing on crucial areas of the image, thereby enhancing the accuracy of edge detection [24]. Through multi-scale feature fusion, edge detection algorithms are able to consider both local and global information of the image, thus enhancing the performance of edge detection [25]. Additionally, researchers have proposed a multitude of optimized network structures to augment the accuracy and efficiency of edge detection, for instance, generating precise edge information through convolutional pyramid features and multi-path aggregation [24]. With increases in computational memory and processing, real-time edge detection has become a reality. This is of significance for applications requiring real-time processing, such as autonomous driving and video surveillance [26].

The evolution of deep neural networks is trending towards increased complexity. To enhance performance in image identification tasks within computer vision, proposed CNN models have become complex, often encompassing millions of parameters [27,28,29]. YOLO (You Only Look Once) stands as a well-known object detection algorithm [30], known for its speed and precision. In contrast to traditional object detection approaches that involve prior feature extraction and selection techniques, YOLO employs a singular neural network model to perform bounding box regression and class label prediction in a single forward pass, achieving its "only look once" effect [31]. Over time, YOLO has undergone numerous iterations and enhancements, leading to the emergence of versions like YOLO 9000 [32], YOLOv3 [33], and YOLOv4 [34]. The study herein utilizes the latest in the YOLO series, the YOLOv8 structure, which introduces novel modules, further elevating the model's usability.

3. Data and Methods

There is currently no publicly available dataset of overlapping shoeprints and so overlapping shoeprints have to be generated from single shoeprint images from an existing dataset sourced from the German State Criminal Police Offices from Baden-Wuerttemberg, Bayern, Brandenburg and Niedersachsen and Forensity AG [35]. The dataset comprises 300 original single-shoe images and 1175 single-shoe reference images, with the former being actual photographs of crime scenes depicting shoeprints preserved in soil or on hard surfaces, which were subsequently collected as evidence using gelatine lifters. The reference images, on the other hand, were obtained by scanning the surface of a reference shoe sole covered with gelatine lifters to produce a complete image. Both types of images share a similar generative logic, thus enabling the use of imaging data for model training and testing on the 300 crime scene images. Overlapping images were generated from this dataset, as described below.

3.1. Data

The overlapped shoeprint samples are generated by code, with each instance producing distinct features, including noise, shoeprint position, rotation, and overlapping relationships.

Stage 1: Data Generation.

The primary package used is Pillow. In the first step, a blank image is created. 300 to 600 random colour noise points of random sizes ranging from 4x6 to 10x12 are added to simulate sand and grit (noise). In the second step, random samples are selected from the FID-300 references folder, and a transparency channel is added with a transparency of 60% to 80%. Through multiple experiments, it was found that images with too low transparency were overly difficult to recognize and did not align with the logic of real samples, while too high transparency would completely obscure underlying pixels, contrary to the conditions of "overlapping" in this task. This step is repeated 1500 times and saved in a new folder named ‘refer_transparent’. In the third step, one photo is randomly selected from the 1800 photos in the FID-300 references folder, and one is randomly chosen from the newly created semi-transparent folder ‘refer_transparent’. The two images are overlapped on the blank base plate containing noise. The position and rotation angle of these two images are kept random. This process is repeated 200 times to obtain an unlabelled dataset.

Due to the complete randomness of the samples in this study, the generated images encompass various positional relationships, including those that are not overlapped at all (Figure 1a). almost overlapping, as shown in Figure 1b, and those partially overlapped, as illustrated in Figure 1c. To validate the sensitivity of neural networks to a wide variety of samples, these non-overlapping samples (Figure 1a) were not removed from this study.

Stage 2: Image Labelling.

The first step in separating shoeprints is the addition of bounding boxes. The image labelling for this study was accomplished using the Labelme annotation software. In this experiment, rectangular bounding boxes were used to annotate the shoeprints. The shoeprints were identified visually, with the annotation boxes extending from the toe to the heel to completely enclose the shoeprints as much as possible. Covered areas were also included in the annotations, aiming to enable the neural network to learn the complex textures of obscured regions. Therefore, there are overlapping areas between two bounding boxes, with some having significantly large overlaps (Figure 2). The annotation files were saved in JSON format and required conversion to TXT documents usable by the YOLO framework through corresponding Python code. In the YOLO format annotation files, the four points of each bounding box are relative positions with the top-left corner of the image as the origin, rather than absolute pixel points.

Sample labelling includes only one category: shoeprints.

The total number of labelled samples for training is 200, divided into two parts: the training set and the validation set, comprising 80% and 20%, respectively, i.e., 160 images for model training and 40 for validation. The test set consists of 20 newly generated images using the method from Stage 1.

3.2. Edge Detection

Edge detection is commonly achieved through the computation of image gradients, with the magnitude and direction of the gradients typically used for edge identification. The computation of gradients necessitates the employment of operators. These operators compute the horizontal and vertical gradients of the image through convolution operations, thereby deriving the magnitude and direction of the gradients. The specific formulae are as follows:

The computation of gradients is usually executed by applying operators (such as Sobel, Scharr, or Prewitt operators). These operators, through convolution operations, compute the horizontal and vertical gradients of the image, thus obtaining the magnitude and direction of the gradients. The specific formulae are as follows:

$$\left[G_x=I\ast K_x\right]$$

(1)

$$\left[G_y=I\ast K_y\right]$$

(2)

where $\left({\mathrm{G}}_{\mathrm{x}}\right)$ and $\left({\mathrm{G}}_{\mathrm{y}}\right)$ represent the gradients of the image $\mathrm{I}$ in the x and y directions respectively, $\left({\mathrm{K}}_{\mathrm{x}}\right)$ and $\left({\mathrm{K}}_{\mathrm{y}}\right)$ denote the convolution kernels in the x and y directions, and $\left(\ast \right)$ symbolizes the convolution operation.

A commonly employed operator for gradient computation is the Sobel operator:

It utilizes two 3x3 convolution kernels, one estimating the gradient in the horizontal direction, and the other in the vertical direction.

Kernel for the horizontal direction:

$$\left[\begin{array}{ccc}-1& 0& 1\\ -2& 0& 2\\ -1& 0& 1\end{array}\right]$$

(3)

Kernel for the vertical direction:

$$\left[\begin{array}{ccc}-1& -2& -1\\ 0& 0& 0\\ 1& 2& 1\end{array}\right]$$

(4)

In routine applications, another operator known as the Scharr operator is also utilized, which holds greater weight in its kernels compared to the Sobel operator, thereby providing more accurate edge detection:

Kernel for the horizontal direction:

$$\left[\begin{array}{ccc}-3& 0& 3\\ -10& 0& 10\\ -3& 0& 3\end{array}\right]$$

(5)

Kernel for the vertical direction:

$$\left[\begin{array}{ccc}-3& -10& -3\\ 0& 0& 0\\ 3& 10& 3\end{array}\right]$$

(6)

The main differences among the Sobel, Scharr, and Prewitt operators lies in the different values of their convolution kernels, which lead to differences in computing image gradients. The variance in kernel values affects the results of edge detection, such as the clarity of edges and the number of edges detected. The Sobel operator is simple to implement and boasts high computational efficiency, capable of detecting edges in both horizontal and vertical directions. However, it is sensitive to noise, prone to false detections in images with a higher level of noise, and may fail to detect diagonal or curved edges [13]. Its edge localization is not as precise as some other advanced edge detection algorithms [36]. In this experiment, we utilized the Canny algorithm of the Sobel operator [37]. The Canny algorithm initially employs a two-dimensional Gaussian filter to smooth the image for noise reduction, followed by the Sobel operator's method to compute the image's gradient magnitude and direction. Hence, the Canny algorithm employs a Gaussian filter in conjunction with a gradient computation method akin to the Sobel operator [37]. The two-dimensional Gaussian function is a common algorithm used for image noise filtering [38]. This function convolves with the image, smoothing each pixel value to alleviate image noise while preserving the image structure. During the convolution process, the new value of each pixel is the weighted average of the values of surrounding pixels, with the weights determined by the Gaussian function:

$$\left[G\left(x,y\right)=\frac{1}{2\pi {\sigma }^2}\exp \left(-\frac{x^2+y^2}{2{\sigma }^2}\right)\right]$$

(7)

where:

- $\left(\mathrm{x}\right)$ and $\left(\mathrm{y}\right)$ are the coordinates in two-dimensional space,

- $\left(\mathsf{\sigma }\right)$ is the standard deviation, controlling the width of the Gaussian function.

Subsequently, Non-Maximum Suppression (NMS) is incorporated for edge thinning, similar to the pooling principle in CNN, selecting only the pixel with the maximum gradient change within a region [39]. After setting maximum and minimum thresholds, gradients exceeding the maximum threshold are deemed as edges, while those below the minimum threshold are considered non-edges. Finally, all strong edge pixels are connected, along with those termed as "weak edges", which are adjacent to strong edges and fall between the upper and lower thresholds.

The image on the Figure 3b illustrates a sample of overlapped shoeprints post-application of the Canny algorithm. In comparison to the previous image, all filled pixels have been discarded in this image. The newly generated image is of identical dimensions to the original image, hence the annotations from the previous image can be directly applied to the new edge image (see Figure 4).

3.3. Object Detection

This stage utilizes the YOLO v8 model [40]. Due to recent iterations across multiple versions, the neural network's size and depth have become quite substantial. The model comprises 168 layers, with 11,125,971 parameters (Figure 5). Its primary modules include the Backbone and Head. The model mainly consists of 22 layers (see Table 1), with different layers corresponding to different modules (e.g., Conv, C2f, SPPF). In order to improve the training speed, we selected the v8s version in the v8 model series as the baseline model. Compared with other versions, v8s has the least number of parameters and channels, reducing the total number of model parameters.

To enhance the customizability of large neural networks, the network is designed in modular stages, from P1 to P5, which serve as the main feature extraction phases of the model. Convolutional layers are used as the primary feature extraction layers within these stages. Across different stages, the dimensions and channels of the feature maps vary, but the convolutional kernel size remains fixed at 3x3. This choice balances the shortfall in feature collection with larger kernels. Following the convolutional layers, Batch Normalization operations and the SiLU activation function are applied [41]. Compared to the commonly used ReLU [42] activation function in traditional CNN models, the non-zero centred characteristic of SiLU, its smoother activation curve, and the preservation of information for negative inputs provide a more reliable and comprehensive set of information for the network to proceed to the next training layer.

After the feature extraction through stages P1 to P5, the size of the neural network's receptive field increases, and each pixel in the feature map represents a larger original size, reaching 32x32 pixels. To enhance sensitivity towards detecting and analysing medium and small-sized targets, YOLO incorporates an upsampling mechanism. For identifying medium-sized targets, the small-sized feature map extracted after the P5 stage undergoes upsampling to match the size of the P4 feature map. After concatenating the output of P4, further feature extraction is performed before entering the loss function for target detection. Similarly, a third detection module concatenates the P3 stage to address small targets.

The advantage of this approach is that the output from each feature extraction module in the target detection can be preserved. The fusion of deeper and shallower features can significantly enhance the neural network's sensitivity when facing complex tasks. A drawback of the traditional AlexCNN [43] is that deeper network models usually have a larger receptive field, which tends to be less sensitive to small targets. Fine edges, textures, and colour features may be lost. However, these details are particularly important for our task.

Among the different layers, the convolutional neural network's size varies, with dimensions of 20x20, 40x40, 80x80, 160x160, and 320x320 all being utilized.

C2F is a unique module to YOLOv8, allowing YOLOv8 to obtain richer gradient flow information while ensuring a lightweight structure.

SPPF (Spatial Pyramid Pooling - Fast) is a specialized pooling module developed after SPP [44]. SPP replaced the traditional single-layer max-pooling structure, implementing a maximum pooling module without changing the image size. SPPF further optimized the module structure, improving the running speed.

For further details of the full YOLO architecture including Backbone and Head, see [40].

3.4. Evaluation Matrix

3.4.1. Precision and Recall

For this task, precision (how often the model is correct) and recall (whether all shoeprints are found) are the most important metrics, since the task is to identify all possible overlapping shoeprints in images for further identification and classification. Assessment of predictive outcomes is conducted through the quantification of various classification result ratios.

More precisely, precision represents the proportion of samples that are actually correct within all samples predicted as positive. Recall, on the other hand, quantifies the fraction of samples predicted as positive out of all the samples that are inherently positive.

3.4.2. mAP

mAP (mean Average Precision) is a commonly used metric for evaluating object detection model performance. mAP50 refers to the average precision at an IoU (Intersection over Union) threshold of 0.5. IoU is a metric that measures the degree of overlap between predicted and actual bounding boxes. When IoU is greater than or equal to 0.5, the prediction is considered correct. mAP50-95 is the average of the average precision at different IoU thresholds. Typically, these thresholds range from 0.5 to 0.95, in steps of 0.05. Therefore, mAP50-95 is the average of mAP at these different thresholds, providing a more comprehensive assessment of model performance.

3.4.3. Heating Map

To investigate the relationship between the image and the activated regions in the neural network, various visualization techniques were employed. This aimed to observe the sensitivity of certain features (regions) within the neural network. Class Activation Mapping (CAM) is a prevalent image visualization method that facilitates in-depth analysis of specific layers in deep neural networks [45]. The Class Activation Mapping (CAM) heatmaps illustrate the activation levels across various regions of the network during decision-making processes. The heatmap employs a colour spectrum where red or yellow indicates high activation, and blue signifies low activation. These activation levels suggest the areas of the image that the network deems crucial for object recognition. The activated regions are essential for the successful detection of objects. However, neural networks typically make decision based on a comprehensive integration of multiple channels. They rely not only on these highly activated areas but also on knowledge learned from other regions, based on the overall distribution of features. Moreover, they utilize contextual information, acquiring auxiliary details beyond the important features. Nevertheless, these heat maps can provide useful insights into how and why neural networks reach convergence in their output at various layers (further details below).

4. Experiments and Results

Three experiments were conducted, as follows. All experiments were executed on the Google Colab platform, utilizing the Nvidia A100 SXM4 40GB graphics card for training.

(a) In the first experiment (E1) we employed a proprietary dataset and set various hyperparameters after initial trial runs to identify effective values. The image size was set at 640x640, with a batch size of 16. Dropout was disabled, and the learning rate was set at 0.01, remaining constant throughout the training process. Momentum was set at 0.937, which aids in preventing gradient vanishing and enhances the convergence speed of the algorithm. Weight decay was set to 0.0005 to regularize the model and prevent overfitting. The model underwent training for a total of 1000 epochs. The best results were observed at epoch 360. Training was halted prematurely as no improvement was noted in the last 50 epochs, resulting in a total of 410 training iterations. This is determined by a hyperparameter named 'patience,' aimed at reducing the duration and cost of training. This hyperparameter's purpose is to cease training prematurely if no improvements are noted over several epochs. The patience parameter was set at 50 The training duration amounted to 0.2 hours.

(b) in the second experiment (E2), we evaluate the difference between the number of training iterations and the final results. We had reservations about the effectiveness of the initial setting of 50 patience. In this experiment, we eliminated the 'patience' hyperparameter, allowing the training to fully reach the initially set 1000 epochs. The total training duration was 0.5 hours.

(c) In the third experiment (E3), the aim was to study the performance impact of edge detection technology on the target recognition stage, so the model and hyperparameter settings that performed best in previous experiments E1 and E2 were selected.

After 410 training iterations, we employed some newly generated samples (test set). The images were roughly of two types: one where two shoeprints were nearly orthogonally overlapped, and the other where two shoeprints were almost entirely overlapped. We used the newly trained model to detect the shoeprints form images, and the confidence level thresholds was adjusted to greater than 40%. Below are some samples' performances in this model:

Figure 6a,b reflect two degrees of overlapping images, with minor overlapping and almost complete overlapping. In these two scenarios, the YOLOv8 model achieved an accuracy rate exceeding 85% for samples exemplified in Figure 6a and over 70% for samples exemplified in Figure 6b.

The log curve during the training process displayed some interesting properties. As shown in Figure 7a (Precision) and Figure 7b (Recall), the trend is to increase with the addition of epochs, but the fluctuations within each epoch are substantial, even oscillating between 0 (worst) and 1 (best). This is due to the varying difficulty brought by different samples, but the specific reasons and training strategies require further study.

In Experiment 2, which underwent a complete training of 1000 iterations, Figure 7a,b show the fluctuations in precision and recall during the training process. The curves experienced significant fluctuations in the early stages of training, especially before 450 epochs, where the detection precision dropped sharply and then rapidly increased on several occasions. After 500 epochs, the model's convergence rate decreased, with precision slowly improving.

From Figure 7c,d, which represent 410 training sessions, the model converged very quickly, over 0.8 in recall and precision around 150 epochs. However, in the context of the current task, the model's learning rate was not stable, fluctuating between approximately 0.1 and 0.85. However, as evidenced in Table 2, in comparison to Experiment 1, mAP50 has slight improve from 0.984 to 0.994, and mAP 50-95 has increased of 0.055.

During the forward propagation process, a neural network generates multiple feature maps, which are outputs from the last convolutional layer. Each feature map can be viewed as an encoded version of the input image, highlighting specific features within the image. For Class Activation Mapping (CAM), the contribution of each feature map is determined by learned weights. These weights are optimized through the backpropagation algorithm during the training of the neural network, reflecting the importance of each feature map for the final class decision. By multiplying each feature map by its corresponding weight and summing them up, a single 'activation map' is obtained. This map displays the most critical regions within the input image. This process is achieved through weighted averaging, ensuring that each feature map contributes appropriately to the outcome based on its importance. Finally, this activation map is usually transformed into a heatmap through a colour mapping and superimposed on the original input image. High activation areas may be represented in warm colours (such as red or yellow), while low activation areas in cool colours (such as blue). This colour-region mapping allows us to visually identify which areas are most crucial for the model when making specific category predictions. YOLOv8 inherently contains multiple hidden layers, yet CAM retrieves a visualization of one output of coevolution layer. In this experiment, the heatmaps were generated from the output values of the SPPF module, which is the last module in the backbone of the YOLOv8 model. Having undergone multiple feature extractions, the SPPF module amalgamates features across various scales. The output of the SPPF layer represents a collection of all significant features extracted by the model. the SPPF output size is 40x40x512, convolution kernel size is 3x3, and a step size is 2. Distinct areas representing shoe shapes can be discerned at this level. It is possible to discern some activated neuron positions, especially around the sole and non-overlapped regions (as seen in Figure 8a). Conversely, when encountering overlapped regions, there's a heightened likelihood that the neurons within that area remain inactivated (as illustrated by the heel area in Figure 8a and the overlapped shoeprints in Figure 8b).

Result by Edge Detection Method

Table 3 presents the hyperparameter settings for this experiment, utilizing the v8s model from the YOLOv8 series to compare the training results of two datasets. As discerned from Table 4, employing edge images reduced the epochs required for model convergence from 340 to 230. Although the maximum training epochs were set at 1000, due to the design of the patience value, training would cease upon achieving the optimal results. However, the final test results indicate that the evaluation parameters for the edge image dataset have decreased. The mAP50 dropped from 0.966 to 0.957. For more challenging tests, the mAP50-95 decreased from 0.673 to 0.589. Recall reduced from 0.925 to 0.899. Precision also fell from 0.945 to 0.878.

The comparison between Figure 9 and Figure 6 shows that problems continue to exist with edge detection in some cases, with only one shoe being recognized out of more than one in the image, or multiple recognitions of the same show.

5. Discussion

5.1. Discussion on Training

As epochs increase, there is an overall enhancement in model accuracy, with metrics such as mAP, Precision, and Recall steadily rising, and losses progressively declining (Figure 7a,c). A sharp decline in accuracy around the 400th epoch is suspected to stem from overfitting. By the time training reaches 1000 epochs, significant fluctuations are still observed around the 700th epoch (Figure 7b). The model's hyperparameters require optimization, and the training strategy needs refinement. For this experiment, we set the learning rate at 0.01 and added additional Momentum for rapid convergence. Future experiments should further probe the balance between a lower learning rate and cost efficiency to remove the possibility of oscillation. One hyperparameter in this experiment is "patience", aimed at conserving computational resources and avoiding redundant training. Extra training after reaching the evaluation threshold of "No improvement" yields marginal enhancements in model limits yet consumes vast computational resources.

5.2. Discussion on Results

The objective of this research was to employ a deep model to pinpoint shoeprint locations. When presented with samples of varying overlapping degrees, the model's confidence fluctuated, typically ranging from 70% to 85% (Figure 6a,b). The inherent complexity of the images dictated the neural network's accuracy. Samples that are almost entirely overlapped represent a challenging detection task, and many labelling errors emerge when handling such images. Common issues include marking only one shoeprint or marking beyond two. The heatmap (Figure 8) reveals that the neural network exhibits distinct activation marks on the edges of the shoeprints, yet overlapped regions, owing to their textured covering, remain unlearned. Subsequent predictions then exclusively depend on non-overlapped regions. This is exemplified in Figure 8b, where shoeprints, due to extensive overlapping, are detected as a singular entity by the model, and their bounding box encapsulates both shoeprints. Subsequent training might explore the use of non-overlapped images, essentially raw data. This would ascertain if original samples could achieve comparable or nearly similar outcomes, further reducing research costs.

5.3. Discussion on Data Annotation

For this experiment, shoeprints were labelled using rectangular bounding boxes parallel to the image frame. However, shoeprints on photographs present in various orientations, leading to a sizable inclusion of noisy regions during image labelling. In this experiment, the proportion of noise was minimal, and the model seemingly remained unaffected by it. Yet in real-world images, regions beyond the shoeprint edges equate to noise. The impact of extraneous regions on the task remains uncertain. Future research might consider employing rotatable rectangular bounding boxes for shoeprint annotation, effectively minimizing the chances of encapsulating noise. Resorting to "segmentation" tasks using polygons is our ultimate research objective.

5.4. Discussion on Edge Detection

The results of object recognition tasks using datasets containing only edge images are unfavourable; The Canny algorithm reduces most of the pixel content in the image, leaving only the edge information. In the existing processing steps, the value of the internal information cannot be judged. Deleting these pixels does not bring any benefit to the accuracy of the model, but instead causes a decline in the accuracy rate. As seen in Figure 7, the obscured areas, due to a decline in clarity, saw the textures of overlapped parts significantly fall below the threshold and get discarded. The model struggles to detect the underlying shoeprints based solely on edges.

The computational load decreased, and training speed saw an increase, with training duration dropping from over 15 minutes to around 9 minutes. This effectively reduces the complexity of training. However, this set of experiments also suggests that employing edge detection images and CNN model together do not enhance detection performance; other integrative methods might be required. For instance, overlaying the edges as a layer onto the original image could enhance the clarity of the shoeprint boundaries. Yet, as previously mentioned, the overlapping areas cannot be accurately segmented based on the edge detection algorithm, which adversely impacts our ultimate research objectives.

6. Conclusions

To the best of our knowledge, this study is the first to implement a fully supervised neural network model for detecting more than one partially covered shoeprint in images containing overlapping shoeprints and in the presence of noise. Previous research was only capable of detecting the presence or affiliation of shoeprints in clear, complete images. However, this study achieves detection of incomplete and texture-mixed shoeprints in complex environments. The neural network exhibited over 85% confidence for partially obscured samples and over 70% confidence for almost fully covered samples, based on a dataset containing only 200 samples. It is anticipated that detection results will improve with the expansion of the database. The heat map shows the sensitivity of the neural network to different regions. Especially at the boundary between shoe prints and noise, the shoe prints area is activated, and the background area is almost not activated. This verifies the value of edge detection and the possibility of future image segmentation.

A limitation of the study is that generated samples did not involve variations in shoeprint scale, and the robustness of the model to shoeprint size variation remains to be studied. The shoeprint images used in this study were also limited to having only two shoeprints per image. Introducing additional shoeprints or noise will pose further challenges in subsequent studies.

This research employed heatmaps as an analytical tool, helping in our understanding of the sensitivity of shoeprints in different regions. Neurons at covered shoeprint areas were difficult to activate, and accurate detection of these regions could enhance the final classification results. This constitutes an important topic for future research.

Future work includes the following. (1) Research on neural network structures: The YOLOv8 model employed in this experiment is among the most rapidly evolving neural network architectures. Compared to the early stages of the project that utilized a simple 7-layer model [7], consisting only of convolutional and max pooling layers, YOLOv8 has expanded to 168 layers. The necessity and value of such more complex structures warrant further exploration. (2) Changing sample images: The shoeprint images in this study were sourced from the 'references' folder of the FID-300 database, where the shoeprints were directly replicated from the manufacturers using gelatine lifts, resulting in clear and complete images. The database also contains 300 raw shoeprint samples collected from natural environments such as mud, ceramic, and carpet. The noise from natural sources and the natural incompleteness due to uneven pressure present substantial challenges for the neural network. (3) Once shoeprints are detected, the next stage is to identify (label) the shoeprint against a databank of stored images for forensic investigation purposes.

In summary, employing the YOLO neural network model to detect obscured shoeprints has proven effective, achieving an accuracy rate of over 70%. Visualization of neuronal activity by heatmaps demonstrates that the system learns critical features of shoeprint shapes for detection. This lays a foundation for future research, especially in other areas where separating objects may be useful in forensic investigations, such as overlapping fingerprints.