## 3 Proposed Methods  
### Shape/Texture Bias Metric  
Establishing a metric for assessing bias is essential to preemptively comprehend the potential prejudices exhibited by pre-trained models. This study mainly considers the congruity between model biases and data. Although [PERSON] et al. [9] have proposed a method, it can be applied to only a limited range of datasets and requires a greater degree of versatility. Furthermore, their method is primarily designed to compare human perception with vision models and is unsuited for comparing them with datasets. The proposed method introduces a more generic bias metric to address this issue. Figure 1 presents an overview diagram for measuring shape/texture bias. Algorithm 1 provides a detailed procedure for generating combined shape-texture images. Shape- and texture-dominant images were created using an edge-preserving smoothing method [46]. The original image \(I_{\text{orig}}\) is smoothed to obtain a shape-dominant image \(I_{\text{shape}}\), and a texture-dominant image is then created by increasing the pixel values of the difference between \(I_{\text{orig}}\) and \(I_{\text{shape}}\) to half their maximum values. Subsequently, a combined shape/texture image is obtained. [PERSON] et al. [47] reported that neural networks favor more straightforward features. This implies that features more favorable for the CNN model are used for classification. The models trained in simple two-class classification measure the shape or texture bias. \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{**Shape/Texture Bias Metric**} & \multicolumn{1}{c}{**Our Work [9]**} \\ \hline \multirow{3}{*}{Enhancing shape bias} & Data preprocessing or augmentation & [9; 13; 18; 20; 42; 45] \\ \cline{2-3}  & Multi network & [15; 16; 17] \\ \cline{2-3}  & Model architecture & **Our work** \\ \hline \hline \end{tabular}
\end{table} 
Table 1: A summary of related work on shape bias and this study. Previous research has primarily focused on increasing shape bias through data preprocessing, augmentation, and multi-network approaches. In contrast, this study focuses on model architecture to enhance shape bias. Additionally, we propose a new method for measuring shape and texture bias, which represents one of the few existing approaches in this domain. Finally, the focus area is calculated using Grad-CAM [48]. The method for measuring bias using Grad-CAM is outlined in Algorithm 2. An attention area predominantly on the upper side (shape-dominant image) indicates shape bias, whereas that on the lower side (texture-dominant image) suggests texture bias. The specific bias values are calculated using the attention region heatmaps. Additionally, an object mask ensures that only the classification object is evaluated and only the area where the background image has been removed is assessed. Shape bias is calculated using Grad-CAM heatmaps: first, for both shape-dominant and texture-dominant images, the sum of the Grad-CAM heatmap values is divided by the image size, excluding the background areas. \(H_{s}\) and \(H_{t}\) denote the values for the shape- and texture-dominant images, respectively. To evaluate whether the CNN model exhibits shape or texture bias, these two values are used to compute the proposed shape/texture bias \(B\) as follows:  
\[B=\frac{H_{s}}{H_{s}+H_{t}}\]  
As indicated in Equation (1), the shape-bias value ranges from zero to one, with values closer to one indicating a higher shape bias and those closer to zero indicating a lower shape bias (higher texture bias). Figure 1: The combined shape/texture images used to calculate the bias metric (on the left side) included a shape-dominant image in the upper part and a texture-dominant image in the lower part. This combined image is used for transfer learning in a two-class classification. Subsequently, these test-combined images are input into the model, and the shape/texture bias is calculated through gradient-weighted class activation mapping (Grad-CAM).