## 1 Introduction
To ameliorate these issues, a spectrum of digital image processing techniques and advanced machine learning methodologies have been applied, thereby enhancing detection rates and specificity [15; 16; 17]. The swift development in computer application technologies has precipitated a paradigm shift towards the reliance on computer-aided diagnosis (CAD) systems for the expeditious processing of digitized imaging data. These advancements facilitate the attenuation of background noise, the enhancement of image contrast, the precise detection of regions of interest, and the differentiation of tumors from surrounding tissues, thus aiding in the distinction between benign and potentially malignant lesions [18; 19; 20; 21]. Among the multifaceted functionalities of CAD systems, the paramount objective remains the accurate classification of tumors into benign or suspicious categories. To encode a mass within a computational framework, sonographic features are converted into computerized sonographic descriptors. The morphological formation of a mass can be elucidated through the characterization of its shape and margin. Mass shape, which is one of the most significant image features, can be quantified using moments and Fourier descriptors [22] or by evaluating factors such as roundness, aspect-ratio, convexity, and solidity [23]. The shapes of malignant breast tumors are typically more complex than benign lesions due to their tendency to infiltrate surrounding tissues. While malignant lesions are often irregular, microbolulated, or spiculated, benign lesions tend to be oval, round, or macrobolulated. Therefore, accurately quantifying the irregularity of sonographic findings can significantly enhance the accuracy of CAD systems. Several boundary-based methods, analyzed in the spatial domain, have been used to describe mass shape, such as roundness, concavers, and convexity [24; 25]. However, these methods primarily express shape irregularity at a local level and fail to account for comprehensive shape dynamics. For example, if a shape exhibits irregular characteristics only in certain local areas, while most other regions appear regular, boundary-based methods may incorrectly classify the shape as irregular. Consequently, there is a need to develop advanced feature extraction techniques that can effectively characterize shape irregularity across the entire lesion structure. The Breast Imaging Reporting and Data System (BI-RADS), an initiative developed by the American College of Radiology, meticulously standardizes the lexicon and evaluative criteria for clinical findings [26]. The BI-RADS lexicon is designed to standardize the reporting of mammographic and ultrasound findings, ensuring that the resultant reports are clear, succinct, and consistent among different readers. Although the terms within the BI-RADS framework are inherently descriptive rather than quantitative, there is a necessity to \"translate\" these descriptors into quantifiable features that a computer-aided diagnosis (CAD) system can automatically compute. To address this, several research groups have proposed sophisticated methodologies for the quantification of BI-RADS features [27; 28; 29]. Moreover, BI-RADS sonographic characteristic features, when correlated with patient medical history, as shown by [PERSON] et al. [30], or with patient age, as demonstrated by [PERSON] et al. [31], can serve as the foundation for constructing a CAD system utilizing artificial Neural Networks. Additionally, [PERSON] et al. [32] explored the reliability of CAD system predictions compared to the clinical biopsy decisions made by five radiologists, revealing that a CAD system leveraging BI-RADS evaluations significantly enhances radiologists' interpretation of abnormalities. The primary advantage of integrating BI-RADS sonographic evaluations within CAD systems lies in their versatile applicability across diverse ultrasound platforms [25].