# AdaptiveConv2d: A Novel Convolutional Module for Medical Image Segmentation
## 1 Introduction  
In modern medicine, with the rapid development of imaging technology, medical images have become an essential basis for disease diagnosis, treatment planning, and intraoperative navigation. As a core tool for automatically extracting key medical information, such as organ structure, pathological information, and medical data, medical image segmentation technology plays a vital role in tasks such as tumor identification, chromosomal karyotype analysis, organ contour extraction, and lesion localization [1]. Accurate image segmentation not only significantly improves the accuracy of clinical diagnosis but also provides strong support for the formulation of personalized treatment plans [2]. However, medical images often have unique characteristics, such as complex tissue structures, irregular boundaries, low contrast, and high noise levels, which make it challenging to accurately extract useful medical information [3]. Medical image segmentation technology was developed to automate the extraction of organ morphology, lesion location, and pathologicalfeatures from these complex medical images [4]. The goal of medical image segmentation is to divide an image into different regions, each corresponding to a specific anatomical structure or lesion. Currently, a variety of technical methods have been developed for medical image segmentation tasks. The first category is traditional image segmentation methods, including threshold-based methods [5], region-growing methods [6], and edge detection methods [7]. These methods segment image regions based on simple pixel intensity or gradient information. Despite their computational simplicity, they are susceptible to noise and perform poorly in low-contrast regions when processing complex medical images [8]. The second category is model-based segmentation methods, such as active contour models (Snake) [9] and level set methods [10]. These methods gradually optimize the boundary of the target region through prior shape knowledge and image gradient information, allowing them to cope better with complex boundaries and shape changes. However, these methods depend on initialization and parameter settings, and are computationally inefficient. With the advancement of computing power and the development of deep learning, deep learning-based segmentation methods have become mainstream [11]. Convolutional neural networks (CNNs) [12], particularly U-Net [13] and its variants, have been widely used in medical image segmentation. Trained with a large amount of labeled data, these networks can automatically learn and extract deep features from images, significantly improving segmentation accuracy and robustness. However, deep learning methods also present challenges, such as their dependence on large amounts of labeled data, long training times, and sensitivity to image quality and feature distributions. Despite varying degrees of success across applications, the complexity and diversity of medical images mean that segmentation tasks are still a significant challenge. Therefore, developing a segmentation algorithm that can better adapt to different image features, with robustness and high accuracy, remains an important research direction in the field of medical image processing. The field of medical image segmentation is developing rapidly, and in recent years many effective neural network architectures have emerged. These architectures have improved segmentation accuracy and robustness through different strategies. One of the most classic networks is U-Net [13] which adopts a symmetric encoder-decoder structure and fuses the high-resolution features of the encoder layer with the decoder layer through skip connections, thereby retaining the important spatial information in the segmentation task. The design of U-Net makes it excel in various biomedical image segmentation tasks and has become the basis for many subsequent networks.