# Voting-Based Contour-Aware Framework for Medical Image Segmentation
## 1 Introduction  
Segmentation of anatomical structures in medical images is one of the most important topics in medical image analysis for assisting the diagnosis of anomalies, monitoring disease progression, and planning surgery. Manual segmentation is laborious, subjective, and time-consuming. With the advent of deep learning [1, 2, 3], automated segmentation algorithms have become increasingly reliable and potentially applicable for practical use, among which convolutional neural networks (CNNs) have shown enormous potential in open-data challenges in various segmentation tasks involving the liver [4, 5, 6], kidney [4, 7], tumors [8], and bone segmentation [9]. Since 2012, many classification and segmentation CNNs have been proposed, including AlexNet [10], Google-Net [11], and the Deeplab series network [12, 13, 14]. Specialized deep learning algorithms have also been proposed for medical image segmentation. For example, a U-shaped model was proposed in [15] by combining a contracting path and expanding path, allowing the use of global location and context and enabling higher performance for segmentation tasks. Many encoder-decoder CNNs based on the same concepts have since been invented, including V-Net [16], Res-UNet [17], Dense-UNet [18], R2U-Net [19], Attention U-Net [20], and nnU-Net [21]. Considering human intelligence, humans prefer to classify new items, usually considering some object properties such as texture, color, and shape information [22; 23; 24]. CNNs are also capable of learning complicated representations of objects, including the features mentioned above [22; 23; 24]. Many researchers have proposed that CNNs can learn sophisticated information about the shape associated with each class [25], and the shape information of objects is more significant to CNNs than color [23; 24]. It was reported in [22] that CNNs are more likely to recognize texture features than shape information and highlight the performance and robustness benefits of shape-based representations. Since CNNs have learning biases, it is necessary to consider the shape information when designing networks. Various research efforts have been dedicated to edge prediction and contour representation enhancement. A deep contour-aware network for gland segmentation was proposed to extract multi-level contextual features as explored with an auxiliary supervision [26]. A multi-label learning framework without deep supervision was introduced to improve the boundary identification [27]. In addition, the Thinned Edge Alignment approach was introduced, which included a basic contour thinning layer and a novel loss to generate thinner and more exact edges [28]. A two-stream CNN architecture consisting of a conventional and shaped stream was also established, with innovative gates connecting intermediate layers between these two streams [29]. An edge guidance module was integrated to learn edge-attention representations in the early encoding layers to guide the segmentation [30]. Several Edge-Gated blocks were cascaded and integrated with CNNs that accentuated and untangled texture and edge representations during the training [31]. A weighted self-information map was used to highlight the shape information of prediction maps in the shape-entropy-aware adversarial learning framework [6]. In human education, there is a curriculum plan to learn courses in a meaningful order, which means people always master basic knowledge before moving on to advanced courses [32]. Many researchers have pondered if this learning strategy could promote machine learning. Curriculum learning (CL) [32; 33; 34] imitated the human learning strategy to train the model with samples from easy to hard. More specifically, in contrast to the standard training process, which is usually a random data shuffle, CL initially trains the model with easier subsets of data and then gradually adds harder data into the subset, up to the entire dataset.