SIAM Journal on Imaging Sciences, Volume 13, Issue 4, Page 2105-2139, January 2020.
Image segmentation aims to partition an image into meaningful regions and extract important objects therein. In real applications, the given images may contain multiple overlapping objects with noisy background, creating great challenges to the segmentation task. In these cases, prior information of the target object is essential for an accurate and meaningful segmentation result. In this paper, we present a new convexity shape prior segmentation framework to guarantee the segmented region to be fully or partially convex according to the user's preference. The basic idea is to incorporate a registration-based segmentation model with a specially designed convexity constraint. The convexity constraint is based on the discrete conformality structures of the image mesh. To solve the segmentation model, we propose an iterative scheme, which smoothly deforms a template object to trace the boundary of the target object. A projection is carried out to enforce the convexity constraint. The target object is then captured by a (fully or partially) convex region. Convexity is the only prior information needed for a (fully) convex shape, whereas the location of partial convexity is needed for a partially convex shape. Experiments have been carried out on both synthetic and real images and the results demonstrate the effectiveness of our proposed framework.

中文翻译：

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先使用离散共形结构的具有部分凸形的图像分割

SIAM影像科学杂志，第13卷，第4期，第2105-2139页，2020年1月。
图像分割旨在将图像划分为有意义的区域并在其中提取重要对象。在实际应用中，给定图像可能包含多个背景杂乱的对象，这给分割任务带来了巨大挑战。在这些情况下，目标对象的先验信息对于准确而有意义的分割结果至关重要。在本文中，我们提出了一种新的凸形先验分割框架，以确保分割区域根据用户的喜好全部或部分凸出。基本思想是将基于注册的细分模型与经过特殊设计的凸度约束结合在一起。凸度约束基于图像网格的离散共形结构。为了解决细分模型，我们提出了一种迭代方案，它可以平滑地使模板对象变形以跟踪目标对象的边界。进行投影以强制实施凸度约束。然后通过（全部或部分）凸面区域捕获目标对象。凸性是（完全）凸形所需的唯一先验信息，而部分凸形需要局部凸的位置。已经对合成图像和真实图像进行了实验，结果证明了我们提出的框架的有效性。而部分凸形需要局部凸的位置。已经对合成图像和真实图像进行了实验，结果证明了我们提出的框架的有效性。而部分凸形需要局部凸的位置。已经对合成图像和真实图像进行了实验，结果证明了我们提出的框架的有效性。