Image segmentation is a fundamental and tedious task of computer vision. Because of inherent noise and intensity inhomogeneity in real-world images, it remains a difficult problem in practical applications such as image analysis, scene understanding, object detection, and many others. Several mathematical models proposed for image segmentation in the past few decades with an effective policy. Among these models, deformable models earned more attention and are widely used techniques due to their accuracy, efficiency, and robust effectiveness. This study reviews and compares various deformable models for the segmentation of digital images available in the literature. First, for a comprehensive study, these deformable models are classified into two classes such as direct partial differential equation (PDE) based approaches and variational based approaches. Beside this, variational based approaches are further classified into parametric and geometric models. Their advantages as well as shortcomings are discussed in detail from an objective viewpoint. Then, to check the robustness of various discussed classes of deformable models, a set of synthetic, natural, and real medical images are considered along with inhomogeneity and noise. Also, to measure the segmentation accuracy, different quantitative metrics based on contour and region are utilized. Numerical experiments with different classes of images, reveal that both direct PDE based and variation based models perform well in clean and noisy images. Whereas, the variational based approaches are superior for images having intensity inhomogeneity with high computational time. The qualitative and quantitative investigations confirm that the subtle change in model assumptions can have a significant impact on segmentation.

图像分割是计算机视觉的一项基本而繁琐的任务。由于现实世界图像中固有的噪声和强度不均匀性，它在图像分析、场景理解、对象检测等实际应用中仍然是一个难题。在过去的几十年中，提出了几种具有有效策略的图像分割数学模型。在这些模型中，可变形模型因其准确性、效率和稳健的有效性而受到更多关注，并被广泛使用。本研究回顾并比较了文献中可用的数字图像分割的各种可变形模型。首先，为了综合研究，这些可变形模型分为两类，例如基于直接偏微分方程 (PDE) 的方法和基于变分的方法。除此之外，基于变分的方法进一步分为参数模型和几何模型。从客观的角度详细讨论了它们的优点和缺点。然后，为了检查各种讨论过的可变形模型的鲁棒性，我们考虑了一组合成的、自然的和真实的医学图像以及不均匀性和噪声。此外，为了测量分割精度，使用了基于轮廓和区域的不同量化指标。不同类别图像的数值实验表明，基于直接 PDE 和基于变分的模型在干净和嘈杂的图像中表现良好。然而，基于变分的方法对于具有高计算时间的强度不均匀性的图像是优越的。定性和定量研究证实，模型假设的细微变化会对细分产生重大影响。