The level set method is one of the most widely used and powerful techniques in image science such as image/motion segmentation, object tracking, etc. This paper brings up an unstudied issue with discretized level set algorithms about ‘the non-uniqueness’ of segmentation results which is different from the problem of ‘the existence’ of a result. Our solution is to numerically approximate the level set formulation based on suitable combination of some visual joint invariants, leading to the unique segmentation results, therefore unique visual joint invariant numerical signatures—independent of contour initialization and what visual group is applied. To figure out ‘the cause’ of resulting unique segmentations in this scheme, we utilize the level set algorithm to introduce three energy features—called fingerprints, flows, and stem charts. Our experimental results indicate that curvature-based energies can be classified in terms of these characteristics—depending merely on the nature of each energy. Besides, the energies generated by the current discretization are ‘positive,’ while the visual joint invariant curvature-based energies sketch charts with ‘negative’ values.

水平集方法是图像科学中使用最广泛，功能最强大的技术之一，例如图像/运动分割，对象跟踪等。本文提出了离散化水平集算法中关于“非唯一性”分割的未研究问题结果与结果的“存在”问题不同。我们的解决方案是根据一些视觉关节不变式的适当组合在数值上近似化水平集公式，从而得出独特的分割结果，因此获得独特的视觉关节不变式数字签名-与轮廓初始化和所应用的视觉组无关。为了找出此方案中产生的唯一细分的“原因”，我们利用水平集算法引入了三个能量特征，即指纹，流量和主干图。我们的实验结果表明，基于曲率的能量可以根据这些特性进行分类-仅取决于每种能量的性质。此外，当前离散化生成的能量为“正”，而基于视觉关节不变曲率的能量绘制的图表具有“负”值。