Abstract
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 characterist ics—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.
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