Hierarchical projective invariant contexts for shape recognition

• We propose a new shape descriptor (HCNC) invariant to projective deformations.
• HCNC is compact with a hierarchical strategy, rendering efficient matching.
• HCNC is robust to noise, part-missing and articulated deformations.

Shape descriptors play an important role in various computer vision tasks. Many existing descriptors are typically derived from pair-wise measures, such as distances and angles, which may vary with severe geometrical deformations including affine and projective transformations. In this paper, we propose a new shape descriptor from a newly developed projective invariant, the characteristic number (CN). This new descriptor is invariant to projective (or perspective) transformations by computing CN values on a series of 5 sample points along the shape contour with the intervals varying from coarse to fine. This hierarchical strategy yields a compacter descriptor so that the time complexity for both descriptor construction and shape matching are less or comparable to many existing methods. We also use the derived points out of the contour and the ratio of two invariant values, in order to improve the stability at finer scales and robustness to noise. We demonstrate the performance of the descriptor by comparing with the state-of-the-art on the MCD and other public shape sets with severe perspective transformations and other type variations including noise, missing parts and articulated deformations.

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