An affine invariant relative attitude relationship descriptor for shape matching based on ratio histograms

A novel shape descriptor, named as ratio histograms (R-histogram), is proposed to represent the relative attitude relationship between two independent shapes. For a pair of two shapes, the shapes are treated as the longitudinal segments parallel to the line connecting centroids of the two shapes, and the R-histogram is composed of the length ratios of collinear longitudinal segments. R-histogram is theoretically affine invariant due to collinear distance invariance of the affine transformation. In addition, as the computation of the length ratio weakens the noise contribution, R-histogram is robust to noise. Based on the R-histogram, the shape-matching algorithm includes two major phases: preprocessing and matching. The first phase, which can be processed off-line, is trying to obtain the R-histograms of all original shape pairs. In the second phase, for each transformed shape pair, its R-histogram is computed and the candidate matched shape pair with minimal R-histogram matching error is found. Subsequently, a voting strategy, which further improves the accuracy of shape matching, is adopted for the candidate corresponding shape pairs. Experimental results demonstrate that the proposed R-histogram is robust and efficient.