Abstract
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.
Highlights
Shape matching plays an important role in image processing and computer vision applications
Numerous methods, such as spectral transform [1,2], moment invariants [3,4], iso-area normalization [5], time series [6], B-splines [7], curvature scale space (CSS) [8,9], shape contexts [10], shape signature [11], diagonals of orthogonal projection matrices (DOPM) [12], multiscale oriented corner correlation [13], etc., have been proposed for shape matching under affine transformations
The R-histogram is composed of the length ratios of collinear longitudinal segments from the two shapes
Summary
Shape matching plays an important role in image processing and computer vision applications. Since the images taken from different viewpoints usually suffer from perspective distortions, the matching algorithm should be capable of dealing with them Numerous methods, such as spectral transform [1,2], moment invariants [3,4], iso-area normalization [5], time series [6], B-splines [7], curvature scale space (CSS) [8,9], shape contexts [10], shape signature [11], diagonals of orthogonal projection matrices (DOPM) [12], multiscale oriented corner correlation [13], etc., have been proposed for shape matching under affine transformations. The R-histogram is composed of the length ratios of collinear longitudinal segments from the two shapes This descriptor has a clear physical interpretation and can be applied to shape matching without searching for affine transformation parameters. R-histogram and its fundamental properties R-histogram, which represents the relative attitude relationship between two shapes, is first defined, and its symmetry and affine invariance are explored. If two shapes A and B are transformed into A0 and B0 by an affine transformation, we have
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