A Novel Line Integral Transform for 2D Affine-Invariant Shape Retrieval

Abstract

Radon transform is a popular mathematical tool for shape analysis. However, it cannot handle affine deformation. Although its extended version, trace transform, allow us to construct affine invariants, they are less informative and computational expensive due to the loss of spatial relationship between trace lines and the extensive repeated calculation of transform. To address this issue, a novel line integral transform is proposed. We first use binding line pairs that have the desirable property of affine preserving as a reference frame to rewrite the diametrical dimension parameters of the lines in a relative manner which make them independent on affine transform. Along polar angle dimension of the line parameters, a moment-based normalization is then conducted to degrade the affine transform to similarity transform which can be easily normalized by Fourier transform. The proposed transform is not only invariant to affine transform, but also preserves the spatial relationship between line integrals which make it very informative. Another advantage of the proposed transform is that it is more efficient than the trace transform. Conducting it one time can allow us to achieve a 2D matrix of affine invariants. While conducting the trace transform once only generates a single feature and multiple trace transforms of different functionals are needed to derive more to make the descriptors informative. The effectiveness of the proposed transform has been validated on two types of standard shape test cases, affinely distorted contour shape dataset and region shape dataset, respectively.