Retrieval of Similar Shapes Under Affine Transform Using Affine Length Parameterization

Problem statement: In this study, a new descriptor for shape retrieval under affine transformations had been proposed; the affine length parameterization was used in this approach. Approach: The zero crossing of affine curvature was used to extract a descriptor of shapes in database. For each two successive zero crossing points we extract two parameters: the first parameter was a maximal surface area of the triangle constructed by these points and a point between them. The second parameter is the average of affine curvature of the arc constructed by these two points. Results: The method was also evaluated objectively through a three classified databases which are a subset of the MCD database with a vast variety of shapes. The obtained results and the comparison with geometric moment and Fourier descriptors indicated a promising performance of our method. Conclusion: In this study, we examined the performance of the proposed descriptor under affine transformations. It was observed that the performance of the proposed method is promising even under severe deformations caused by shear.