A new shape retrieval method using the Group delay of the Fourier descriptors

In this paper, we introduced a new way to analyze the shape using a new Fourier based descriptor, which is the smoothed derivative of the phase of the Fourier descriptors. It is extracted from the complex boundary of the shape, and is called the smoothed group delay (SGD). The usage of SGD on the Fourier phase descriptors, allows a compact representation of the shape boundaries which is robust to noise and can be easily made independent of translation, scaling, rotation and changes in the starting point used to describe each boundary. In the proposed method, we used phase normalization for invariance against rotation and translation and scaling and changes in the starting point. Then Cross-Correlation of the SGDs of shapes is used as a similarity measure. In this paper Precision-recall curve and the average normalized modified retrieval rank (ANMRR) are used to evaluate the retrieval performance of the proposed method. Finally, the proposed method is applied on the standard shape database MPEG-7 CE-Shape-1 and experimental results are shown the superiority of the proposed method compared to the other methods.