A New Shape Retrieval Method Using the Group Delay of The Fourier Descriptors

In this paper, we have introduced a new way to analyze binary shapes 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 it 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 this study, we have used phase normalization for invariance against rotation and translation and scaling and changes in the starting point. Then the 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, this method is applied on the standard shape database MPEG-7 CE-Shape-1 and the experimental results show the superiority of the proposed method compared to the other methods.