Research on the describing method of product's shape based on complex coordinates and Fourier operator

The product shape innovation design has possessed a very important ability to develop more pleasurable products, in which Shape Descriptor is one of key technologies. A new describing method of product's shape based on complex coordinates and Fourier operator is presented, which includes the following five steps. The first is to pre-process, which can obtain the form contour information from product image. The second is to abstract the shape's signature, which uses a complex coordinate function to express product form information. The third is to normalize the signature, which standardizes the sampling point number and the size when the different product forms are analysed. The fourth is to do Fourier transform, which converts the shape's signature to the frequency domain, so the product form is expressed by the Fourier operators (harmonics). The fifth is to find an ideal number of harmonics, which represents the main shape feature of product shape and eliminates the noise. The goblet shapes are chosen to do experimental study. The result appears that a few first harmonics are suitable for representing product shape and shows that the describing method is robust, compact and simple, which is promising to apply in the product shape innovation design and the shape retrieval.