Theapplications Of Fractional Fourier Transform In 3D Model Processing

With the advancement of the computer graphics technology and the internet, 3D data acquisition is increasingly easy .The application of 3D models is more and more widely. In the 3D model processing field, content-based 3D model retrieval technology and 3D model watermarking technology become research spots recently.The factional Fourier transform (FRFT), as a generalization of the classical Fourier transform (FT), has many applications in the field of optics and signal processing. Owing to the advantage of FRFT, it is introduced into the 3D model processing field. In this paper, we propose new 3D model retrieval algorithm and 3D watermarking algorithm, which are based on fractional Fourier transform theory, from two aspects of shape-based 3D model retrieval and 3D watermarking.3DFRFT–based 3D model retrieval algorithm: in order to make the data of 3D model are fit for 3DFRFT, we will apply the algorithm of voxelization to voxelize 3D model firstly. Between the spatial and frequency domain, we select a particular order to process 3DFRFT. We take a part of low-frequency coefficients as components of the feature vector in the fractional domain. A set of (complex) coefficient is obtained the absolute values of coefficients are considered as components of the feature vector in each order. In experiments, the Euclidean distance is used to compute the similarity. According to the P-R plot of the retrieval results, the effect of retrieval is evaluated. According to the experiments, we also can integrate these feature vectors into the mixed feature vector, which is named as Multi-Order fractional Fourier Feature Vector (MOFFFV). MOFFFV performs better than the feature vector based on the traditional 3D Fourier transform. 3DFRFT–based 3D watermarking algorithm: The main idea of the algorithm is to reconstruct a 3D spherical helix curve that represents the 3D model and to embed watermark. We choose a part of vertex that their margin are smaller. Then their vertex make up a vertex sequence that will embed the watermark according the vertex sequence of 3D spherical helix curve. The radius of the model is seen as a 1D signal that represents the 3D model. We choose a suitable order to process FRFT and embed watermark. Then the watermarking 1D signal is transformed to the spatial domain. Finally, the embedded watermark is scattered all over the 3D.