A high dimension 3D object representation using Multi-Mother Wavelet Network

This paper presents an approach for 3D object representation. Our major contribution is proves that wavelet network are capable for reconstruction and representing irregular 3D objects used in computer graphics. It consists to transform an input surface vertices into signals and to provide instantaneously an estimation of the output values for input values. To prove this, we will use a new structure of wavelet network founded on several mother wavelet families. This structure uses several mother wavelet, in order to maximize best wavelet selection probability. An algorithm to construct this structure is presented. First, data is taken from 3D object. The vertices and their corresponding normal values of a 3D object are used to create a training set. To this stage, the training set can be expressed according to three functions, which interpolates all their vertices. Second we approximate each function using wavelet network. To achieve a better approximation, the network is trained several iterations to optimize wavelet selection for every mother. To guarantee a small error criterion, we adjust wavelet network parameters (weight, translation and dilation) by using an improved Orthogonal Least Squares method version. We consider our proposed approach on two 3D examples to prove that the new approach is able to approximate 3D objects with a good approximation ability.