The current study presents a new 3D mesh deformation process using multi‐mother wavelet neural network architecture, which relies on genetic algorithm and multiresolution analysis. Classic forming algorithms begin with a predetermined network architecture that may be insufficient or too complicated. In addition, the solving of wavelet neural network training problems is described by their perceived inability to escape local optima. The main objective of the authors' proposed approach is that it prevents both the insufficiency and local minima by integrating the genetic algorithm; their wavelet network is used as an approximation tool to align the features of mesh to have efficient deformation processes. Also, such meshes are especially expensive to transmit and are awkward to deform. For this reason, they propose to use multiresolution analysis to decompose a surface geometry into several levels of detail in order to work only with the approximation coefficient at a chosen decomposition level. Hierarchical triangle mesh representations provide access to a triangle mesh at the desired resolution without omitting any information. The experimental results showed the validity of the generalisation ability and the efficiency of their suggested multi‐mother wavelet network architecture based on genetic algorithm and multiresolution analysis for 3D mesh modelling and deformation.

This paper is part of the study implementation of a new training algorithm for multi-dimensional wavelet networks called MDWNN-GA-MA using the genetic algorithm and multiresolution analysis to approximate and model 3D objects .This new approach aims at avoiding the weaknesses of old approaches such as the slowness and the difficulty in finding an exact reconstruction of objects especially when increasing the level of the decomposition. The result of the simulation reveals that this approach reduces the learning initialization cost and improves the gradient descent robustness. Indeed, multiresolution analysis has some interesting properties: such as starting with an object at high resolution, and generating several approximations can be generated. Details lost during the various stages of simplification can be returned if it requires greater precision. This technique speeds up the display surfaces and allows efficient compression.

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