Research On Shape From Shading Based On Fractal Priors

As one important research direction of computer vision, three dimension passive reconstruction shows more and more important position and role not to be ignored in the various directions of production and life in society and has wide application value in industry, agriculture, country defense, medicine, space technology, etc, especially. Due to its special feature, i.e., it can restore three dimension shape information just need one image, recently, shape from shading (SFS) gets great improvements and rapid developments in methodology and application and becomes a new research hot point of 3D passive reconstruction. On the base of comprehensive summarization and deep analysis for current SFS research work, a three dimension reconstruction technology based on fractal has been proposed in this paper. The new method has obvious advantage in respect of reconstruction for nature scenery.At the beginning, a fully survey about SFS research work is given. The recent hot point problems of this field are summarized. On the base of understanding for SFS problem in nature, a systematic summarize is made for all current SFS algorithm in the world, that is, minimization approaches, propagation approaches, local approaches, and linear approaches. From the different assumption of four algorithms, we have analysed their applicability, and compared them in terms of convergence rate, uniqueness and existence.As most traditional SFS algorithms adopt rigor assumptions that don't correspond to the real condition and unsuitable assumptions that some prior condition has know, they can't get precise and universality 3D reconstruction result. From the application background of extracting 3D information of remote sensing image, a 3D reconstruction algorithm based on fractal is presented in this paper. This method overcomes the defaults of traditional SFS algorithm whose recover result are too smooth to distortion for nature scenery due to use the smoothness constrains. Meanwhile, it does not need any integrability constraint and assumption for boundary conditions. Experiment result shows that it not only get rid of the restrict of some rigor constraint, but also can get good restore result for natural surface comparing with traditional method.Three current popular approaches for creation of artificial fractals are proposed in this paper, i.e., random midpoint displacement, successive random additions and spectral synthesis, so that we can evaluate the algorithm exactly. Based on these approaches, we get some synthetic data that have fractal properties. For natural fractal surfaces are always anisotropic, we developed spectral synthesis method and present a new method to creating anisotropic fractals.Uncertainty modeling is introduced to solve SFS problem in this paper. This method first formulates SFS problem to estimation problem, converts priori information to prior model, using Bayesian modeling to find the maximum a posteriori (MAP) estimate. Sampling from surface height function using the Gibbs random sampler algorithm, we can obtain an optimal result of 3D shape of therestored surface. The experiment results show that new method can get better restoration result corresponding with traditional regularization method.In Gibbs sampler algorithm, temperature parameter controls fractal dimension of recovered surface. However, how to describe and determine the relations between the temperature parameter and fractal dimension, till now, there are no certain method. Therefore, we present a new method to choose temperature parameter. Meanwhile, to choose suitable parameter, we have discussed the method to calculate fractal dimension, based on the statistics method, we present a new method to calculate anisotropic fractal dimension.