A fractal-based relaxation algorithm for shape from terrain image

Abstract

We consider the problem of extracting surface shape from a single terrain image. Although fractal models play an important role in simulating terrain models, the various Shape-from-Shading (SFS) techniques that have been applied to this kind of problem have not been coupled with a fractal prior. In this paper, we define the SFS problem of terrain imaging as a fractal-regularized problem, and solve it using Maximum-A-Posterior (MAP) estimation. In addition, we also propose a relaxation algorithm based on Landweber iteration in order to solve it. The optimum terrain surface corresponding to the observed image does not have to be the convergent result. The result can be picked up during the process of iteration with the number of iterations specified by an image-based estimation method proposed in this paper. Experimental results on both simulated data and real data show that our algorithm can efficiently extract terrain surfaces, and is more accurate than some well-known SFS algorithms, including the Horn, Zheng–Chellappa, Tsai–Shah, Pentland linear, and Lee–Rosenfeld methods.