An analog hopfield network to overcome excessive smoothing in shape from shading

Abstract

The regularization term used in the cost function of the shape from shading (SFS) problem is necessary to make the problem well-posed. However, it has the disadvantage of producing excessive smoothing of the surface even at places where the gradient of the surface slope is very high. To overcome this we propose the use of a line function depending on the gradient of the surface slope in the regularization term. For an analog line function, the SFS energy function is then minimized using an analog Hopfield network. For a binary line function, the SFS energy minimization problem is formulated as a combinatorial minimization problem; the minimization is implemented using a Boltzmann machine (simulated annealing). Simulation results are presented to substantiate our approach.