<title>Shape reconstruction from shading with perspective projection</title>

Abstract

In this research, we propose a novel algorithm which recovers the surface height directly from images obtained via perspective projection. Most existing shape from shading (SFS) algorithms are developed under the assumption of an orthogonal projection model, which is a special case of the general perspective projection model. As a result, there exist substantial reconstruction errors in their real applications especially for the case when the object is not far away from the camera. By introducing an explicit triangular element surface model and combining perspective imaging geometry, we are able to relax the orthogonal projection assumption and derive a more general reflectance model with perspective projection. We formulate the perspective SFS problem as a minimization problem parameterized by surface nodal heights, and determine the surface height by solving an equivalent linear system of equations. Simulation results for several test images are given to demonstrate the performance of the proposed algorithm. The proposed perspective SFS algorithm gives more accurate results than conventional SFS algorithms and is very attractive in practical applications.