Estimation of orientation of a textured planar surface using projective equations and separable analysis with M-channel wavelet decomposition

Estimation of the orientation of a textured planar surface is one of the basic tasks in the area of “shape from texture”. For the solution of this task, many successful approaches were proposed. In this paper, we have examined a few unaddressed questions: First, is there a mathematical formulation that relates the spectral characteristics of the texture pattern and the orientation of an inclined planar surface in a polar-coordinate system? Second, is there a good wavelet-based approach that produces an accurate estimate of the orientation angle of the textured planar surface by analyzing the spectral behavior of one single uncalibrated image?To answer these questions at first we present the formulation of a “texture projective equation”, which relates the depth and orientation of an inclined planar surface in a polar coordinate system with the spectral properties of its image texture. A suitable imaging geometry has been considered to enable separable analysis of the effect of inclination of the texture surface. Next, a method for shape from texture is presented based on discrete wavelet analysis to estimate the orientation of the planar surface. This approach although designed mainly for M-channel wavelets, is also applicable for dyadic wavelet analysis. Texture characteristics in the subbands of wavelet decomposition are analyzed using scalograms, and quantitatively evaluated based on texture projective equations. The proposed method of estimation of the orientation of a planar texture surface is evaluated using a set of simulated and real world textured images.