Shape From Texture: Direct Estimation of Planar Surface Orientations Using Continuous Wavelet Transform

Wen L. Hwang, Chun-Shien Lu and Pau-Choo Chung

TR-IIS-96-015 (Fulltext)

texture, shape from texture, surface orientation, continuous wavelet transform, ridge


In this paper, we propose a new method to estimate the orientations of a planar surface under perspective projection. Texture variations are characterized by the ridges of continuous wavelet transform. The ridges of a continuous wavelet transform mark the places in the spatial frequency where the energy of an image is mostly concentrated. We demonstrate that the ridges contain crucial information in determining the planar surface orientations. %under the perspective projected model. An algorithm to determine the ridge points of a textured image is presented. The ridge points are organized into disjoint ridge surfaces. We show that textural information giving the perception of surface orientations can be characterized from a ridge surface of the textured image. The scale in the ridge surface is a parabolic function of the tilt and slant angles. This provides a closed-form solution to determine %an efficient way in determining the surface orientations directly with information only from the restriction of the wavelet transform to the ridge surface. We have used our algorithm on several textured real-world images in noise-free and noisy environments. The resultant estimation of the tilt and slant angles is accurate up to a $3^{\circ}$ average error even in low $SNR$ environments.