Modeling and synthesis of images of 3D textured surfaces

Abstract

This paper presents a novel and computationally efficient approach to modeling and synthesizing images that result from the projective distortions of textures laid on illuminated 3D surfaces, as they are seen by a camera (texture rendering). The texture model is a 2D random field described by a probability distribution function parametrized by the surface texture characteristics, the surface shape, and the camera model (orthographic or perspective). Because the model depends on the above-mentioned factors, and the surface shape appears as a parameter in the probability distribution function, this model is denoted as a “3D texture” model. We use a Gaussian Markov Random Field (GMRF) for modeling the texture. The GMRF has been shown to reproduce faithfully a vast class of micro- and macroplanar homogeneous image textures. The 3D texture model is synthesizable, and hence one can visually judge its goodness in capturing the projective distortions of a texture laid on an illuminated surface, as it is seen by a camera. The synthesis algorithm is computationally simple, efficient, and fast. For an image size of N × N, it has a computational complexity of O(N 2 log N). It uses just a Gaussian random number generator and FFT computations. The CPU time taken to generate a distorted texture for a 256 × 256 image on a SUN4/260 was in the order of 56 s. Unlike other methods of texture rendering which are either iterative or subdivisional in nature, the method presented here to render a 3D texture needs no data interpolation. The rendering algorithm applies for any 3D analytic surface, or for more complex nonanalytic surfaces which are specified by an array of surface normal directions at different points on the surface.