On image texture

This dissertation reports a collection of new results involving the analysis of roles of image texture in finding the boundaries of surfaces in an image, estimating local surface shape, and determining intrinsic properties of an imaged surface. First, I introduce a formal framework for the boundary-finding problem which permits the isolation of the choice of an image description function as an important subproblem. I propose that functions which are vector-valued, shift-invariant, and polynomial in image irradiance values with local support constitute a general class of image description functions. I prove that there is a polynomial shift-invariant (PSI) image description operator of degree d that discriminates two image regions if, and only if, the regions differ in their d -point autocorrelation functions, and use this result to compare various existing texture discrimination techniques and to treat, to some extent, the problem of designing new ones. I also present a theorem and empirical evidence which suggest that PSI description operators of degree 2 are likely to be adequate for discriminating differently textured image regions. Second, I analyze several approaches to the problem of determining local surface shape from image contours and texture, concentrating on a class of probabilistic estimation methods. Previous implementations of these methods have characteristically overestimated the slant of imaged surfaces. I identify four causes of this problem and use the analysis to construct a new probabilistic estimator. I prove a theorem and present the results of experiments which show the superiority of the new estimator. Third, I investigate the problem of determining the properties of fractional Brownian surfaces from their images; the problem has not previously been addressed for this class of surface models, though they are of widespread use in computer graphics. I use a finite-difference approximation to the partial derivatives of the surface and the leading terms of the Taylor series expansion of the surface reflectance map to investigate the spectral properties of the resulting image. I show that, under certain stated assumptions, the fractal dimension and average slant of the surface, as well as the direction of the ambient light source, can be determined.