Computing Local Surface Orientation and Shape from Texture forCurved Surfaces

  • Authors:
  • Jitendra Malik;Ruth Rosenholtz

  • Affiliations:
  • Department of Electrical Engineering and Computer Science, University of California at Berkeley, Berkeley, CA 94720. E-mail: malik@cs.berkeley.edu, rruth@parc.xerox.com;Department of Electrical Engineering and Computer Science, University of California at Berkeley, Berkeley, CA 94720. E-mail: malik@cs.berkeley.edu, rruth@parc.xerox.com

  • Venue:
  • International Journal of Computer Vision
  • Year:
  • 1997

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Abstract

Shape from texture is best analyzed in two stages, analogous to stereopsis and structure from motion: (a) Computing the’texture distortion‘ from the image, and (b) Interpreting the ’texturedistortion‘ to infer the orientation and shape of the surface inthe scene. We model the texture distortion for a given point and directionon the image plane as an affine transformation and derivethe relationship between the parameters of this transformationand the shape parameters. We have developed a techniquefor estimating affine transforms between nearby image patches which isbased on solving a system of linear constraints derived from adifferential analysis. One need not explicitly identifytexels or make restrictive assumptions about the nature of the texture such as isotropy. We use non-linear minimization of a least squares error criterion to recover the surface orientation (slant and tilt)and shape (principal curvatures and directions) based on the estimatedaffine transforms in a number of different directions. A simple linearalgorithm based on singular value decomposition of the linear parts of theaffine transforms provides the initial guess for the minimization procedure.Experimental results on both planar and curved surfaces under perspectiveprojection demonstrate good estimates for both orientation and shape.A sensitivity analysis yields predictions for both computer vision algorithms and human perception of shape from texture.