Estimation of 3D Surface Shape and Smooth Radiance from 2D Images: A Level Set Approach

  • Authors:

  • Hailin Jin;Anthony J. Yezzi;Yen-Hsi Tsai;Li-Tien Cheng;Stefano Soatto

  • Affiliations:

  • Department of Electrical Engineering, Washington University, Saint Louis, Missouri 63130. hljin@ee.wustl.edu;School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332. ayezzi@ece.gatech.edu;PACM and Mathematics Department, Princeton University, Princeton, New Jersey 08544. ytsai@math.princeton.edu;Department of Mathematics, University of California San Diego, La Jolla, California 92093. lcheng@math.ucsd.edu;Computer Science Department, University of California, Los Angeles, California 90095. soatto@cs.ucla.edu

  • Venue:
  • Journal of Scientific Computing
  • Year:
  • 2003

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Abstract

We cast the problem of shape reconstruction of a scene as the global region segmentation of a collection of calibrated images. We assume that the scene is composed of a number of smooth surfaces and a background, both of which support smooth Lambertian radiance functions. We formulate the problem in a variational framework, where the solution (both the shape and radiance of the scene) is a minimizer of a global cost functional which combines a geometric prior on shape, a smoothness prior on radiance and a data fitness score. We estimate the shape and radiance via an alternating minimization: The radiance is computed as the solutions of partial differential equations defined on the surface and the background. The shape is estimated using a gradient descent flow, which is implemented using the level set method. Our algorithm works for scenes with smooth radiances as well as fine homogeneous textures, which are known challenges to traditional stereo algorithms based on local correspondence.