Journal of Scientific Computing,Vol.19,Nos.1–3,December2003(©2003) Estimation of3D Surface Shape and Smooth Radiancefrom2D Images:A Level Set ApproachHailin Jin,1Anthony J.Yezzi,2Yen-Hsi Tsai,3Li-Tien Cheng,4and Stefano Soatto5 Received May3,2002;accepted(in revised form)September14,2002We cast the problem of shape reconstruction of a scene as the global region segmen-tation of a collection of calibrated images.We assume that the scene is composed ofa number of smooth surfaces and a background,both of which support smoothLambertian radiance functions.We formulate the problem in a variational frame-work,where the solution(both the shape and radiance of the scene)is a minimizer ofa global cost functional which combines a geometric prior on shape,a smoothnessprior on radiance and a data fitness score.We estimate the shape and radiance via analternating minimization:The radiance is computed as the solutions of partial differ-ential equations defined on the surface and the background.The shape is estimatedusing a gradient descent flow,which is implemented using the level set method.Ouralgorithm works for scenes with smooth radiances as well as fine homogeneous tex-tures,which are known challenges to traditional stereo algorithms based on localcorrespondence.KEY WORDS:Variational methods;Mumford–Shah functional;image segmenta-tion;multi-frame stereo reconstruction;partial differential equations;level setmethods.1.INTRODUCTIONInferring the three-dimensional shape of a scene from a collection of images is one of the most studied problems in Computer Vision.In the case of multiple images, this problem is typically approached in two steps:first image points or regions are 1Department of Electrical Engineering,Washington University,Saint Louis,Missouri63130. E-mail:hljin@ee.wustl.edu2School of Electrical and Computer Engineering,Georgia Institute of Technology,Atlanta,Georgia 30332.E-mail:ayezzi@ece.gatech.edu3PACM and Mathematics Department,Princeton University,Princeton,New Jersey08544.E-mail: ytsai@math.princeton.edu.Research was performed while the author was with University of California,Los Angeles.4Department of Mathematics,University of California San Diego,La Jolla,California92093. E-mail:lcheng@math.ucsd.edu5Computer Science Department,University of California,Los Angeles,California90095.E-mail: soatto@cs.ucla.edu2670885-7474/03/1200-0267/0©2003Plenum Publishing Corporation
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