A New Algorithm for Gradient Field Integration

This paper proposes two improvements for reflectance based shape recovery. First, it is shown that albedo-independent photometric stereo allows albedo computation. This computation is based on photometric equations that relate surface normals to triplets of the image irradiances. Second, the paper also presents as the main result a new algorithm for depth recovery from surface normals. In order to improve the accuracy and robustness and to strengthen the relation between the depth map and surface normals, two new constraints are added into the associated cost function. They constrain the behavior of high-order change rate between the variables. Therefore, the changes of depth maps will be more regular. The Frankot-Chellappa-algorithm is a special case of our algorithm in the sense that it uses a subset of constraints only. 1 Center for Image Technology and Robotics Tamaki Campus, The University of Auckland, Auckland, New Zealand. tangong@ec.auckland.ac.nz and r.klette@auckland.ac.nz You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) days from the most recent time that you verified that this technical report is still available from the CITR Tamaki web site under terms that include this permission. All other rights are reserved by the author(s). A New Algorithm for Gradient Field Integration Tiangong Wei and Reinhard Klette