Wei, TiangongKlette, Reinhard2008-08-212008-08-212002Communication and Information Technology Research Technical Report 115, (2002)1178-3630http://hdl.handle.net/2292/2850You 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 original CITR web site; http://citr.auckland.ac.nz/techreports/ under terms that include this permission. All other rights are reserved by the author(s).This paper presents a regularization method for surface reconstruction from noisy gradient vector fields. The algorithm takes as its input a discrete gradient vector field, obtained by applying a Shape from Shading or Photometric Stereo method. To derive this algorithm, we combine the integrability constraint and the surface curvature and area constraints into a single functional, which is then minimized. Therefore, value changes in the height or depth map will be more regular. To solve the minimization problem, we employ the Fourier transform theory rather than the Variational Principle. The Fourier transform of the (unknown) surface is expressed as a function of the (given) gradient's Fourier transforms. The relative depth values can be obtained by an inverse Fourier Transform and by choosing associated weighting parameters. The method is evaluated on gradient data delivered by a Photometric Stereo algorithm.Copyright CITR, The University of Auckland. 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 original CITR web site under terms that include this permission. All other rights are reserved by the author(s).https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htmTechnical ReportFields of Research::280000 Information, Computing and Communication Sciences