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Denoising Images: Non-linear Leap-Frog for Shape and Light-Source Recovery

  • Lyle Noakes
  • Ryszard Kozera
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2616)

Abstract

In 3-source photometric stereo, a Lambertian surface is illuminated from 3 known independent light-source directions, and photographed to give 3 images. The task of recovering the surface reduces to solving systems of linear equations for the gradients of a bivariate function u whose graph is the visible part of the surface [9], [16], [17], [24]. In the present paper we consider the same task, but with slightly more realistic assumptions: the photographic images are contaminated by Gaussian noise, and light-source directions may not be known. This leads to a non-quadratic optimization problem with many independent variables, compared to the quadratic problems resulting from addition of noise to the gradient of u and solved by linear methods in [6], [10], [20], [21], [22], [25]. The distinction is illustrated in Example below. Perhaps the most natural way to solve our problem is by global Gradient Descent, and we compare this with the 2-dimensional Leap-Frog Algorithm [23]. For this we review some mathematical results of [23] and describe an implementation in sufficient detail to permit code to be wrtten. Then we give examles comparing the behavior of Leap-Frog with GradientDescent, and explore an extension of Leap-Frog (not covered in [23]) to estimate light source directions when these are not given, as well as the reflecting surface.

Keywords

Initial Guess Gradient Descent Noisy Image Denoising Image Photometric Stereo 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Lyle Noakes
    • 1
  • Ryszard Kozera
    • 2
  1. 1.School of Mathematics and StatisticsThe University of Western AustraliaCrawleyAustralia
  2. 2.School of Computer Science and Software EngineeringThe University of Western AustraliaCrawleyAustralia

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