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)


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.


Initial Guess Gradient Descent Noisy Image Denoising Image Photometric Stereo 
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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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