Integrated Parallel 2D-Leap-Frog Algorithm for Noisy Three Image Photometric Stereo

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• 关键词：Noisy Photometric Stereo ; 2D ; Leap ; Frog ; Parallelization
• 刊名：Lecture Notes in Computer Science
• 出版年：2016
• 出版时间：2016
• 年：2016
• 卷：9555
• 期：1
• 页码：73-87
• 全文大小：3,618 KB
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• 作者单位：Ryszard Kozera (15)
  Felicja Okulicka-Dłużewska (16)
  Lyle Noakes (17)
  
  15. Faculty of Applied Mathematics and Informatics, Warsaw University of Life Sciences-SGGW, Nowoursynowska Street 159, 02-776, Warsaw, Poland
  16. Faculty of Mathematics and Information Science, Warsaw University of Technology, Koszykowa Street 75, 00-662, Warsaw, Poland
  17. School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley, Perth, WA, 6009, Australia
  
• 丛书名：Image and Video Technology ᾿PSIVT 2015 Workshops
• ISBN：978-3-319-30285-0
• 刊物类别：Computer Science
• 刊物主题：Artificial Intelligence and Robotics
  Computer Communication Networks
  Software Engineering
  Data Encryption
  Database Management
  Computation by Abstract Devices
  Algorithm Analysis and Problem Complexity
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1611-3349

文摘

In this paper a feasible computational scheme for reconstructing a smooth Lambertian surface \(S_L\) from noisy images is discussed. The noiseless case of Photometric Stereo relies on solving image irradiance equations. In fact, the entire shape recovery consists of gradient computation and gradient integration. The presence of added noise re-transforms the latter (depending on the adopted model) into a high-dimensional linear or non-linear optimization, solvable e.g. by a 2D-Leap-Frog. This algorithm resorts to the overlapping local image snapshot optimizations to reduce a large dimension of the original optimization task. Several practical steps to improve the feasibility of 2D-Leap-Frog are integrated in this work. Namely, an initial guess is obtained from a linear version of denoising Photometric Stereo. A non-integrable vector field estimating the normals to \(S_L\) is rectified first to yield an initial guess \(S_{L_a}\approx S_L\) for a non-linear 2D-Leap-Frog. Computationally, the integrability of non-integrable normals is enforced here by Conjugate Gradient which avoids numerous inversions of the large size matrices. In sequel, \(S_{L_a}\) is fed through to the adjusted version of non-linear 2D-Leap-Frog. Such setting not only improves the recovery of \(S_L\) (from \(S_{L_a}\approx S_L\) to \(\hat{S}_{L_a}\approx S_L\)) but also it removes potential outliers (upon enforcing a continuity on \(\hat{S}_{L_a}\)) occurring in the previous version of 2D-Leap-Frog. In addition, a speed-up of shape reconstruction is achieved with parallelization of non-linear 2D-Leap-Frog applied to the modified cost function. The experiments are performed on images with different resolutions and varying number of kernels. Finally, the comparison tests between standard 2D-Leap-Frog (either linear or non-linear) and its improved outlier-free version are presented illustrating differences in the quality of the reconstructed surface.