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A robust multi-scale integration method to obtain the depth from gradient maps

Leitão, Helena C.G.; Saracchini, Rafael F.V.; Atkinson, Gary A.; Smith, Melvyn L.; Saracchini, Rafael; Leitão, Helena; Atkinson, Gary; Smith, Melvyn; Stolfi, Jorge


Helena C.G. Leitão

Rafael F.V. Saracchini

Gary A. Atkinson

Melvyn L. Smith

Rafael Saracchini

Helena Leitão

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Melvyn Smith
Research Centre Director Vision Lab/Prof

Jorge Stolfi


We describe a robust method for the recovery of the depth map (or height map) from a gradient map (or normal map) of a scene, such as would be obtained by photometric stereo or interferometry. Our method allows for uncertain or missing samples, which are often present in experimentally measured gradient maps, and also for sharp discontinuities in the scene's depth, e.g. along object silhouette edges. By using a multi-scale approach, our integration algorithm achieves linear time and memory costs. A key feature of our method is the allowance for a given weight map that flags unreliable or missing gradient samples. We also describe several integration methods from the literature that are commonly used for this task. Based on theoretical analysis and tests with various synthetic and measured gradient maps, we argue that our algorithm is as accurate as the best existing methods, handling incomplete data and discontinuities, and is more efficient in time and memory usage, especially for large gradient maps. © 2012 Elsevier Inc. All rights reserved.


Smith, M. L., Atkinson, G. A., Leitão, H. C., Saracchini, R. F., Saracchini, R., Stolfi, J., …Smith, M. (2012). A robust multi-scale integration method to obtain the depth from gradient maps. Computer Vision and Image Understanding, 116(8), 882-895.

Journal Article Type Article
Publication Date Aug 1, 2012
Journal Computer Vision and Image Understanding
Print ISSN 1077-3142
Electronic ISSN 1090-235X
Publisher Elsevier
Peer Reviewed Not Peer Reviewed
Volume 116
Issue 8
Pages 882-895
Keywords computer vision, multi-scale methods, gradient map integration, surface reconstruction
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