Edge-Preserving Integration of a Normal Field: Weighted Least-Squares, TV and $$L^1$$ Approaches

Quéau, Yvain; Durou, Jean‐Denis

doi:10.1007/978-3-319-18461-6_46

Cited by 25 publications

(37 citation statements)

References 16 publications

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“…In this section, we numerically evaluate our proposed DLS method on several datasets. In each case we compare our method to the spectral regularization method (SR) [8], the isotropic total variation (TV) method [9], and DCT based least squares (DCTLS) [5]. For methods that include tunable parameters, we sweep over a wide range of values, reporting the best results obtained.…”

Section: Resultsmentioning

confidence: 99%

Robust surface reconstruction from gradients via adaptive dictionary regularization

Wagenmaker

Moore

Nadakuditi

2017

2017 IEEE International Conference on Image Processing (ICIP)

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This paper introduces a novel approach to robust surface reconstruction from photometric stereo normal vector maps that is particularly well-suited for reconstructing surfaces from noisy gradients. Specifically, we propose an adaptive dictionary learning based approach that attempts to simultaneously integrate the gradient fields while sparsely representing the spatial patches of the reconstructed surface in an adaptive dictionary domain. We show that our formulation learns the underlying structure of the surface, effectively acting as an adaptive regularizer that enforces a smoothness constraint on the reconstructed surface. Our method is general and may be coupled with many existing approaches in the literature to improve the integrity of the reconstructed surfaces. We demonstrate the performance of our method on synthetic data as well as real photometric stereo data and evaluate its robustness to noise.Index Terms-Dictionary learning, photometric stereo, sparse representations, inverse problems.

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Section: Resultsmentioning

confidence: 99%

Robust surface reconstruction from gradients via adaptive dictionary regularization

Wagenmaker

Moore

Nadakuditi

2017

2017 IEEE International Conference on Image Processing (ICIP)

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“…The first method computes the normal field and then modifies the gradient field based on the perspective projection, as also proposed in Refs. [44,45]. As it manipulates normal vectors, we refer to this technique as the perspective projection based on normal field (PPN) method.…”

Section: Perspective Projectionmentioning

confidence: 99%

Photometric stereo for strong specular highlights

2018

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Photometric stereo is a fundamental technique in computer vision known to produce 3D shape with high accuracy. It uses several input images of a static scene taken from one and the same camera position but under varying illumination. The vast majority of studies in this 3D reconstruction method assume orthographic projection for the camera model. In addition, they mainly use the Lambertian reflectance model as the way that light scatters at surfaces. Thus, providing reliable photometric stereo results from real world objects still remains a challenging task. We address 3D reconstruction by use of a more realistic set of assumptions, combining for the first time the complete Blinn-Phong reflectance model and perspective projection. Furthermore, we compare two different methods of incorporating the perspective projection into our model. Experiments are performed on both synthetic and real world images; the latter do not benefit from laboratory conditions. The results show the high potential of our method even for complex real world applications such as medical endoscopy images which may include many specular highlights.

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“…Yet, this would require detecting the discontinuities beforehand, which might be tedious. It is actually more convenient to introduce weights in the least-squares functionals, which are inversely proportional to the probability of lying on a discontinuity [47,50]. We discuss this weighted least-squares approach in Subsection 4.4, where a statistical interpretation of the Perona and Malik's anisotropic diffusion model [44] is also exhibited.…”

Section: Ground Truthmentioning

confidence: 99%

Variational Methods for Normal Integration

Quéau¹,

Durou

Aujol

2017

J Math Imaging Vis

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The need for an efficient method of integration of a dense normal field is inspired by several computer vision tasks, such as shape-from-shading, photometric stereo, deflectometry, etc. Inspired by edgepreserving methods from image processing, we study in this paper several variational approaches for normal integration, with a focus on non-rectangular domains, free boundary and depth discontinuities. We first introduce a new discretization for quadratic integration, which is designed to ensure both fast recovery and the ability to handle non-rectangular domains with a free boundary. Yet, with this solver, discontinuous surfaces can be handled only if the scene is first segmented into pieces without discontinuity. Hence, we then discuss several discontinuity-preserving strategies. Those inspired, respectively, by the Mumford-Shah segmentation method and by anisotropic diffusion, are shown to be the most effective for recovering discontinuities.

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Edge-Preserving Integration of a Normal Field: Weighted Least-Squares, TV and $$L^1$$ Approaches

Cited by 25 publications

References 16 publications

Robust surface reconstruction from gradients via adaptive dictionary regularization

Robust surface reconstruction from gradients via adaptive dictionary regularization

Photometric stereo for strong specular highlights

Variational Methods for Normal Integration

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