Fast Regularization of Matrix-Valued Images

Rosman, Guy; Wang, Yu; Tai, Xue–Cheng; Kimmel, Ron; Bruckstein, Alfred M.

doi:10.1007/978-3-642-33712-3_13

Cited by 9 publications

(17 citation statements)

References 40 publications

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“…This algorithm extends our recent work on fast total variation regularization of group-valued images [31], modifying it algorithm to handle smoothness on parameteric surfaces.…”

Section: Introductionmentioning

confidence: 75%

“…The estimation of motion coefficients takes in Matlab about 5 seconds on an Intel i3 CPU. The regularization is similar algorithmically to [31], which took about a tenth of a second to compute on GPU. Preliminary results support this efficiency claim.…”

Section: Resultsmentioning

confidence: 99%

“…The smoothing process we describe and associated preprocessing steps are highly parallelizable, lending themselves to real-time implementation on parallel hardware such as graphics processing units (GPUs), as shown for example, in [31]. The results obtained demonstrate the method's usefulness in identifying components of piecewise-rigid motion in real-life, noisy, range data.…”

Section: Introductionmentioning

confidence: 90%

“…We note that while the update step for v comes from minimizing the cost function, it is highly linked to the intuitive choice of updating u and then projecting it, as well as to optimization by proximal operators [11], and can be made provably convergent with minor modifications, as shown in [31]. We now modify the augmented Lagrangian TV framework for the smoothness term described in (2).…”

Section: Methodsmentioning

confidence: 99%

“…We update μ according to the augmented Lagrangian method [28,16]. Optimization with respect to v is using the same projection operator per-pixel as in [31]. Looking at optimization with respect to v, we obtain…”

Section: Augmented Lagrangian Regularization Of Group-valued Maps On mentioning

confidence: 99%

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Group-Valued Regularization for Analysis of Articulated Motion

Rosman

Bronstein

et al. 2012

Lecture Notes in Computer Science

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Abstract. We present a novel method for estimation of articulated motion in depth scans. The method is based on a framework for regularization of vector-and matrix-valued functions on parametric surfaces.We extend augmented-Lagrangian total variation regularization to smooth rigid motion cues on the scanned 3D surface obtained from a range scanner. We demonstrate the resulting smoothed motion maps to be a powerful tool in articulated scene understanding, providing a basis for rigid parts segmentation, with little prior assumptions on the scene, despite the noisy depth measurements that often appear in commodity depth scanners.

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“…This algorithm extends our recent work on fast total variation regularization of group-valued images [31], modifying it algorithm to handle smoothness on parameteric surfaces.…”

Section: Introductionmentioning

confidence: 75%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 90%

Section: Methodsmentioning

confidence: 99%

Section: Augmented Lagrangian Regularization Of Group-valued Maps On mentioning

confidence: 99%

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Group-Valued Regularization for Analysis of Articulated Motion

Rosman

Bronstein

et al. 2012

Lecture Notes in Computer Science

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Generalized Gradient on Vector Bundle – Application to Image Denoising

Batard

Bertalmío

2013

Lecture Notes in Computer Science

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Abstract. We introduce a gradient operator that generalizes the Euclidean and Riemannian gradients. This operator acts on sections of vector bundles and is determined by three geometric data: a Riemannian metric on the base manifold, a Riemannian metric and a covariant derivative on the vector bundle. Under the assumption that the covariant derivative is compatible with the metric of the vector bundle, we consider the problems of minimizing the L2 and L1 norms of the gradient. In the L2 case, the gradient descent for reaching the solutions is a heat equation of a differential operator of order two called connection Laplacian. We present an application to color image denoising by replacing the regularizing term in the Rudin-Osher-Fatemi (ROF) denoising model by the L1 norm of a generalized gradient associated with a well-chosen covariant derivative. Experiments are validated by computations of the PSNR and Q-index.

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Active Contour Models for Manifold Valued Image Segmentation

Bansal

Tatu

2015

J Math Imaging Vis

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Image segmentation is the process of partitioning an image into different regions or groups based on some characteristics like color, texture, motion or shape etc. Active contours are a popular variational method for object segmentation in images, in which the user initializes a contour which evolves in order to optimize an objective function designed such that the desired object boundary is the optimal solution. Recently, imaging modalities that produce Manifold valued images have come up, for example, DT-MRI images, vector fields. The traditional active contour model does not work on such images. In this paper, we generalize the active contour model to work on Manifold valued images. As expected, our algorithm detects regions with similar Manifold values in the image. Our algorithm also produces expected results on usual gray-scale images, since these are nothing but trivial examples of Manifold valued images. As another application of our general active contour model, we perform texture segmentation on gray-scale images by first creating an appropriate Manifold valued image. We demonstrate segmentation results for manifold valued images and texture images. * sumukh bansal@daiict.ac.in † Queries and comments to be addressed to aditya.

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Fast Regularization of Matrix-Valued Images

Cited by 9 publications

References 40 publications

Group-Valued Regularization for Analysis of Articulated Motion

Group-Valued Regularization for Analysis of Articulated Motion

Generalized Gradient on Vector Bundle – Application to Image Denoising

Active Contour Models for Manifold Valued Image Segmentation

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