A Geometric Functional for Derivatives Approximation

Sochen, Nir; Haralick, Robert M.; Zeevi, Yehoshua Y.

doi:10.1007/3-540-48236-9_51

Cited by 4 publications

(2 citation statements)

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“…The difficulty represented in the problem of projection is transformed to the problem of the choice of local coordinate system as we describe below. Other examples of enhancement by the Beltrami framework of non-flat feature spaces, like the color perceptual space and the derivatives vector field, can be found in [10,13]. This paper is organized as follows: We review the Beltrami framework and point to the relation with harmonic maps in Section 2.…”

Section: Introductionmentioning

confidence: 99%

Orientation Diffusion or How to Comb a Porcupine

Kimmel

Sochen

2002

Journal of Visual Communication and Image Representation

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This paper addresses the problem of feature enhancement in noisy images, when the feature is known to be constrained to a manifold. As an example, we approach the orientation denoising problem via the geometric Beltrami framework for image processing. The feature (orientation) field is represented accordingly as the embedding of a two dimensional surface in the spatial-feature manifold. The resulted Beltrami flow is a selective smoothing process that respects the feature constraint. Orientation diffusion is treated as a canonical example where the feature (orientation in this case) space is the unit circle S 1 . Applications to color analysis are discussed and numerical experiments demonstrate again the power of the Beltrami framework for nontrivial geometries in image processing. C 2002 Elsevier Science (USA)

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Section: Introductionmentioning

confidence: 99%

Orientation Diffusion or How to Comb a Porcupine

Kimmel

Sochen

2002

Journal of Visual Communication and Image Representation

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“…The difficulty represented in the problem of projection is transformed into the problem of the choice of a local coordinate system, as we describe below. Other examples of enhancement by the Beltrami framework of nonflat feature spaces, like the color perceptual space and the derivatives vector field, can be found in [20,17].…”

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confidence: 99%

StereographicCombing a Porcupine or Studies on Direction Diffusion in Image Processing

Sagiv¹,

Sochen²,

Kimmel³

2004

SIAM J. Appl. Math.

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Abstract. This paper addresses the problem of feature enhancement in noisy images when the feature is known to be constrained to a manifold. As an example, we approach the direction denoising problem in a general dimension via the geometric Beltrami framework for image processing. The spatial-direction space is a fiber bundle in which the spatial part is the base manifold and the direction space is the fiber. The feature (direction) field is represented accordingly as a section of the spatial-feature fiber bundle. The resulting Beltrami flow is a selective smoothing process that respects the bundle's structure, i.e., the feature constraint. Direction diffusion is treated as a canonical example of a non-Euclidean feature space. The structures of the fiber spaces of interest in this paper are the unit circle S 1 , the unit sphere S 2 , and the unit hypersphere S n . Applications to color analysis are discussed, and numerical experiments demonstrate again the benefits of the Beltrami framework in comparison to other feature enhancement schemes for nontrivial geometries in image processing.

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Using Beltrami Framework for Orientation Diffusion in Image Processing

Kimmel

Sochen

2001

Lecture Notes in Computer Science

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A Geometric Functional for Derivatives Approximation

Cited by 4 publications

References 8 publications

Orientation Diffusion or How to Comb a Porcupine

Orientation Diffusion or How to Comb a Porcupine

StereographicCombing a Porcupine or Studies on Direction Diffusion in Image Processing

Using Beltrami Framework for Orientation Diffusion in Image Processing

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