Gabor Feature Space Diffusion via the Minimal Weighted Area Method

Sagiv, Chen; Sochen, Nir; Zeevi, Yehoshua Y.

doi:10.1007/3-540-44745-8_41

Cited by 7 publications

(5 citation statements)

References 24 publications

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“…Partial derivative wavelets are well adapted to detect edges or sharp transitions but do not have enough frequency and directional resolution to discriminate complex directional structures. For texture analysis, many researchers [19], [30], [28] have been using averaged wavelet coefficient amplitudes |x ⋆ ψ λ | ⋆ φ J (u), but calculated with a complex wavelet ψ having a better frequency and directional resolution.…”

Section: Scattering Convolution Networkmentioning

confidence: 99%

Invariant Scattering Convolution Networks

Bruna

Mallat

2013

IEEE Trans. Pattern Anal. Mach. Intell.

1,423

1,244

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A wavelet scattering network computes a translation invariant image representation which is stable to deformations and preserves high-frequency information for classification. It cascades wavelet transform convolutions with nonlinear modulus and averaging operators. The first network layer outputs SIFT-type descriptors, whereas the next layers provide complementary invariant information that improves classification. The mathematical analysis of wavelet scattering networks explains important properties of deep convolution networks for classification. A scattering representation of stationary processes incorporates higher order moments and can thus discriminate textures having the same Fourier power spectrum. State-of-the-art classification results are obtained for handwritten digits and texture discrimination, with a Gaussian kernel SVM and a generative PCA classifier.

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Section: Scattering Convolution Networkmentioning

confidence: 99%

Invariant Scattering Convolution Networks

Bruna

Mallat

2013

IEEE Trans. Pattern Anal. Mach. Intell.

1,423

1,244

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“…The solution to this problem may be a better selection of the feature space, and adding some statistical data, in the spirit of [17], [22], [36], [51]. A simpler approach to the one applied here, is to improve the Gabor feature space by incorporating a Beltrami-based diffusion scheme [43], [44]. Moreover, when the full set of Gabor responses was selected, we have used a Gaussian-Beltrami diffusion scheme to eliminate noise.…”

Section: Discussionmentioning

confidence: 99%

Integrated active contours for texture segmentation

Sagiv

Sochen

Zeevi

2006

IEEE Trans. on Image Process.

166

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Abstract-We address the issue of textured image segmentation in the context of the Gabor feature space of images. Gabor filters tuned to a set of orientations, scales and frequencies are applied to the images to create the Gabor feature space. A two-dimensional Riemannian manifold of local features is extracted via the Beltrami framework. The metric of this surface provides a good indicator of texture changes and is used, therefore, in a Beltrami-based diffusion mechanism and in a geodesic active contours algorithm for texture segmentation. The performance of the proposed algorithm is compared with that of the edgeless active contours algorithm applied for texture segmentation. Moreover, an integrated approach, extending the geodesic and edgeless active contours approaches to texture segmentation, is presented. We show that combining boundary and region information yields more robust and accurate texture segmentation results.

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“…The motivation for this study comes from our previous studies on texture segmentation and representation [24][25][26][27][28]. A major concern encountered in dealing with these issues is the selection of an appropriate filter bank.…”

Section: Introductionmentioning

confidence: 99%

The Uncertainty Principle: Group Theoretic Approach, Possible Minimizers and Scale-Space Properties

2006

Self Cite

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Abstract. The uncertainty principle is a fundamental concept in the context of signal and image processing, just as much as it has been in the framework of physics and more recently in harmonic analysis. Uncertainty principles can be derived by using a group theoretic approach. This approach yields also a formalism for finding functions which are the minimizers of the uncertainty principles. A general theorem which associates an uncertainty principle with a pair of self-adjoint operators is used in finding the minimizers of the uncertainty related to various groups. This study is concerned with the uncertainty principle in the context of the Weyl-Heisenberg, the SIM(2), the Affine and the Affine-WeylHeisenberg groups. We explore the relationship between the two-dimensional affine group and the SIM(2) group in terms of the uncertainty minimizers. The uncertainty principle is also extended to the Affine-Weyl-Heisenberg group in one dimension. Possible minimizers related to these groups are also presented and the scale-space properties of some of the minimizers are explored.

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Gabor Feature Space Diffusion via the Minimal Weighted Area Method

Cited by 7 publications

References 24 publications

Invariant Scattering Convolution Networks

Invariant Scattering Convolution Networks

Integrated active contours for texture segmentation

The Uncertainty Principle: Group Theoretic Approach, Possible Minimizers and Scale-Space Properties

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