Multiresolution segmentation of natural images: from linear to nonlinear scale-space representations

Petrović, Ana; Escoda, O. Divorra; Vandergheynst, Pierre

doi:10.1109/tip.2004.828431

Cited by 51 publications

(34 citation statements)

References 28 publications

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“…Equation (27) indicates that it is redundancy to compute some of the terms for the mutual information in (25). Thus, we simplify the i-Se algorithm to increase computation speed by deleting redundancy term.…”

Section: From (1) We Have I(u S T U) = H(u) + H(s T U) − H(u S T Umentioning

confidence: 99%

“…The second type is derived from the diffusion process and based on partial differential equations [20]. It originates from the conventional isotropic heat flow equation and has been widespread used in image filtering [21][22][23][24], segmentation [25][26][27] and inpainting [28][29][30]. And the third type is based on the mathematical morphology [31][32][33].…”

Section: Introductionmentioning

confidence: 99%

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Mutual Information Criterion-Based Optimal Scale Selection for Image Denoising and Segmentation

Wen¹,

Zhu²,

Gu³

2013

Appl. Math. Inf. Sci.

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Scale-spaces play an important role in many computer vision tasks. Automatic scale selection is at the foundation of multiscale image analysis, but its performance is still very subjective and empirical. To automatically select the appropriate scale for a particular issue, a scale selection model based on information theory is proposed in this paper. The proposed model utilizes mutual information as a measuring criterion of similarity for the optimal scale selection in multi-scale analysis, with applications to image denoising and segmentation. Firstly, we focus on the morphological operator based scale selection to image denoising. This technique does not require the prior knowledge of the noise variance and can effectively eliminate the variation of illumination. Secondly, we develop a clustering based unsupervised image segmentation algorithm by recursively pruning the Huffman coding tree. The proposed clustering algorithm can preserve the maximum amount of information at a specific clustering number from the information-theoretical point of view. Finally, for the feasibility of the proposed algorithms, its theoretical properties are analyzed mathematically and its performance is tested by a series of experiments, which demonstrate that it yields the optimal scale for our developed image denoising and segmentation algorithms.

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Section: From (1) We Have I(u S T U) = H(u) + H(s T U) − H(u S T Umentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Mutual Information Criterion-Based Optimal Scale Selection for Image Denoising and Segmentation

Wen¹,

Zhu²,

Gu³

2013

Appl. Math. Inf. Sci.

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show abstract

“…Among non-linear techniques, the seminal work detailed in the paper by Perona and Malik (Perona and Malik, 1990) received a special attention from the vision community (Ghita et al, 2005;Ilea and Whelan, 2007;Smolka and Plataniotis, 2002;Weickert et al, 1998). Total variation (TV) flow algorithms have been viewed by many authors as a special case of the geometrical-driven anisotropic diffusion (Dibos and Koepfler, 1999;Gothandaraman et al, 2001;Petrovic et al, 2004;Rudin et al, 1992;Strong and Chan, 2003). The TV flow formulation has been evaluated from a numerical perspective by Breuβ et al, 2006 and they concluded that this data smoothing feature preserving technique is well-posed and it leads to constant signals in finite times.…”

Section: Introductionmentioning

confidence: 99%

“…Also in line with other non-linear smoothing strategies such as anisotropic diffusion (Ilea and Whelan, 2007;Smolka and Plataniotis, 2002;Weickert, 1998), the TV flow formulation is implemented as an iterative scheme where the number of iterations is typically a user defined parameter (Andreu et al, 2001;Breuβ et al, 2006;Petrovic et al, 2004). In this paper we show that the application of a time-ageing procedure to the time step size parameter, implements a data smoothing framework where the evolution in time of the TV flow becomes predictable and the algorithm will converge naturally to the optimal result.…”

Section: Introductionmentioning

confidence: 99%

Image feature enhancement based on the time-controlled total variation flow formulation

Ghita

Ilea

Whelan

2009

Pattern Recognition Letters

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Data smoothing and feature enhancement are two important precursors to many higher-level computer vision applications such as image segmentation and scene understanding. Total variation (TV) flow algorithms are a distinct subcategory of diffusion-based filtering techniques that have been widely applied to reduce the level of noise in the image but not at the expense of poor feature preservation. In this paper we address a number of numerical aspects associated with the TV flow and in particular we are interested to redefine the TV flow regularization in order to reduce the effect of oscillations and improve the convergence of the implementations in the discrete domain. TV flow algorithms are implemented using iterative schemes and one difficult problem is the selection of appropriate criteria to identify the optimal number of iterations. In this paper we show that the application of a time-ageing procedure leads to an elegant formulation were the TV flow algorithms converge naturally to the optimal solution. To evaluate the performance of the proposed algorithm (referred in this paper to as time-controlled (TC)-TV flow), a large number of experiments on various types of natural images were conducted.

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“…In order to preserve (or even enhance) edges and to simultaneously smooth within more homogeneous regions, the diffusivity function g(|∇u|) is chosen as a decreasing nonnegative function. While early proposals for nonlinear diffusion filters use bounded diffusivities [15,6], more recently there has been a growing interest in unbounded diffusivities that become singular in zero [2,9,10,11,16]. Experimentally one observes that singular diffusion filters lead to piecewise constant images.…”

Section: Introductionmentioning

confidence: 99%

A Four-Pixel Scheme for Singular Differential Equations

Welk

Weickert

Steidl

2005

Lecture Notes in Computer Science

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Abstract. Singular diffusion equations such as total variation (TV) and balanced forward-backward (BFB) diffusion are appealing: They have a finite extinction time, and experiments show that piecewise constant structures evolve. Unfortunately, their implementation is awkward. The goal of this paper is to introduce a novel class of numerical methods for these equations in the 2D case. They are simple to implement, absolutely stable and do not require any regularisation in order to make the diffusivity bounded. Our schemes are based on analytical solutions for 2×2-pixel images which are combined by means of an additive operator splitting (AOS). We show that they may also be regarded as iterated 2D Haar wavelet shrinkage. Experiments demonstrate the favourable performance of our numerical algorithm.

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Multiresolution segmentation of natural images: from linear to nonlinear scale-space representations

Cited by 51 publications

References 28 publications

Mutual Information Criterion-Based Optimal Scale Selection for Image Denoising and Segmentation

Mutual Information Criterion-Based Optimal Scale Selection for Image Denoising and Segmentation

Image feature enhancement based on the time-controlled total variation flow formulation

A Four-Pixel Scheme for Singular Differential Equations

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