A segmentation-based regularization term for image deconvolution

Mignotte, Maurice

doi:10.1109/tip.2006.873446

Cited by 52 publications

(35 citation statements)

References 41 publications

(92 reference statements)

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“…Total Variation (TV) [27], as already mentioned, favors piece-wise constant solutions, whereas some wavelet-based deconvolution does not explicitly enforce a regularizer, except for [8], but exercises regularization through complexity bounds [7,[12][13][14]24]. Segmentation-based regularization is discussed in [23]. Deconvolution is also directly extended from denoising algorithms, such as BLS-GSM [17,25], kernel regression [28,29] and BM3D [4,5].…”

Section: State Of the Artmentioning

confidence: 99%

Direct Sparse Deblurring

Lou¹,

Bertozzi²,

Soatto³

2010

J Math Imaging Vis

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We propose a deblurring algorithm that explicitly takes into account the sparse characteristics of natural images and does not entail solving a numerically illconditioned backward-diffusion. The key observation is that the sparse coefficients that encode a given image with respect to an over-complete basis are the same that encode a blurred version of the image with respect to a modified basis. Following an "analysis-by-synthesis" approach, an explicit generative model is used to compute a sparse representation of the blurred image, and its coefficients are used to combine elements of the original basis to yield a restored image.

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Section: State Of the Artmentioning

confidence: 99%

Direct Sparse Deblurring

Lou¹,

Bertozzi²,

Soatto³

2010

J Math Imaging Vis

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“…Usually there is no guarantee that the resultant restoration yields an unambiguous segmentation since the obtained contours are not necessarily closed. The other approach is to construct a two-step process where image restoration and image segmentation are realized in an alternating way, with each dependent on the result of the other [33]. The process has to start with an initial guess for the segmentation whose importance is critical for the success of the overall method.…”

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confidence: 99%

Efficient Reconstruction of Piecewise Constant Images Using Nonsmooth Nonconvex Minimization

Nikolova¹,

Ng²,

Zhang³

et al. 2008

SIAM J. Imaging Sci.

183

171

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Abstract. We consider the restoration of piecewise constant images where the number of the regions and their values are not fixed in advance, with a good difference of piecewise constant values between neighboring regions, from noisy data obtained at the output of a linear operator (e.g., a blurring kernel or a Radon transform). Thus we also address the generic problem of unsupervised segmentation in the context of linear inverse problems. The segmentation and the restoration tasks are solved jointly by minimizing an objective function (an energy) composed of a quadratic data-fidelity term and a nonsmooth nonconvex regularization term. The pertinence of such an energy is ensured by the analytical properties of its minimizers. However, its practical interest used to be limited by the difficulty of the computational stage which requires a nonsmooth nonconvex minimization. Indeed, the existing methods are unsatisfactory since they (implicitly or explicitly) involve a smooth approximation of the regularization term and often get stuck in shallow local minima. The goal of this paper is to design a method that efficiently handles the nonsmooth nonconvex minimization. More precisely, we propose a continuation method where one tracks the minimizers along a sequence of approximate nonsmooth energies {Jε}, the first of which being strictly convex and the last one the original energy to minimize. Knowing the importance of the nonsmoothness of the regularization term for the segmentation task, each Jε is nonsmooth and is expressed as the sum of an 1 regularization term and a smooth nonconvex function. Furthermore, the local minimization of each Jε is reformulated as the minimization of a smooth function subject to a set of linear constraints. The latter problem is solved by the modified primal-dual interior point method, which guarantees the descent direction at each step. Experimental results are presented and show the effectiveness and the efficiency of the proposed method. Comparison with simulated annealing methods further shows the advantage of our method.

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“…and in [59] for restoration application. 5 Another reliable strategy consist of initializing the ICM with the first NI optimal input segmentations (in the mean F measure sense) and to finally retain, after convergence of the ICM procedure, the segmentation result ensuring the highest mean Fα measure.…”

Section: 3: Fusion Model Optimizationmentioning

confidence: 99%

A Precision-Recall Criterion Based Consensus Model For Fusing Multiple Segmentations

Mignotte

Hélou

Montréal³

2014

IJSIP

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This paper presents a general framework for seamlessly combining multiple low cost and inaccurate estimated segmentation maps (with an arbitrary number of regions) of the same scene to achieve a final improved segmentation. The proposed fusion model is derived from the well-known precision-recall criterion, specially dedicated to the specific clustering problem of any spatially indexed data and which is also efficient and widely used in the vision community for evaluating both a region-based segmentation and the quality of contours produced by this segmentation map compared to one or multiple ground-truth segmentations of the same image. The proposed combination framework is here specifically designed to be robust with respect to outlier segmentations (that appear to be inconsistent with the remainder of the segmentation ensemble) and includes an explicit internal regularization factor reflecting the inherent ill-posed nature of the segmentation problem. We propose also a hierarchical and efficient way to optimize the consensus energy function related to this fusion model that exploits a simple and deterministic iterative relaxation strategy combining the different segments or individual regions belonging to the segmentation ensemble in the final solution. The experimental results on the Berkeley database with manual ground truth segmentations show the effectiveness of our combination model.

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A segmentation-based regularization term for image deconvolution

Cited by 52 publications

References 41 publications

Direct Sparse Deblurring

Direct Sparse Deblurring

Efficient Reconstruction of Piecewise Constant Images Using Nonsmooth Nonconvex Minimization

A Precision-Recall Criterion Based Consensus Model For Fusing Multiple Segmentations

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