New region force for variational models in image segmentation and high dimensional data clustering

Ke, Wei; Yin, Ke; Tai, Xue–Cheng; Chan, Tony F.

doi:10.4310/amsa.2018.v3.n1.a8

Cited by 13 publications

(14 citation statements)

References 37 publications

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“…The region force term plays an important role in the performance of image segmentation model (20). Probability based method is one of the widely investigated approaches in the literature for image segmentation and data clustering due to its flexibility and robustness of intensities [4], [25], [26], [27], [28], [29].…”

Section: Convex Shape Prior With Signed Distance Functionsmentioning

confidence: 99%

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Convex Shape Priors for Level Set Representation

Luo¹,

Tai²

2018

Preprint

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For many applications, we need to use techniques to represent convex shapes and objects. In this work, we use level set method to represent shapes and find a necessary and sufficient condition on the level set function to guarantee the convexity of the represented shapes. We take image segmentation as an example to apply our technique. Numerical algorithm is developed to solve the variational model. In order to improve the performance of segmentation for complex images, we also incorporate landmarks into the model. One option is to specify points that the object boundary must contain. Another option is to specify points that the foreground (the object) and the background must contain. Numerical experiments on different images validate the efficiency of the proposed models and algorithms. We want to emphasize that the proposed technique could be used for general shape optimization with convex shape prior. For other applications, the numerical algorithms need to be extended and modified.

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Section: Convex Shape Prior With Signed Distance Functionsmentioning

confidence: 99%

“…Both constraints in (26) make the solution to be convex signed distance function. The constraint |∇φ| = 1 is to guarantee that φ is a signed distance function, and the constraint φ ≥ 0 makes φ to be convex by Theorem 2.…”

Section: Convex Shape Prior With Signed Distance Functionsmentioning

confidence: 99%

Convex Shape Priors for Level Set Representation

Luo¹,

Tai²

2018

Preprint

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“…In the future, we will consider applying the weighted anisotropic-isotropic penalty to other types of segmentation models, such as piecewise-smooth models [27,23], the Potts models [46,49,52], and fuzzy segmentation models [39,30,31]. Since the two-stage methods are generally faster than the CV methods, we plan to develop a weighted anisotropic-isotropic variant as a faster alternative.…”

Section: Discussionmentioning

confidence: 99%

A Weighted Difference of Anisotropic and Isotropic Total Variation for Relaxed Mumford-Shah Color and Multiphase Image Segmentation

Bui¹,

Park²,

Lou³

et al. 2020

Preprint

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In a class of piecewise-constant image segmentation models, we incorporate a weighted difference of anisotropic and isotropic total variation (TV) to regularize the partition boundaries in an image. To deal with the weighted anisotropic-isotropic TV, we apply the differenceof-convex algorithm (DCA), where the subproblems can be minimized by the primal-dual hybrid gradient method (PDHG). As a result, we are able to design an alternating minimization algorithm to solve the proposed image segmentation models. The models and algorithms are further extended to segment color images and to perform multiphase segmentation. In the numerical experiments, we compare our proposed models with the Chan-Vese models that use either anisotropic or isotropic TV and the two-stage segmentation methods (denoising and then thresholding) on various images. The results demonstrate the effectiveness and robustness of incorporating weighted anisotropic-isotropic TV in image segmentation.

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“…There have been many approaches to this task and one of the most popular is the use of variational methods involving active contours; this technique will be the primary focus of this paper. Applications for segmentation are numerous: medical imaging [29,42,19], computer vision [33], stereo reconstruction [25,26,40], illusory contour [43,21,20], point-cloud surface reconstruction Copyright © SIAM Unauthorized reproduction of this article is prohibited [27], scene reconstruction from range data [13], and data clustering [41]. In this work, we consider the application of edge based segmentation with shape priors on difficult settings that include illusory contours, clutter and, occlusions.…”

Section: Introductionmentioning

confidence: 99%

Geodesic Active Contours with Shape Priors for Segmentation, Disocclusion, and Illusory Contour Capture

Householder¹

2020

SIURO

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Image segmentation is the task of finding salient regions of importance in an image. In this work, we take a curve evolution approach to this problem where we deform an initial curve in the inward normal direction with the objective of finding the boundaries of objects in an image. To achieve this, we propose a variational image segmentation model that incorporates a clique based shape signature with a geodesic active contours energy. The model scheme consists of evolving a parametric representation of an active contour to minimize the penalty that the model induces. This penalty is minimized when the curve is on the boundaries of objects in the image, areas with sudden change in pixel intensity i.e. light to dark. We demonstrate successful capture of illusory contours, segmentation of objects in a cluttered background, and segmentation of occluded objects.

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New region force for variational models in image segmentation and high dimensional data clustering

Cited by 13 publications

References 37 publications

Convex Shape Priors for Level Set Representation

Convex Shape Priors for Level Set Representation

A Weighted Difference of Anisotropic and Isotropic Total Variation for Relaxed Mumford-Shah Color and Multiphase Image Segmentation

Geodesic Active Contours with Shape Priors for Segmentation, Disocclusion, and Illusory Contour Capture

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