Topology-Preserving Image Segmentation by Beltrami Representation of Shapes

Chan, Hei Long; Yan, Shi; Lui, Lok Ming; Tai, Xue–Cheng

doi:10.1007/s10851-017-0767-8

Cited by 18 publications

(7 citation statements)

References 34 publications

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“…We note that for these 2D and 3D examples, our proposed model (18) possesses the same advantage with [10]: the shapes of the priors do not need to be similar with the target objectives. However, our proposed model (18) can deal with the 3D segmentation, which is a bottleneck of the registration-based segmentation model using the Beltrami representation (11).…”

Section: Remarkmentioning

confidence: 90%

“…Next, we review a registration-based segmentation model using the Beltrami representation proposed in [10]. Before reviewing this work, we briefly recall the quasi-conformal theory.…”

Section: Registration-based Segmentationmentioning

confidence: 99%

“…In this work, we consider the topological structure of the target object as the prior information. In 2018, Chan et al proposed a topology-preserving quasiconformal-based segmentation model [10]. The main idea of this work is to bijectively deform a reference template with the prescribed topology to segment the target object in an image.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, our main goal is to extend the idea of [10] to 3D segmentation. More specifically, we propose a novel 3D topology-preserving registration-based segmentation model with the hyperelastic regularization [7,25].…”

Section: Introductionmentioning

confidence: 99%

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Topology-Preserving 3D Image Segmentation Based On Hyperelastic Regularization

Zhang

Lui

2021

Preprint

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Image segmentation is to extract meaningful objects from a given image. For degraded images due to occlusions, obscurities or noises, the accuracy of the segmentation result can be severely affected. To alleviate this problem, prior information about the target object is usually introduced. In [10], a topology-preserving registration-based segmentation model was proposed, which is restricted to segment 2D images only. In this paper, we propose a novel 3D topologypreserving registration-based segmentation model with the hyperelastic regularization, which can handle both 2D and 3D images. The existence of the solution of the proposed model is established. We also propose a converging iterative scheme to solve the proposed model. Numerical experiments have been carried out on the synthetic and real images, which demonstrate the effectiveness of our proposed model.

show abstract

Section: Remarkmentioning

confidence: 90%

“…Next, we review a registration-based segmentation model using the Beltrami representation proposed in [10]. Before reviewing this work, we briefly recall the quasi-conformal theory.…”

Section: Registration-based Segmentationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Topology-Preserving 3D Image Segmentation Based On Hyperelastic Regularization

Zhang

Lui

2021

Preprint

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show abstract

“…Another example is the segmentation of objects with complicated interiors, noises, or occlusions, where a topological constraint can be used to prevent over-segmentation, i.e., the forming of "holes" due to image complexity [2], or under-segmentation, i.e., when the contours of separate objects merge. Much active research is undergone in the area, such as image segmentation and registration using the Beltrami representation of shapes [3] and non-local shape descriptors [4,5], multi-label image segmentation with preserved topology [6], and min-cut/max-flow segmentation using topology priors [7].…”

Section: Introductionmentioning

confidence: 99%

Using the Split Bregman Algorithm to Solve the Self-repelling Snakes Model

et al. 2022

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Preserving contour topology during image segmentation is useful in many practical scenarios. By keeping the contours isomorphic, it is possible to prevent over-segmentation and under-segmentation, as well as to adhere to given topologies. The Self-repelling Snakes model (SR) is a variational model that preserves contour topology by combining a non-local repulsion term with the geodesic active contour model. The SR is traditionally solved using the additive operator splitting (AOS) scheme. In our paper, we propose an alternative solution to the SR using the Split Bregman method. Our algorithm breaks the problem down into simpler sub-problems to use lower-order evolution equations and a simple projection scheme rather than re-initialization. The sub-problems can be solved via fast Fourier transform or an approximate soft thresholding formula which maintains stability, shortening the convergence time, and reduces the memory requirement. The Split Bregman and AOS algorithms are compared theoretically and experimentally.

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Recent Development of Medical Shape Analysis via Computational Quasi-Conformal Geometry

Chan¹,

Lui²

2021

Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging

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Topology-Preserving Image Segmentation by Beltrami Representation of Shapes

Cited by 18 publications

References 34 publications

Topology-Preserving 3D Image Segmentation Based On Hyperelastic Regularization

Topology-Preserving 3D Image Segmentation Based On Hyperelastic Regularization

Using the Split Bregman Algorithm to Solve the Self-repelling Snakes Model

Recent Development of Medical Shape Analysis via Computational Quasi-Conformal Geometry

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