Convexity Shape Prior for Level Set-Based Image Segmentation Method

Yan, Shi; Tai, Xue–Cheng; Li, Jun; Huang, Haiyang

doi:10.1109/tip.2020.2998981

Cited by 41 publications

(17 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [1], an Euler's Elastica energy-based model was studied for convex contours by penalizing the integral of absolute curvatures. Recently, the continuous methods or curvature-based methods were developed further in [24,37]. For a given object in 2-dimensional space, it was proved in [37] that the non-negative Laplacian of the associated signed distance function [32] (SDF) is sufficient to guarantee the convexity of shapes.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, the continuous methods or curvature-based methods were developed further in [24,37]. For a given object in 2-dimensional space, it was proved in [37] that the non-negative Laplacian of the associated signed distance function [32] (SDF) is sufficient to guarantee the convexity of shapes. In [24], the authors also proved that this condition is also necessary.…”

Section: Introductionmentioning

confidence: 99%

“…This method has also been extended for multiple convex objects segmentation in [25]. Projection algorithm and the alternating direction method of multipliers (ADMM) were presented in [24,37].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Level Set Representation Method for $N$-Dimensional Convex Shape and Applications

Li¹

2021

CMR

View full text Add to dashboard Cite

In this work, we present a new method for convex shape representation, which is regardless of the dimension of the concerned objects, using level-set approaches. To the best of our knowledge, the proposed prior is the first one which can work for high dimensional objects. Convexity prior is very useful for object completion in computer vision. It is a very challenging task to represent high dimensional convex objects. In this paper, we first prove that the convexity of the considered object is equivalent to the convexity of the associated signed distance function. Then, the second order condition of convex functions is used to characterize the shape convexity equivalently. We apply this new method to two applications: object segmentation with convexity prior and convex hull problem (especially with outliers). For both applications, the involved problems can be written as a general optimization problem with three constraints. An algorithm based on the alternating direction method of multipliers is presented for the optimization problem. Numerical experiments are conducted to verify the effectiveness of the proposed representation method and algorithm.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Level Set Representation Method for $N$-Dimensional Convex Shape and Applications

Li¹

2021

CMR

View full text Add to dashboard Cite

show abstract

“…Recently, shape-based active contour models have been constructed to regularize the smoothness of the contour for image segmentation [13][14][15][16][17]. Qin et al [18] developed a level set framework for bladder MR image segmentation, which used an adaptive shape priors constrained to obtain the desired boundaries.…”

Section: Introductionmentioning

confidence: 99%

A Shape Prior-Based Active Contour Model for Automatic Images Segmentation

Jiang

2020

IEEE Access

View full text Add to dashboard Cite

Due to the variable shapes of objects, high noise intensity and complex environments, the field of image segmentation still has great challenges. To address these issues, we present a new image segmentation strategy based on active contour model and shape priori information, which can accurately and efficiently segment various images. The data fitting term, inspired by Chan-Vese (C-V) model, is used to guide the curve evolving to desired target boundary. Meanwhile, the contour is utilized to reconstruct a prior shape so that can help to deal with images in the presence of complex target. After that, the length regularity term of energy functional is incorporated to ensure the stable calculation of the evolution curve. The quantitative and qualitative experiments on various real and medical images indicate that our method is more efficient and accurate than the existing unified models.

show abstract

“…This forms the first Gamma-convergence family for variational image segmentation. The second family is the variational level set method [32,28,33] based 150 LU TAN, LING LI, SENJIAN AN AND ZHENKUAN PAN piece-wise constant approximation of the Mumford-Shah model. In 2001, Chan and Vese proposed the two-phase Chan-Vese model [11], which is especially applicable to the circumstance of blurring or discontinuous boundaries.…”

mentioning

confidence: 99%

Nonlinear diffusion based image segmentation using two fast algorithms

Liu¹,

Li²,

An³

et al. 2019

Mathematical Foundations of Computing

View full text Add to dashboard Cite

In this paper, a new variational model is proposed for image segmentation based on active contours, nonlinear diffusion and level sets. It includes a Chan-Vese model-based data fitting term and a regularized term that uses the potential functions (PF) of nonlinear diffusion. The former term can segment the image by region partition instead of having to rely on the edge information. The latter term is capable of automatically preserving image edges as well as smoothing noisy regions. To improve computational efficiency, the implementation of the proposed model does not directly solve the high order nonlinear partial differential equations and instead exploit the efficient alternating direction method of multipliers (ADMM), which allows the use of fast Fourier transform (FFT), analytical generalized soft thresholding equation, and projection formula. In particular, we creatively propose a new fast algorithm, normal vector projection method (NVPM), based on alternating optimization method and normal vector projection. Its stability can be the same as ADMM and it has faster convergence ability. Extensive numerical experiments on grey and colour images validate the effectiveness of the proposed model and the efficiency of the algorithms.

show abstract

Convexity Shape Prior for Level Set-Based Image Segmentation Method

Cited by 41 publications

References 32 publications

A Level Set Representation Method for $N$-Dimensional Convex Shape and Applications

A Level Set Representation Method for $N$-Dimensional Convex Shape and Applications

A Shape Prior-Based Active Contour Model for Automatic Images Segmentation

Nonlinear diffusion based image segmentation using two fast algorithms

Contact Info

Product

Resources

About