Multi-object Convexity Shape Prior for Segmentation

Gorelick, Lena; Veksler, Olga

doi:10.1007/978-3-319-78199-0_30

Cited by 8 publications

(12 citation statements)

References 17 publications

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“…The results are presented in figure 5. The radius of the radial functions for the images from left to right in figure 5 are [4,10,14,20], [5,10,15,24] and [6,9,16,30], respectively. By comparing the results with different r i s, we can safely draw a conclusion that the proposed method is robust to the choices of the r i s.…”

Section: Sensitivity To the Radiusmentioning

confidence: 99%

Convex Shape Representation with Binary Labels for Image Segmentation: Models and Fast Algorithms

Luo,

Tai,

Wang

2020

Preprint

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We present a novel and effective binary representation for convex shapes. We show the equivalence between the shape convexity and some properties of the associated indicator function. The proposed method has two advantages. Firstly, the representation is based on a simple inequality constraint on the binary function rather than the definition of convex shapes, which allows us to obtain efficient algorithms for various applications with convexity prior. Secondly, this method is independent of the dimension of the concerned shape. In order to show the effectiveness of the proposed representation approach, we incorporate it with a probability based model for object segmentation with convexity prior. Efficient algorithms are given to solve the proposed models using Lagrange multiplier methods and linear approximations. Various experiments are given to show the superiority of the proposed methods.

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Section: Sensitivity To the Radiusmentioning

confidence: 99%

Convex Shape Representation with Binary Labels for Image Segmentation: Models and Fast Algorithms

Luo,

Tai,

Wang

2020

Preprint

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“…The energy minimization can be addressed by the graph cut algorithm [4]. In [18], [19], the convexity prior was incorporated into graphbased segmentation framework to solve multi-region segmentation tasks. The hedgehog-like shape prior [20] generalizes the geodesic star convexity constraint [19] to enlarge the applicable scope of the original case.…”

Section: Introductionmentioning

confidence: 99%

“…In [18], [19], the convexity prior was incorporated into graphbased segmentation framework to solve multi-region segmentation tasks. The hedgehog-like shape prior [20] generalizes the geodesic star convexity constraint [19] to enlarge the applicable scope of the original case. Isack et al [21] proposed a flexible k-convexity prior-based segmentation model which allows overlaps between different regions.…”

Section: Introductionmentioning

confidence: 99%

Geodesic Models with Convexity Shape Prior

Chen,

Mirebeau,

Shu

et al. 2021

Preprint

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The minimal geodesic models based on the Eikonal equations are capable of finding suitable solutions in various image segmentation scenarios. Existing geodesic-based segmentation approaches usually exploit image features in conjunction with geometric regularization terms, such as Euclidean curve length or curvature-penalized length, for computing geodesic curves. In this paper, we take into account a more complicated problem: finding curvature-penalized geodesic paths with a convexity shape prior. We establish new geodesic models relying on the strategy of orientation-lifting, by which a planar curve can be mapped to an high-dimensional orientation-dependent space. The convexity shape prior serves as a constraint for the construction of local geodesic metrics encoding a particular curvature constraint. Then the geodesic distances and the corresponding closed geodesic paths in the orientation-lifted space can be efficiently computed through state-of-the-art Hamiltonian fast marching method. In addition, we apply the proposed geodesic models to the active contours, leading to efficient interactive image segmentation algorithms that preserve the advantages of convexity shape prior and curvature penalization.

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“…outside) the considered object. This method was then generalized for multiple convex objects segmentation in [13]. In [30], the authors proposed a segmentation model that can handle multiple convex objects.…”

Section: Introductionmentioning

confidence: 99%

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

Li¹

2021

CMR

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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.

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Multi-object Convexity Shape Prior for Segmentation

Cited by 8 publications

References 17 publications

Convex Shape Representation with Binary Labels for Image Segmentation: Models and Fast Algorithms

Convex Shape Representation with Binary Labels for Image Segmentation: Models and Fast Algorithms

Geodesic Models with Convexity Shape Prior

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

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