Curvature Regularity for Multi-label Problems - Standard and Customized Linear Programming

Schoenemann, Thomas; Kuang, Yubin; Kahl, Fredrik

doi:10.1007/978-3-642-23094-3_12

Cited by 4 publications

(4 citation statements)

References 29 publications

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“…In this paper, we concentrate on improving the methodology for optimizing the functional and we compare with current state-of-the-art methods, cf. [2,3,8]. Experimental results are mainly given for segmentation, but other applications include surface completion [9] and inpainting [3,10].…”

Section: Curvature In Visionmentioning

confidence: 99%

“…To enforce consistency between the region and boundary variables, surface continuation constraints [3] are used in the 2D case. We use completely analogous constrains (8) in three dimensions.…”

Section: Length and Area Regularizationmentioning

confidence: 99%

“…The constraints introduced by [3] admit too many feasible solutions, which is discussed in the recent work [8]. The problem is illustrated in Fig.…”

Section: Avoiding Extraneous Arcsmentioning

confidence: 99%

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Curvature Regularization for Curves and Surfaces in a Global Optimization Framework

Strandmark

Kahl

2011

Lecture Notes in Computer Science

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Abstract. Length and area regularization are commonplace for inverse problems today. It has however turned out to be much more difficult to incorporate a curvature prior. In this paper we propose several improvements to a recently proposed framework based on global optimization. We identify and solve an issue with extraneous arcs in the original formulation by introducing region consistency constraints. The mesh geometry is analyzed both from a theoretical and experimental viewpoint and hexagonal meshes are shown to be superior. We demonstrate that adaptively generated meshes significantly improve the performance. Our final contribution is that we generalize the framework to handle mean curvature regularization for 3D surface completion and segmentation.

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Section: Curvature In Visionmentioning

confidence: 99%

Section: Length and Area Regularizationmentioning

confidence: 99%

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Curvature Regularization for Curves and Surfaces in a Global Optimization Framework

Strandmark

Kahl

2011

Lecture Notes in Computer Science

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“…In the mean time, curvature regularity for region based segmentation approach has drawn lots of attentions [104,106,105,47]. A linear programming relaxation is proposed and extended in [106], they are solving linear programming relaxation of an integer optimization formula of the problem. Due to the size of the linear program, the computation complexity is very heavy compared to our graph cuts approach.…”

Section: Curvature Based Variational Modelmentioning

confidence: 99%

Fast numerical methods for image restoration

Shi¹

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Foremost, I would like to express my deep appreciation to my supervisor, Prof. Xue-Cheng Tai for his wise guidance and encouraging engagement in supervising my PhD study these four years. He had the phone interview with me, introduced me to the interesting imaging field, led me to learn more and deeper, supported me to investigate the beauty of mathematics. I really appreciate all his help and suggestions as a supervisor, family and friend. I also want to thank for his generous financial supports that gave me the chance to travel for conference. I am happy to live and study at Nanyang Technological University. I also enjoy the lively and productive environment of the School of Physical and Mathematical Sciences. In particular, I appreciate the management and leadership of Prof. San

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Curvature Prior for MRF-Based Segmentation and Shape Inpainting

Shekhovtsov

Kohli

Rother

2012

Lecture Notes in Computer Science

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Most image labeling problems such as segmentation and image reconstruction are fundamentally ill-posed and suffer from ambiguities and noise. Higher order image priors encode high level structural dependencies between pixels and are key to overcoming these problems. However, these priors in general lead to computationally intractable models. This paper addresses the problem of discovering compact representations of higher order priors which allow efficient inference. We propose a framework for solving this problem which uses a recently proposed representation of higher order functions where they are encoded as lower envelopes of linear functions. Maximum a Posterior inference on our learned models reduces to minimizing a pairwise function of discrete variables, which can be done approximately using standard methods. Although this is a primarily theoretical paper, we also demonstrate the practical effectiveness of our framework on the problem of learning a shape prior for image segmentation and reconstruction. We show that our framework can learn a compact representation that approximates a prior that encourages low curvature shapes. We evaluate the approximation accuracy, discuss properties of the trained model, and show various results for shape inpainting and image segmentation.

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Curvature Regularity for Multi-label Problems - Standard and Customized Linear Programming

Cited by 4 publications

References 29 publications

Curvature Regularization for Curves and Surfaces in a Global Optimization Framework

Curvature Regularization for Curves and Surfaces in a Global Optimization Framework

Fast numerical methods for image restoration

Curvature Prior for MRF-Based Segmentation and Shape Inpainting

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