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2017 Italian Chapter Conference - Smart Tools and Apps in computer graphics, STAG 2017

作者： Livesu, Marco CNR IMATI Genoa Italy

ISBN: (纸本)9783038680482

We consider the problem of relaxing a discrete (n − 1) dimensional hyper surface defining the boundary between two adjacent n dimensional regions in a discrete segmentation. This problem often occurs in computer graphics and vision, where objects are represented by discrete entities such as pixel/voxel grids or polygonal/polyhedral meshes. A common approach consists in assigning to each element of the domain a value (or label). Elements sharing the same label belong to the same region, whereas elements with different labels belong to different regions. Segmentation boundaries are therefore only intrinsically defined, and amount to the union of the interfaces between adjacent elements having different label, which tend to be geometrically poor and expose a typical jagged behavior. We propose a relaxation scheme that replaces the original boundary with a smoother version of it, defined as the level set of a continuous function. The problem has already been considered in recent years, but current methods are specifically designed to relax curves on discrete 2-manifolds embedded in R3, and do not clearly scale to multiple discrete representations or to higher dimensions. Our biggest contribution is a smoothing operator that is based only on three canonical differential operators: namely the Laplacian, gradient and divergence. These operators are ubiquitous in applied mathematics, are available for a variety of discretization choices, and exist in any dimension. To the best of the author's knowledge, this is the first intrinsically dimension-independent method, and can be used to relax curves on 2-manifolds, surfaces in R3, or even hyper-surfaces in Rn. As such, not only it is useful to refine the boundaries of discrete segmentations, but also for applications like data mining, where clustering in high dimensional spaces often occur, and the refinement of the clusters' boundaries may be beneficial for classification algorithms. © 2017 The Author(s) Eurographics Proceedin

关键词： Data mining

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Structuring 3D medial skeletons: A comparative study 21

Structuring 3D medial skeletons: A comparative study

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21st International Symposium on vision, Modeling and Visualization, VMV 2016

作者： Delame, T. Kustra, J. Telea, A. INRIA France Philips Research Netherlands Institute Johann Bernoulli Univ. of Groningen Netherlands

ISBN: (纸本)9783038680253

Medial skeletons provide an effective alternative to boundary or volumetric representations for applications that focus on shape structure. This capability is provided by the skeletal structure, i.e., the curves and surfaces computed from centers of maximally inscribed balls by a process called structuration. Many several structuration methods exist, all having various challenges in terms of delivering a high-quality medial skeleton. This paper provides a first overview of existing structuration methods. We formally define the skeletal structure by giving its theoretical properties, and use these properties to propose quality criteria for structurations. We next review existing structuration methods and compare them using the established criteria. The obtained insights help both practitioners in choosing a suitable structuration method and researchers in further perfecting such methods. © 2016 The Author(s) Eurographics Proceedings © 2016 The Eurographics Association.

关键词： computer graphics

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Fast parallel solver for the levelset equations on unstructured meshes

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CONCURRENCY AND COMPUTATION-PRACTICE & EXPERIENCE 2015年第7期27卷 1639-1657页

作者： Fu, Zhisong Yakovlev, Sergey Kirby, Robert M. Whitaker, Ross T. Univ Utah Sci Comp & Imaging Inst Salt Lake City UT 84112 USA

The levelset method is a numerical technique that tracks the evolution of curves and surfaces governed by a nonlinear partial differential equation (levelset equation). It has applications within various research areas such as physics, chemistry, fluid mechanics, computer vision, and microchip fabrication. Applying the levelset method entails solving a set of nonlinear partial differential equations. This paper presents a parallel algorithm for solving the levelset equations on unstructured 2D and 3D meshes. By taking into account constraints and capabilities of different computing architectures, the method is suitable for both the coarse-grained parallelism found on CPU-based systems and the fine-grained parallelism of modern massively single instruction, multiple data architectures such as graphics processors. In order to solve the levelset equations efficiently, we combine the narrowband scheme with a domain decomposition that is adapted for several different architectures. We also introduce a novel parallelism strategy, which we call hybrid gathering, which allows regular and lock-free computations of local differential operators. Finally, we provide the detailed description of the implementation and data structures for the proposed strategies, as well as performance data for both CPU and graphics processing unit implementations. Copyright (c) 2014 John Wiley & Sons, Ltd.

关键词： levelset equations unstructured meshes parallel computing graphics processing unit

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A geodesic based approach for an accurate and invariant 3D surfaces representation 23

A geodesic based approach for an accurate and invariant 3D s...

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23rd International Conference in Central Europe on computer graphics, Visualization and computer vision, WSCG 2015

作者： Jribi, Majdi Ghorbel, Faouzi CRISTAL Laboratory GRIFT research group ENSI La Manouba University La manouba2010 Tunisia

ISBN: (纸本)9788086943664

In this paper, we propose a novel 3D invariant surface representation under the 3D motion group M(3). It is obtained by combining two main representations: the three-polar representation and the one defined by the radial line curves from a starting point. The retained invariant points correspond to the geometrical locations of the intersection between the two last representations. The approximation of the novel surfaces description method on the 3D discrete meshes is studied. Its accuracy for the 3D faces description and retrieval is evaluated in the mean of the Hausdorff shape distance.

关键词： Geodesy

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Direct Extraction of Feature curves from Volume Image for Illustration and Vectorization based on 2D/3D Curve Mapping

Direct Extraction of Feature Curves from Volume Image for Il...

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13th International Conference on computer-Aided Design and computer graphics (CAD/graphics)

作者： Wang, Liping Wang, Lili Hou, Fei Hao, Aimin Qin, Hong Beihang Univ Beijing 100191 Peoples R China SUNY Stony Brook Stony Brook NY USA

ISBN: (纸本)9781479925766

This paper proposes a parallel and direct semantic feature curve extraction method from 3D volume image for vectorization and illustration. Our approach is motivated by reconstructing 3D geometric information from multiple rendered images under multi-view in computer vision. The 2D rendered images are rich in the visual sense by color and opacity that convey the structure of volume data, so it is significant for the user to understand the structure of 3D volume data better if we can recover feature curves from those 2D images. Compared with conventional line extraction methods, which mainly focus on extracting feature curves from iso-surfaces in object space, we extract feature curves directly from volume images. Most of the computation can be computed in parallel on GPU with CUDA acceleration. © 2013 IEEE.

关键词： Extraction

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Direct Extraction of Feature curves from Volume Image for Illustration and Vectorization Based on 2D/3D Curve Mapping

Direct Extraction of Feature Curves from Volume Image for Il...

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IEEE International Conference on computer-Aided Design and computer graphics

作者： Liping Wang Lili Wang Fei Hou Aimin Hao Hong Qin Beihang University Stony Brook University (SUNY Stony Brook)

关键词： Feature extraction Three-dimensional displays graphics processing units Image color analysis Data mining Acceleration Educational institutions

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Markov surfaces: A probabilistic framework for user-assisted three-dimensional image segmentation

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computer vision AND IMAGE UNDERSTANDING 2011年第10期115卷 1375-1383页

作者： Pan, Yongsheng Jeong, Won-Ki Whitaker, Ross Univ Utah Sci Comp & Imaging Inst Salt Lake City UT 84112 USA Harvard Univ Sch Engn & Appl Sci Initiat Innovat Comp Cambridge MA 02138 USA

This paper presents Markov surfaces, a probabilistic algorithm for user-assisted segmentation of elongated structures in 3D images. The 3D segmentation problem is formulated as a path-finding problem, where path probabilities are described by Markov chains. Users define points, curves, or regions on 2D image slices, and the algorithm connects these user-defined features in a way that respects the underlying elongated structure in data. Transition probabilities in the Markov model are derived from intensity matches and interstice correspondences, which are generated from a slice-to-slice registration algorithm. Bezier interpolations between paths are applied to generate smooth surfaces. Subgrid accuracy is achieved by linear interpolations of image intensities and the interstice correspondences. Experimental results on synthetic and real data demonstrate that Markov surfaces can segment regions that are defined by texture, nearby context, and motion. A parallel implementation on a streaming parallel computer architecture, a graphics processor, makes the method interactive for 3D data. (C) 2011 Elsevier Inc. All rights reserved.

关键词： Image segmentation Probabilistic framework Markov chain GPU

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A Level Set Formulation of Geodesic Curvature Flow on Simplicial surfaces

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IEEE TRANSACTIONS ON VISUALIZATION AND computer graphics 2010年第4期16卷 647-662页

作者： Wu, Chunlin Tai, Xuecheng Nanyang Technol Univ Sch Phys & Math Sci Div Math Sci Singapore 637371 Singapore Univ Bergen Dept Math N-5020 Bergen Norway

Curvature flow (planar geometric heat flow) has been extensively applied to image processing, computer vision, and material science. To extend the numerical schemes and algorithms of this flow on surfaces is very significant for corresponding motions of curves and images defined on surfaces. In this work, we are interested in the geodesic curvature flow over triangulated surfaces using a level set formulation. First, we present the geodesic curvature flow equation on general smooth manifolds based on an energy minimization of curves. The equation is then discretized by a semi-implicit finite volume method (FVM). For convenience of description, we call the discretized geodesic curvature flow as dGCF. The existence and uniqueness of dGCF are discussed. The regularization behavior of dGCF is also studied. Finally, we apply our dGCF to three problems: the closed-curve evolution on manifolds, the discrete scale-space construction, and the edge detection of images painted on triangulated surfaces. Our method works for compact triangular meshes of arbitrary geometry and topology, as long as there are no degenerate triangles. The implementation of the method is also simple.

关键词： Geodesic curvature flow level set triangular mesh surfaces curve evolution scale-space edge detection

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2D and 3D level-set algorithms on GPU

2D and 3D level-set algorithms on GPU

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2010 12th International Workshop on Cellular Nanoscale Networks and their Applications, CNNA 2010

作者： Tornai, Ǵabor J. Cserey, Gÿorgy Faculty of Information Technology Ṕazḿany Ṕeter Catholic University Pŕater U. 50/A H-1083 Budapest Hungary Hungarian Academy of Sciences Ṕazḿany Ṕeter Catholic University Semmelweis University Pŕater U. 50/a Budapest H-1083 Hungary

ISBN: (纸本)9781424466795

Locating object boundaries, modeling shapes is still an interesting and important task in many applications such as computer vision, object detection, image segmentation and tracking. In this paper we show the implementation of 2D and 3D algorithms based on the level sets using the advantages residing in today's common GPUs. One main goal of this paper is to contribute a development and give one new local-parallel implementation of a fast level set based algorithm via the locally organized processing elements and memory. This algorithm can model and detect any object with arbitrary complex shape and can be applied to situations where no or very few a priori information is available. Our accelerated implementation can handle more initial curves and surfaces which can fuse or merge according to the requirements. This might be a good base to achieve fast and robust detection, segmentation or tracking in medical or autonomous tasks. © 2010 IEEE.

关键词： graphics processing unit

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Tessellating algebraic curves and surfaces using a-patches

Tessellating algebraic curves and surfaces using a-patches

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4th International Conference on computer graphics Theory and Applications, GRAPP 2009

作者： Luk, Curtis Mann, Stephen University of Waterloo 200 University Ave W. Waterloo ON Canada

ISBN: (纸本)9789898111678

This work approaches the problem of triangulating algebraic curves and surfaces with a subdivision-style algorithm using A-patches. An algebraic curve or surface is converted from the monomial basis to the Bernstein-Bezier basis over a simplex. If the coefficients are all positive or all negative, then the curve or surface does not pass through the domain simplex. If the scalar Bernstein coefficients are of mixed sign and have a layer separating the positive from the negative, then the patch is in A-patch format and can be efficiently tessellated. Cases of mixed sign without a separating layer are resolved by subdividing the structure into a set of smaller patches and repeating the algorithm. Using A-patches to generate a tessellation of the surface has the advantage of reducing the amount of subdi-vision required. And because of the A-patch properties, we are guaranteed that features within the designated region will not be missed.

关键词： Algebra

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