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Parallel Banding Algorithm to Compute Exact Distance Transform with the GPU ∗
"... We propose a Parallel Banding Algorithm (PBA) on the GPU to compute the exact Euclidean Distance Transform (EDT) for a binary image in 2D and higher dimensions. Partitioning the image into small bands to process and then merging them concurrently, PBA computes the exact EDT with optimal linear total ..."
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We propose a Parallel Banding Algorithm (PBA) on the GPU to compute the exact Euclidean Distance Transform (EDT) for a binary image in 2D and higher dimensions. Partitioning the image into small bands to process and then merging them concurrently, PBA computes the exact EDT with optimal linear total work, high level of parallelism and a good memory access pattern. This work is the first attempt to exploit the enormous power of the GPU in computing the exact EDT, while prior works are only on approximation. Compared to these other algorithms in our experiments, our exact algorithm is still a few times faster in 2D and 3D for most input sizes. We illustrate the use of our algorithm in applications such as computing the Euclidean skeleton using the integer medial axis transform, performing morphological operations of 3D volumetric data, and constructing 2D weighted centroidal Voronoi diagrams.
Robust skeletonization using the discrete lambdamedial axis
, 2011
"... Medial axes and skeletons are notoriously sensitive to contour irregularities. This lack of stability is a serious problem for applications in e.g. shape analysis and recognition. In 2005, Chazal and Lieutier introduced the λmedial axis as a new concept for computing the medial axis of a shape subj ..."
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Cited by 5 (3 self)
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Medial axes and skeletons are notoriously sensitive to contour irregularities. This lack of stability is a serious problem for applications in e.g. shape analysis and recognition. In 2005, Chazal and Lieutier introduced the λmedial axis as a new concept for computing the medial axis of a shape subject to single parameter filtering. The λmedial axis is stable under small shape perturbations, as proved by these authors. In this article, a discrete λmedial axis (DLMA) is introduced and compared with the recently introduced integer medial axis (GIMA). We show that DLMA provides measurably better results than GIMA, with regard to stability and sensibility to rotations. We give efficient algorithms to compute the DLMA, and we also introduce a variant of the DLMA which may be computed in lineartime.
Surface thinning in 3D cubical complexes
 13TH INTERNATIONAL WORKSHOP ON COMBINATORIAL IMAGE ANALYSIS (IWCIA'09), FRANCE
, 2009
"... We introduce a parallel thinning algorithm with directional substeps based on the collapse operation, which is guaranteed to preserve topology and to provide a thin result. Then, we propose two variants of a surfacepreserving thinning scheme, based on this parallel directional thinning algorithm. ..."
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Cited by 4 (2 self)
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We introduce a parallel thinning algorithm with directional substeps based on the collapse operation, which is guaranteed to preserve topology and to provide a thin result. Then, we propose two variants of a surfacepreserving thinning scheme, based on this parallel directional thinning algorithm. Finally, we propose a methodology to produce filtered surface skeletons, based on the above thinning methods and the recently introduced discrete λmedial axis.
Efficient Euclidean Distance Transform Using Perpendicular Bisector Segmentation
"... In this paper, we propose an efficient algorithm for computing the Euclidean distance transform of twodimensional binary image, called PBEDT (Perpendicular Bisector Euclidean Distance Transform). PBEDT is a twostage independent scan algorithm. In the first stage, PBEDT computes the distance from e ..."
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Cited by 2 (0 self)
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In this paper, we propose an efficient algorithm for computing the Euclidean distance transform of twodimensional binary image, called PBEDT (Perpendicular Bisector Euclidean Distance Transform). PBEDT is a twostage independent scan algorithm. In the first stage, PBEDT computes the distance from each point to its closest feature point in the same column using one time columnwise scan. In the second stage, PBEDT computes the distance transform for each point by row with intermediate results of the previous stage. By using the geometric properties of the perpendicular bisector, PBEDT directly computes the segmentation by feature points for each row and each segment corresponding to one feature point. Furthermore, by using integer arithmetic to avoid time consuming float operations, PBEDT still achieves exact results. All these methods reduce the computational complexity significantly. Consequently, an efficient and exact linear time Euclidean distance transform algorithm is implemented. Detailed comparison with stateoftheart linear time Euclidean distance transform algorithms shows that PBEDT is the fastest on most cases, and also the most stable one with respect to image contents.
A stable skeletonization for tabletop gesture recognition
 Computational Science and Its Applications ICCSA
, 2010
"... All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. ..."
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All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.
A 3D curvilinear skeletonization algorithm with application to path tracing
 DISCRETE GEOMETRY FOR COMPUTER IMAGERY, SPAIN
, 2013
"... ..."
The final publication is available at link.springer.com. Qualitative Comparison of Contractionbased Curve Skeletonization Methods
"... Abstract. In recent years, many new methods have been proposed for extracting curve skeletons of 3D shapes, using a meshcontraction principle. However, it is still unclear how these methods perform with respect to each other, and with respect to earlier voxelbased skeletonization methods, from the ..."
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Abstract. In recent years, many new methods have been proposed for extracting curve skeletons of 3D shapes, using a meshcontraction principle. However, it is still unclear how these methods perform with respect to each other, and with respect to earlier voxelbased skeletonization methods, from the viewpoint of certain quality criteria known from the literature. In this study, we compare six recent contractionbased curveskeletonization methods and one recent voxelbased method, against six accepted quality criteria, on a set of complex 3D shapes. Our results reveal previously unknown limitations of the compared methods, and link these limitations to algorithmic aspects of the studied methods.
Feature Preserving Sketching of Volume Data
"... In this paper, we present a novel method for extracting feature lines from volume data sets. This leads to a reduction of visual complexity and provides an abstraction of the original data to important structural features. We employ a new iteratively reweighted leastsquares approach that allows us ..."
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In this paper, we present a novel method for extracting feature lines from volume data sets. This leads to a reduction of visual complexity and provides an abstraction of the original data to important structural features. We employ a new iteratively reweighted leastsquares approach that allows us to detect sharp creases and to preserve important features such as corners or intersection of feature lines accurately. Traditional leastsquares methods This is important for both visual quality as well as reliable further processing in feature detection algorithms. Our algorithm is efficient and easy to implement, and nevertheless effective and robust to noise. We show results for a number of different data sets.
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"... s a nim rop rite niza spec d co ferences between skeletons obtained by different methods. with rieval, it two ed by Curve s hape a and practical contexts. Recognizing these challenges, Cornea et al. [3] have presented a taxonomy of curve skeletonization methods and the way these satisfy a set of des ..."
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s a nim rop rite niza spec d co ferences between skeletons obtained by different methods. with rieval, it two ed by Curve s hape a and practical contexts. Recognizing these challenges, Cornea et al. [3] have presented a taxonomy of curve skeletonization methods and the way these satisfy a set of desirable skeletal properties, and illustrated these for four such methods. Since this publication, several new s by presenting a tion methods. In thods. In a after their was published. We use in our comparison the same desirabl ria as in [3]. In addition, we also propose a detailed comp that aims to provide a finegrained detail view on the subtle ences between skeletons computed by different methods, including comparisons of curve with surface skeletons. Our results offer additional insight in limitations and challenges of current methods which, to our knowledge, have not been highlighted so far. These results represent further support for the quest of designing better skeletonization methods. q This paper has been recommended for acceptance by Cris L. Luengo Hendriks.
1Pattern Recognition Letters journal homepage: www.elsevier.com Computing Refined Skeletal Features from Medial Point Clouds
"... Medial representations have been widely used for many shape analysis and processing tasks. Large and complex 3D shapes are, in this context, a challenging case. Recently, several methods have been proposed that extract pointbased medial surfaces with high accuracy and computational scalability. How ..."
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Medial representations have been widely used for many shape analysis and processing tasks. Large and complex 3D shapes are, in this context, a challenging case. Recently, several methods have been proposed that extract pointbased medial surfaces with high accuracy and computational scalability. However, the resulting medial clouds are of limited use for shape processing due to the difficulty of computing refined medial features from such clouds. In this paper, we show how to bridge the gap between having a raw medial cloud and enriching this cloud with feature points, medialpoint classification, medial axis decomposition into sheets, robust regularization, and Ynetwork extraction. We further show how such properties can be used to support several shape processing sample applications including edge detection and shape segmentation, for a wide range of complex 3D shapes. c © 2015 Elsevier Ltd. All rights reserved. 1.