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13
Discrete Topological Transformations for Image Processing
, 2012
"... Topologybased image processing operators usually aim at transforming an image while preserving its topological characteristics. This chapter reviews some approaches which lead to efficient and exact algorithms for topological transformations in 2D, 3D and grayscale images. Some transformations whi ..."
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Topologybased image processing operators usually aim at transforming an image while preserving its topological characteristics. This chapter reviews some approaches which lead to efficient and exact algorithms for topological transformations in 2D, 3D and grayscale images. Some transformations which modify topology in a controlled manner are also described. Finally, based on the framework of critical kernels, we show how to design a topologically sound parallel thinning algorithm guided by a priority function.
2D Parallel Thinning Algorithms Based on IsthmusPreservation
"... Abstract—Skeletons are widely used shape descriptors which summarize the general form of binary objects. A technique to obtain skeletons is the thinning, that is an iterative layerbylayer erosion in a topologypreserving way. Conventional thinning algorithms preserve line endpoints to provide impor ..."
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Abstract—Skeletons are widely used shape descriptors which summarize the general form of binary objects. A technique to obtain skeletons is the thinning, that is an iterative layerbylayer erosion in a topologypreserving way. Conventional thinning algorithms preserve line endpoints to provide important geometric information relative to the object to be represented. Bertrand and Couprie proposed an alternative strategy by accumulating isthmus points that are line interior points. In this paper we present six new 2D parallel thinning algorithms that are derived from some sufficient conditions for topology preserving reductions and based on isthmuspreservation. I.
Presented by Ramzi MAHMOUDI Advised by Mohamed AKIL
, 2011
"... Common parallelization strategy of topological operators on SMP machines ..."
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On parallel thinning . . . critical kernels
, 2009
"... Critical kernels constitute a general framework in the category of abstract complexes for the study of parallel homotopic thinning in any dimension. In this article, we present new results linking critical kernels to minimal nonsimple sets (MNS) and Psimple points, which are notions conceived to st ..."
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Critical kernels constitute a general framework in the category of abstract complexes for the study of parallel homotopic thinning in any dimension. In this article, we present new results linking critical kernels to minimal nonsimple sets (MNS) and Psimple points, which are notions conceived to study parallel thinning in discrete grids. We show that these two previously introduced notions can be retrieved, better understood and enriched in the framework of critical kernels. In particular, we propose new characterizations which hold in dimensions 2, 3 and 4, and which lead to efficient algorithms for detecting Psimple points and minimal nonsimple sets.
Robust and Efficient Fully Parallel 2D Thinning Algorithm
"... Thinning is a wellknown iterative layerbylayer reduction operator to obtain skeletons of the binary objects. These skeletons are used as shape descriptors in many image processing, image analysis and pattern recognition applications. Thus obtaining topology preserved, centrally aligned and connec ..."
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Thinning is a wellknown iterative layerbylayer reduction operator to obtain skeletons of the binary objects. These skeletons are used as shape descriptors in many image processing, image analysis and pattern recognition applications. Thus obtaining topology preserved, centrally aligned and connected single pixel thin skeleton, without spurs and excessive erosions, and noise tolerant at preprocessing stage is essential to the success of later processing stages. The endpoint based algorithms preserve original shape but results in extra spurs due to the presence of unwanted endpoints. The isthmusbased algorithms produce less spurs but causes excessive erosions. Hence in this paper, we proposed an efficient fully parallel thinning algorithm for 2D binary images. we proposed a general methodology for removing noise prior to thinning. A comparison with recent algorithms by the proposed method showed the better skeleton quality, efficiency and robustness.
Comparative Survey of Thinning Algorithms
"... Abstract: Thinning or skeletonization is a process for reducing foreground regions in a binary image to a skeletal remnant that largely preserves the extent and connectivity of the original region while throwing away most of the original foreground. Thinning is commonly used in digital image process ..."
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Abstract: Thinning or skeletonization is a process for reducing foreground regions in a binary image to a skeletal remnant that largely preserves the extent and connectivity of the original region while throwing away most of the original foreground. Thinning is commonly used in digital image processing, pattern recognition, image analysis and not least, in signature verification. The goal of this paper is to introduce the most common thinning methodologies and propose a method to evaluate their performance, especially in the field of signature recognition. The proposed evaluation method is intended to be objective, therefore it takes into account various properties of a thinned skeleton and compares them to those of an ideal reference image. Fifteen different algorithms have been implemented and rated using this method, the results showed that different kinds of skeletonization techniques have different benefits and drawbacks, however none was found to give perfect results.
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"... New characterizations, in the framework of critical kernels, of 2D, 3D and 4D minimal nonsimple sets and Psimple points Critical kernels constitute a general framework in the category of abstract complexes for the study of parallel homotopic thinning in any dimension. In this article, we present n ..."
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New characterizations, in the framework of critical kernels, of 2D, 3D and 4D minimal nonsimple sets and Psimple points Critical kernels constitute a general framework in the category of abstract complexes for the study of parallel homotopic thinning in any dimension. In this article, we present new results linking critical kernels to minimal nonsimple sets (MNS) and Psimple points, which are notions conceived to study parallel thinning in discrete grids. We show that these two previously introduced notions can be retrieved, better understood and enriched in the framework of critical kernels. In particular, we propose new characterizations which hold in dimensions 2, 3 and 4, and which lead to efficient algorithms for detecting Psimple points and minimal nonsimple sets. Key Words: Parallel thinning, topology preservation, critical kernel, Psimple point, minimal nonsimple set, cubical