Some Parallel Thinning Algorithms for Digital Pictures

Stefanelli, R.; Rosenfeld, Azriel

doi:10.1145/321637.321646

Cited by 237 publications

(48 citation statements)

References 10 publications

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“…Since then, many 2D parallel thinning algorithms have been proposed, see in particular [41,35,1,32,8,15,14,19,11,2,30]. A fundamental property required for such algorithms is that they do preserve the topology of the original objects.…”

Section: Introductionmentioning

confidence: 99%

Two-Dimensional Parallel Thinning Algorithms Based on Critical Kernels

Bertrand

Couprie

2008

J Math Imaging Vis

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Critical kernels constitute a general framework settled in the category of abstract complexes for the study of parallel thinning in any dimension. The most fundamental result in this framework is that, if a subset Y of X contains the critical kernel of X, then Y is guaranteed to have "the same topology as X". Here, we focus on 2D structures in spaces of two and three dimensions. We introduce the notion of crucial pixel which permits to make a link with the framework of digital topology. Thanks to simple local characterizations, we are able to express thinning algorithms by the way of sets of masks. We propose several new parallel algorithms, which are both fast and simple to implement, to obtain symmetrical or non-symmetrical skeletons of 2D objects in 2D or 3D grids. We prove some properties of these skeletons, related to topology preservation, to minimality and to the inclusion of the topological axis which may be seen as a generalization of the medial axis. We also show how to use critical kernels in order to prove very simply the topological soundness of existing thinning schemes. At last, we make clear the link between critical kernels, minimal non-simple sets, and P-simple points.

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Section: Introductionmentioning

confidence: 99%

Two-Dimensional Parallel Thinning Algorithms Based on Critical Kernels

Bertrand

Couprie

2008

J Math Imaging Vis

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“…The images segmented by observers AH and VK differ in level of detail, and the resulting set, totaling forty segmented images, is available for download from the STARE project [13] in ppm file format, with resolution of 700x605 pixels. As recently it has been argued [19] that fractal analysis may be more sensitive to changes in vascular patterns when skeletal images of vascular trees are considered, rather then the original segmented images (which contain the vessel width information), in order to verify whether the vessel width information indeed does exert influence on the multifractal analysis, we have also performed skeletonization of the two downloaded sets using the eight connected Rosenfeld algorithm [20], to produce two additional sets of twenty images each. A typical normal and a pathological image, segmented by observers AH and VK (where images segmented by observer VK demonstrate a substantially…”

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confidence: 99%

Multifractal analysis of human retinal vessels

Stošić¹,

Stošić

2006

IEEE Trans. Med. Imaging

179

167

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In this work it is shown that vascular structures of the human retina represent geometrical multifractals, characterized by a hierarchy of exponents rather then a single fractal dimension. A number of retinal images from the STARE database (www.parl.clemson.edu/stare) are analyzed, corresponding to both normal and pathological states of the retina. In all studied cases a clearly multifractal behavior is observed, where capacity dimension is always found to be smaller then the information dimension, which is in turn always smaller then the correlation dimension, all the three being significantly lower then the DLA (Diffusion Limited Aggregation) fractal dimension. We also observe a tendency of images corresponding to the pathological states of the retina to have lower generalized dimensions and a shifted spectrum range, in comparison with the normal cases.PACS numbers: 61.43.Hv, 87.57.Nk Over the past decade, there have been several attempts [1,2,3,4,5,6] in the direction of employing the fractal dimension as a measure for quantifying the "state" of human retinal vessel structures (considered as geometrical objects), with the expectation that such analysis may contribute to automatic detection of pathological cases, and therefore to computerization of the diagnostic process. While this is certainly a valid question with possibly high impact on real world diagnostic issues, there are some issues that should be addressed before such investigations may prove useful for the standard clinical practice. First, the fact that retinal vessels represent "finite size" realizations of a fractal growth process, imposes questions about how exactly should one go about measuring the fractal dimension of a particular instance (e.g. an electronic image of a retinal vessel structure, taken from a given angle, with a given resolution and lightning conditions). A related question is to what extent these calculations may correspond to the limiting fractal (which would have been attained if the growth process could have been extended to infinity), or equivalently, to what degree they may be compared with calculations on other such finite instances. Although various issues related to these questions have already been addressed (for a current review see e.g. [6]), it seems that many of them remain open for further investigation. Second, some of these works [3,4] address the point that the retinal vessels may have different properties in different regions, and do indeed find different characteristics depending on the locale of measurement, although the procedures adopted in these works are only remotely related to established concepts of multifractality, and the corresponding commonly accepted procedures for its measurement (see e.g. [7,8,9,10,11,12] and references therein).In this work we concentrate on the latter of the above issues, that is, we show that the human retinal vessel * Electronic address: borko@ufpe.br structures are geometrical multifractals, characterized by a hierarchy of exponents rather then a single fractal dimens...

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“…Some thinning algorithms have been studied in order to obtain a skeleton of the fingerprint ridge lines. These methods are listed in the Reference section of this paper [7] [8]. Instead of using a conventional thinning method Weber proposed an algorithm which detects the minutiae starting from the thick-ridges in the binary image [9].…”

Section: Intoductionmentioning

confidence: 99%

Fingerprint Ridge Line Reconstruction

Qi¹

2005

Intelligent Information Processing II

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Abstract:Reconstruction of fingerprint ridge lines is a critical pre-processing step in the identification of poor quality fingerprint images. This paper presents a new fingerprint ridge line reconstruction approach by way of ridge line tracing. In our research, the fingerprint ridge line in a gray scale image is viewed as a track of a ridge segment moving along the ridge. The curve tracing problem is solved by the target tracking technique in computer vision. We first formulate the model of fingerprint ridge line segments and then apply a target tracking method to trace each of the ridge lines. In addition, a feedback technique is adopted to correct the fingerprint directional image in each tracing step in order to improve tracing accuracy. By connecting all the traced ridge line segments, a polyline reconstruction of the ridge line can be obtained. We objectively assess the performance of this approach by using NIST fingerprint images.

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Some Parallel Thinning Algorithms for Digital Pictures

Cited by 237 publications

References 10 publications

Two-Dimensional Parallel Thinning Algorithms Based on Critical Kernels

Two-Dimensional Parallel Thinning Algorithms Based on Critical Kernels

Multifractal analysis of human retinal vessels

Fingerprint Ridge Line Reconstruction

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