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Affine invariant detection of perceptually parallel 3D planar curves

Dinggang Shen, Horace H.S. Ip, Eam Khwang Teoh
2000 Pattern Recognition  
Moreover, the proposed technique allows all signi"cant pairs of parallel segments within any two curves in the scene to be detected.  ...  The problem of parallelism detection between two curves has been formulated in this paper as a line detection problem within an azne-invariant local similarity matrix computed for the two curves.  ...  Interestingly, there may exist a set of lines within the matrix, which gives the set of potential parallel curve segments in the two curves.  ... 
doi:10.1016/s0031-3203(99)00172-7 fatcat:avbxcwrcobcd3obpbjlxedrhym

An optimal parallel algorithm for digital curve segmentation

Peter Damaschke
1997 Theoretical Computer Science  
The classical problem of partitioning a digital curve into a minimum number of digital line segments, which is of interest in digital image processsing, turns out to be a special case of this, and can  ...  This strengthens and generalizes all known algorithmic results about digital curve segmentation. As a further prerequisite we use the Dorst-Smeulders parametrization of digital line segments.  ...  Optimal parallel segmentation of digital curves Our digital curve segmentation algorithm we are going to present now assigns to each digital line segment some convex polygon in another plane, called the  ... 
doi:10.1016/s0304-3975(96)00227-7 fatcat:lh5ds4knvnb7hgandqf27q4sie

A Parallel Implementation for Computing the Region-Adjacency-Tree of a Segmentation of a 2D Digital Image [chapter]

Fernando Díaz-del-Río, Pedro Real, Darian Onchis
2016 Lecture Notes in Computer Science  
A design and implementation of a parallel algorithm for computing the Region-Adjacency Tree of a given segmentation of a 2D digital image is given.  ...  The technique is based on a suitable distributed use of the algorithm for computing a Homological Spanning Forest (HSF) structure for each connected region of the segmentation and a classical geometric  ...  The first author gratefully acknowledges the support of the Spanish Ministry of Science and Innovation (project Biosense, TEC2012-37868-C04-02), the second author the support of the V Plan Propio de la  ... 
doi:10.1007/978-3-319-30285-0_9 pmid:28547005 pmcid:PMC5441516 fatcat:iegz267qjvbhphgmaqo4otisxa

Page 6251 of Mathematical Reviews Vol. , Issue 96j [page]

1996 Mathematical Reviews  
Summary: “Partitioning digital curves into digital straight line segments (DLSs) is important in several branches of image pro- cesssing. We present a parallel algorithm for this task which runs  ...  Summary: “In this paper we give an answer to the problem of enumerating the combinatorially distinct segments of given length in digital lines and rectangular blocks of given shape in digital planes.  ... 

Convexity Rule for Shape Decomposition Based on Discrete Contour Evolution

Longin Jan Latecki, Rolf Lakämper
1999 Computer Vision and Image Understanding  
This rule determines not only parts of boundary curves but directly the visual parts of objects. Moreover, the stages of the evolution hierarchy induce a hierarchical structure of the visual parts.  ...  We solve this problem by identifying convex parts at different stages of a proposed contour evolution method in which significant visual parts will become convex object parts at higher stages of the evolution  ...  ACKNOWLEDGMENTS The work of Longin Jan Latecki was supported by Project Ec 170/1-1 of the German Research Foundation (DFG).  ... 
doi:10.1006/cviu.1998.0738 fatcat:ngcqpcbbcffvnpenaxsiq23uja

On cellular straight line segments

Chul E. Kim
1982 Computer Graphics and Image Processing  
It was used in [71 to study digital curves and digital straight line segments and in [4] to characterize convex digital regions in terms of digital straight line segments.  ...  As was shown in [7] , if the radius is infinite, that is, the arc is a straight line segment, then its digital image is always a digital arc. ___/_ I I I I I I I1 The digital image of a curve is a  ... 
doi:10.1016/0146-664x(82)90005-3 fatcat:jfh57umisne6fpztkjslzys6dq

Computational comparison of voting-based and arrangement-based schema for digital line detection

Tetsuo Asano, Yasuyuki Kawamura
1999 Canadian Conference on Computational Geometry  
Then, we need some de nition of digital line segments probably based on another de nition of density of edge points along lines.  ...  Detecting Line Segments Considering Point Density One of the disadvantages of the methods described so far is that it is hard to extract line segments instead of in nite lines, because their basic informations  ... 
dblp:conf/cccg/AsanoK99 fatcat:tmmlfupjdngk5c5uwmoe6uzmqq

Polygonal Approximation of Digital Planar Curve Using Novel Significant Measure [chapter]

Mangayarkarasi Ramaiah, Dilip Kumar Prasad
2020 Parallel Manipulators [Working Title]  
The proposed method differentiates between the situations when a point on the curve between two points on a curve projects directly upon the line segment or beyond this line segment.  ...  Moreover, the technique may find its application in parallel manipulators in detecting target boundary of an image with varying scale.  ...  But the authors thank all anonymous reviewers for their comments on an earlier manuscript for improving the quality of the chapter.  ... 
doi:10.5772/intechopen.92145 fatcat:g5quhn5hcrepjmw5a2vvkcghli

Minimum-Length Polygons in Simple Cube-Curves [chapter]

Reinhard Klette, Thomas Bülow
2000 Lecture Notes in Computer Science  
The length of such a simple digital curve is defined to be the length of the minimum-length polygonal curve fully contained and complete in the tube of this digital curve.  ...  This paper shows that critical edges are the only possible locations of vertices of the minimum-length polygonal curve fully contained and complete in the tube of this digital curve.  ...  This is the first line segment of the desired initial polygonal curve P 0 .  ... 
doi:10.1007/3-540-44438-6_38 fatcat:guldn7l5yrd6nnnws566hvv5dy

Approximation of 3D Shortest Polygons in Simple Cube Curves [chapter]

Thomas Bülow, Reinhard Klette
2001 Lecture Notes in Computer Science  
One possible definition of the length of a digitized curve in 3D is the length of the shortest polygonal curve lying entirely in a cube curve.  ...  One possible de nition of the length of a digitized curve i n 3D is the length of the shortest polygonal curve lying entirely in a cube curve.  ...  straight line segments, all contained in g.  ... 
doi:10.1007/3-540-45576-0_17 fatcat:yfnenxld5zhw7dkkvyfinn5x44

Preface

Sébastien Fourey, Gabor T. Herman, T.Yung Kong
2001 Electronical Notes in Theoretical Computer Science  
The invited paper by Rosenfeld and Klette deals with digital straight segments (digitizations of straight line segments in the Euclidean plane).  ...  ; improvement of 3D parallel thinning operators; a Jordan curve theorem for a class of Cech-closure operations on Z 2 ; sets of "tiles" in R n with the Helly property; hypergraphs with the Helly property  ... 
doi:10.1016/s1571-0661(05)81055-2 fatcat:gxyctocugvge7bstbfpao4b3fy

Length estimation of digital curves

Reinhard Klette, Vladimir V. Kovalevsky, Ben Yip, Longin J. Latecki, Robert A. Melter, David M. Mount, Angela Y. Wu
1999 Vision Geometry VIII  
The paper details two linear-time algorithms, one for the partition of the boundary line of a digital region into digital straight segments, and one for calculating the minimum length polygon within a  ...  Both techniques allow the estimation of the length of digital curves or the perimeter of digital regions due to known multigrid convergence theorems.  ...  The boundary line is a closed-loop polygonal curve. The boundary line may be subdivided into digital straight line segments (DSS's). The exact denition of a DSS is given in Section 2.2.  ... 
doi:10.1117/12.364118 fatcat:iluuohgtfrduddvvlnf6t5kcqq

Supercover Model and Digital Straight Line Recognition on Irregular Isothetic Grids [chapter]

David Coeurjolly
2005 Lecture Notes in Computer Science  
On the classical discrete grid, the analysis of digital straight lines (DSL for short) has been intensively studied for nearly half a century.  ...  More precisely, our goal is to define geometrical properties on irregular isothetic grids that are tilings of the Euclidean plane with different sized axis parallel rectangles.  ...  Introduction When a straight line is digitized on a square grid, we obtain a sequence of grid points defining a digital straight-line segment.  ... 
doi:10.1007/978-3-540-31965-8_29 fatcat:rke3smkvnrayja2m62qsla26wm

Digital straightness—a review

Reinhard Klette, Azriel Rosenfeld
2004 Discrete Applied Mathematics  
A digital arc is called 'straight' if it is the digitization of a straight line segment.  ...  Since the concept of digital straightness was introduced in the mid-1970s, dozens of papers on the subject have appeared; many characterizations of digital straight lines have been formulated, and many  ...  On the parallel line to the left of the digital curve we deÿne a negative base between grid points StartN and EndN; and on the parallel line to the right of the digital curve we deÿne a positive base,  ... 
doi:10.1016/j.dam.2002.12.001 fatcat:qha3kwh3zvgdpkwr4is6ymrema

Cold and Freezing Sets in the Digital Plane [article]

Laurence Boxer
2022 arXiv   pre-print
We study some properties of cold sets for digital images in the digital plane, and we examine some relationships between cold sets and freezing sets.  ...  Cold sets and freezing sets belong to the theory of (approximate) fixed points for continuous self-maps on digital images.  ...  [4] Let s 1 and s 2 be sides of a digital disk X ⊂ Z 2 , i.e., maximal digital line segments in a bounding curve S of X, such that s 1 ∩ s 2 = {p} ⊂ X.  ... 
arXiv:2106.06018v3 fatcat:geipdm6doncflkq3kphenbfcv4
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