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PATTERN RECOGNITION 2019年 95卷 247-260页

作者： Bribiesca, Ernesto Univ Nacl Autonoma Mexico Inst Invest Matemat Aplicadas & Sistemas Dept Ciencias Comp Apdo 20-726 Mexico City DF Mexico

Generally speaking, a spiral is a 2D curve which winds about a fixed point. Now, we present a new, alternative, and easy way to describe and generate spirals by means of the use of the Slope chain Code (SCC) [E. Bribiesca, A measure of tortuosity based on chain coding, Pattern Recognition 46 (2013) 716-724]. Thus, each spiral is represented by only one chain. The chain elements produce a finite alphabet which allows us to use grammatical techniques for spiral classification. Spirals are composed of constant straight-line segments and their chain elements are obtained by calculating the slope changes between contiguous straight-line segments (angle of contingence) scaled to a continuous range from -1 (-180 degrees) to 1 (180 degrees). The SCC notation is invariant under translation, rotation, optionally under scaling, and it does not use a grid. Other interesting properties can be derived from this notation, such as: the mirror symmetry and inverse spirals, the accumulated slope, the slope change mean, and tortuosity for spirals. We introduce new concepts of projective polygonal paths and osculating polygons. We present a new spiral called the SCC polygonal spiral and its chain which is described by the numerical sequence for n >= 3, to the best of our knowledge this is the first time that this spiral and its chain are presented. The importance of this spiral and its chain is that this chain is covering all the slope changes of all the regular polygons composed of n edges (n-gons). Also, we describe the chain which generates the spiral of Archimedes. Finally, we present some results of different kind of spirals from the real world, including spiral patterns in shells. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Slope chain code Polygonal curves Polygonal paths Osculating polygons Broken lines chain coding The SCC polygonal spiral

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A JBIG-based approach to the encoding of contour maps

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IEEE TRANSACTIONS ON IMAGE PROCESSING 2000年第5期9卷 936-941页

作者： Pinho, AJ Univ Aveiro Dept Elect & Telecommun P-3810193 Aveiro Portugal Univ Aveiro Inst Engenharia Electr & Telemat Aveiro P-3810193 Aveiro Portugal

Recently, a new technique for the lossless encoding of contour maps was introduced, based on the concept of "transition points." in this paper we show that by using a simple representation for the transition points, i.e., the map of transition points, the problem of encoding arbitrary contour maps can be easily converted into a problem of lossless image coding. Experimental results show that the joint bilevel image experts group (JBIG) image coding standard can be used successfully For encoding maps of transition points, outperforming, in most cases, differential chain-coding. Moreover, if we take into account that JBIG codecs are available as "off the shelf" components, then the effort required to implement the proposed method is small.

关键词： chain coding contour coding partition coding region-based image coding shape coding transition points

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DM-like differential chain code for handwriting and line graphics

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IEE PROCEEDINGS-VISION IMAGE AND SIGNAL PROCESSING 1996年第2期143卷 96-100页

作者： Yuen, H Department of Electronic Engineering The Hong Kong Polytechnic University Kowloon Hong Kong

A new type of differential chain code, referred to as delta-modulation-like (DM-like) differential chain coding (DM-DCC) which resembles traditional delta modulation proposed coding handwriting and graphics. Since DM-DCC uses only one bit in the encoded vector chain, it achieves the highest coding efficiency when compared with differential chain coding (DCC) and standard chain coding (SCC) in terms of coding rate and encoded file size. DM-DCC has a more uniform data syntax than DCC, and when combined with a robust coding technique DM-DCC is more error resilient than DCC and SCC, Similarly to conventional DM used for one-dimensional waveform coding, however. DM-DCC introduces granular distortion for slowly curving traces and curvature overload distortion for rapidly curving traces. The additional quantisation distortion due to DM-DCC with respect to DCC is calculated. Postprocessing smoothing and adaptive coding techniques are applied in DM-DCC to reduce quantisation distortions, resulting in much improved subjective dynamographical image quality.

关键词： chain coding computer graphics image processing

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MODEL FOR LINE-DRAWING GRAPHICS AND DIFFERENTIAL ANGLE DISTRIBUTIONS

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ELECTRONICS LETTERS 1989年第22期25卷 1473-1474页

作者： LIU, K Dept. of Electr. Eng. Delft Univ. of Technol. Netherlands

A model for line-drawing graphics is presented to study the performance of chain coding, such as quantisation distortions and coding rates. A differential angle distribution of line drawings is proposed based on this model and verified by experiments. The distribution is necessary for the analysis and design of differential chain coding.

关键词： chain coding coding rates differential angle distributions encoding line-drawing graphics model picture processing quantisation distortions

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Block-run run-length coding of handwriting and bilevel graphics based on quadtree segmentation

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PATTERN RECOGNITION LETTERS 1997年第2期18卷 187-191页

作者： Yuen, H Hanzo, L UNIV SOUTHAMPTON DEPT ELECT & COMP SCI SOUTHAMPTON HANTS ENGLAND

An efficient off-line coding scheme for handwriting and bilevel graphics based on quadtree segmentation and block-run run-length coding (RLC) is presented. By segmenting a captured handwriting or graphic image into variable size blocks according to the image activity inside the blocks and run-length coding on a block-run basis, the new scheme is able to achieve higher coding efficiency than the conventional one-dimensional RLC and its bit rate is close to that of on-line dynamographical chain coding. (C) 1997 Elsevier Science B.V.

关键词： segmentation chain coding handwriting and graphics coding

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Adaptive context-based arithmetic coding of arbitrary contour maps

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IEEE SIGNAL PROCESSING LETTERS 2001年第1期8卷 4-6页

作者： Pinho, AJ Univ Aveiro Dept Elect & Telecomunicacoes P-3800 Aveiro Portugal Univ Aveiro Inst Engn Elect & Telemat Aveiro P-3800 Aveiro Portugal

An efficient technique for encoding arbitrary contours is presented. It is based on the concept of transition point of a contour map and relies on a new four-symbol adaptive context-based arithmetic encoder (CAE) that calculates contexts in the (binary) domain of the contour map. The results obtained with this new technique applied to the compression of image partitions are substantially better than those previously attained, showing a clear superiority over adaptive CAE-based differential chain coding and also over the MPEG-4 shape coder.

关键词： chain coding contour coding partition coding region-based image coding shape coding transition points

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A new edge preserving binary images resizing technique

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JOURNAL OF CIRCUITS SYSTEMS AND COMPUTERS 2002年第3期11卷 247-257页

作者： Zahir, S Ward, R Univ British Columbia Dept Elect & Comp Engn Vancouver BC V6T 1Z4 Canada

Efficient methods for resizing two-dimensional binary signals axe increasingly on demand for a variety of applications such as computer graphics, computer cartography, and machine generated text.(2,4,6) Recently, algorithms have been proposed such as those based on interpolation methods including nearest neighbor, linear, and Butterworth. Other methods such as splines,(5) wavelets, and DCT-based algorithms(11,12) are also presented. All these methods generate distortion and noticeable degradation in the quality of the signals (e.g., binary images) especially at and around edges. In this paper, we present a new near optimal edge preserving binary image resizing scheme that produces perceptually perfect edges. This scheme is based on edge detection, edge chain coding, edge code representation, and the uses of predetermined resizing patterns. The results obtained by this method show that the resized images are aesthetically and objectively much better than the results of other published methods.

关键词： images resizing image interpolation image expansion chain coding

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3D-curve representation by means of a binary chain code

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MATHEMATICAL AND COMPUTER MODELLING 2004年第3-4期40卷 285-295页

作者： Bribiesca, E Univ Autonoma Metropolitana Dept Elect Engn Unidad Iztapalapa Mexico City DF Mexico

A binary chain code for representing 3D curves is presented. 3D curves are digitalized and represented as 3D discrete curves. 3D discrete curves are composed of constant straight-line segments using only orthogonal directions. The proposed binary notation is based on the orthogonal direction change chain code. Thus, using the proposed binary chain code it is possible to represent any 3D curve by only two states ("0" and "1"). The proposed binary chain code produces a curve descriptor which is invariant under translation, rotation and may be starting point normalized. Also, we define the complementary chain of a 3D curve which produces the mirror image of the curve. (C) 2004 Elsevier Ltd. All rights reserved.

关键词： 3D curves chain coding binary chain code complementary chains 3D discrete curves

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A ROBUST FILTERING ALGORITHM FOR SUBPIXEL RECONSTRUCTION OF chain CODED LINE DRAWINGS

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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 1987年第3期9卷 451-457页

作者： KOPLOWITZ, J RAJ, APS Department of Electrical and Computer Engineering Clarkson University Potsdam NY 13676

A robust algorithm is presented for smoothing and achieving subpixel accuracy in the reconstruction of chain coded line drawings. The algorithm does not remove sharp corners and does not need a priori knowledge of curvature statistics. A fast on-line implementation can be achieved using a table look-up. A simplified algorithm can be used for reconstructing digitized polygons.

关键词： Robustness Filtering algorithms Image reconstruction Image edge detection Quantization Engineering drawings Algorithm design and analysis Numerical analysis Fourier transforms Optical filters Author Keywords subpixel accuracy chain coding estimation of digital lines filtering line drawings

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An easy and fast algorithm for obtaining minimal discrete knots

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JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS 2006年第5期15卷 613-629页

作者： Bribiesca, Ernesto Univ Nacl Autonoma Mexico Inst Invest Matemat Aplicadas & Sistemas Dept Comp Sci Mexico City 01000 DF Mexico

An easy and fast algorithm for obtaining minimal discrete knots is presented. A minimal discrete knot is the digitalized representation of a knot, which is composed of the minimum number of constant orthogonal straight-line segments and is represented by the knot-number notation. The proposed algorithm for obtaining minimal discrete knots tries to reduce the number of straight-line segments of a given discrete knot preserving its shape. This algorithm is based on two fundamental transformations: U and L. In order to prove the efficiency and rapidity of the algorithm, a great variety of examples of discrete knots are presented: complete families of discrete knots at different orders;random discrete knots;examples of non-trivial and unsolved discrete knots.

关键词： knots chain coding cubic lattice discrete knots minimal discrete knots knot-number notation

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