scholarly journals Digital Level Layers for Digital Curve Decomposition and Vectorization

2014 ◽  
Vol 4 ◽  
pp. 169-186 ◽  
Author(s):  
Laurent Provot ◽  
Yan Gerard ◽  
Fabien Feschet
Keyword(s):  
Digital Curve

POLYGONAL APPROXIMATION OF DIGITAL CURVE BASED ON REVERSE ENGINEERING CONCEPT

2013 ◽  
Vol 13 (04) ◽  
pp. 1350017 ◽  
Author(s):  
KUMAR S. RAY ◽  
BIMAL KUMAR RAY
Keyword(s):  
Reverse Engineering ◽  
Linear Time ◽  
Line Drawing ◽  
Approximation Error ◽  
Zero Approximation ◽  
Polygonal Approximation ◽  
Digital Curve ◽  
Symmetric Approximation ◽  
Engineering Concept ◽  
Automatic Algorithm

This paper applies reverse engineering on the Bresenham's line drawing algorithm [J. E. Bresenham, IBM System Journal, 4, 106–111 (1965)] for polygonal approximation of digital curve. The proposed method has a number of features, namely, it is sequential and runs in linear time, produces symmetric approximation from symmetric digital curve, is an automatic algorithm and the approximating polygon has the least non-zero approximation error as compared to other algorithms.

scholarly journals Fixed Point Sets of k-Continuous Self-Maps of m-Iterated Digital Wedges

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1617 ◽  
Author(s):  
Sang-Eon Han
Keyword(s):  
Fixed Point ◽  
Natural Number ◽  
Digital Image ◽  
Digital Images ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Point Sets ◽  
Digital Curve ◽  
Curve Theory ◽  
Fixed Point Sets

Let Ckn,l be a simple closed k-curves with l elements in Zn and W:=Ckn,l∨⋯∨Ckn,l︷m-times be an m-iterated digital wedges of Ckn,l, and F(Conk(W)) be an alignment of fixed point sets of W. Then, the aim of the paper is devoted to investigating various properties of F(Conk(W)). Furthermore, when proceeding with this work, this paper addresses several unsolved problems. To be specific, we firstly formulate an alignment of fixed point sets of Ckn,l, denoted by F(Conk(Ckn,l)), where l(≥7) is an odd natural number and k≠2n. Secondly, given a digital image (X,k) with X♯=n, we find a certain condition that supports n−1,n−2∈F(Conk(X)). Thirdly, after finding some features of F(Conk(W)), we develop a method of making F(Conk(W)) perfect according to the (even or odd) number l of Ckn,l. Finally, we prove that the perfectness of F(Conk(W)) is equivalent to that of F(Conk(Ckn,l)). This can play an important role in studying fixed point theory and digital curve theory. This paper only deals with k-connected digital images (X,k) such that X♯≥2.

GENETIC ALGORITHMS FOR POLYGONAL APPROXIMATION OF DIGITAL CURVES

1999 ◽  
Vol 13 (07) ◽  
pp. 1061-1082 ◽  
Author(s):  
PENG-YENG YIN
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Learning Strategy ◽  
Approximation Error ◽  
Experimental Results ◽  
Polygonal Approximation ◽  
The Third ◽  
Digital Curve

In this paper, three polygonal approximation approaches using genetic algorithms are proposed. The first approach approximates the digital curve by minimizing the number of sides of the polygon and the approximation error should be less than a prespecified tolerance value. The second approach minimizes the approximation error by searching for a polygon with a given number of sides. The third approach, which is more practical, determines the approximating polygon automatically without any given condition. Moreover, a learning strategy for each of the proposed genetic algorithm is presented to improve the results. The experimental results show that the proposed approaches have better performances than those of existing methods.

Study on Non-Interference Normal Tracking Algorithm for NC Quick-Point Grinding of the Curve Parts

2006 ◽  
Vol 532-533 ◽  
pp. 885-888
Author(s):  
Yu Mei Luo ◽  
Qi Wu ◽  
De Jin Hu
Keyword(s):  
New Technology ◽  
Mathematic Model ◽  
Normal Direction ◽  
Tracking Algorithm ◽  
Grinding Wheel ◽  
Normal Vector ◽  
Grinding Process ◽  
Machining Precision ◽  
New Type ◽  
Digital Curve

In traditional NC curve grinding, the grinding wheel’s rotary surface is generally not on the grinding point’s normal direction, which will bring the distortion of grinding wheel and decrease the machining precision. This paper presents a new technology, which is called the non-interference normal tracking for NC curve grinding process. By controlling the worktable to rotate in the x-y plane, the superposition between the rotary surface of the grinding wheel and the normal vector of the workpiece’s contour is realized, and the interference between the wheel’s body and the workpiece could be avoided at the same time. A mathematic model is established and an algorithm to calculate the worktable’s rotary angle is proposed. Finally, the algorithm is applied in a new-type digital curve grinder successfully. The results show that the method is reliable and effective.

Polygonal approximation of digital curve by graduate iterative merging

1995 ◽  
Vol 31 (6) ◽  
pp. 444-446 ◽  
Author(s):  
K.-M. Ku ◽  
P.K. Chiu
Keyword(s):  
Polygonal Approximation ◽  
Digital Curve
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