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STATEMENT OF PURPOSE / RESEARCH PROPOSAL Shape approximation has received a lot of research attention because of its multiple applications. Some examples of these applications are: its use to optimize machine elements, the simpli cation of CAD models fi and the approximation of trajectory data. Main approaches to solve the shape approximation problem are the approximation of shapes using polygonal segments and the use of splines for the same purpose. Polygonal approximation of digital curves has been addressed by many researchers using different methods that could be categorized into three main classes : i) local optimization (greedy) algorithms , ii) global optimization algorithms and iii) intelligent optimization algorithms. Each has its own merits nd demerits, and depending on the problem at hand, one might be better than the other. My goal is to have Polygonal approximation of real-world digital curves under real world constraints, so as to have an elegant and efficient algorithm compared to the currently achievable levels now. Application No.: 10710 Name : Jitender Ahuja ---------------------------------------------------------------------- -- Approximation of a closed curve by pieces of straight line segments is known as polygonal approximation. Any curve can be approximated by a polygon with any degree of accuracy. Polygonal approximation is useful for reducing the no. of pts. reqd. to rep. a curve & to smooth data. Such rep. facilitates extraction of numerical features for desc. & classfn. of curves. Basically there are two approaches to the problem. One is to subdivide the points into groups each of which satisfies a specific criterion fn. measuring the collinearity of the points. The collinearity is measured either by integral square error or by absolute error or by some other criterion function such as area derivation. This approach treats polygonal approximation as a side detection problem. (Polygonal approximation by measuring collinearity of the points measured either by integral square error, absolute error,or by area
Transcript of Sop
STATEMENT OF PURPOSE / RESEARCH PROPOSAL
Shape approximation has received a lot of research attention because of its multiple applications. Some examples of these applications are: its use to optimize machine elements, the simplification of CAD models and the approximation of trajectory data. Main approaches to solve the shape approximation problem are the approximation of shapes using polygonal segments and the use of splines for the same purpose. Polygonal approximation of digital curves has been addressed by many researchers using different methods that could be categorized into three main classes : i) local optimization (greedy) algorithms , ii) global optimization algorithms and iii) intelligent optimization algorithms. Each has its own merits nd demerits, and depending on the problem at hand, one might be better than the other. My goal is to have Polygonal approximation of real-world digital curves under real world constraints, so as to have an elegant and efficient algorithm compared to the currently achievable levels now.
Application No.: 10710Name : Jitender Ahuja------------------------------------------------------------------------Approximation of a closed curve by pieces of straight line segments is known as polygonal approximation.Any curve can be approximated by a polygon with any degree of accuracy.Polygonal approximation is useful for reducing the no. of pts. reqd. to rep. a curve & to smooth data. Such rep. facilitates extraction of numerical features for desc. & classfn. of curves.Basically there are two approaches to the problem.One is to subdivide the points into groups each of which satisfies a specific criterion fn. measuring the collinearity of the points. The collinearity is measured either by integral square error or by absolute error or by some other criterion function such as area derivation. This approach treats polygonal approximation as a side detection problem.(Polygonal approximation by measuring collinearity of the points measured either by integral square error, absolute error,or by area derivation.)Another app. to polygonal approximation is to detect significant points and join the adjacent significant points by straight line segments. This app. takes treats polygonal appr. as an angle detection problem.(Polygonal approximation by detecting significant points and join the adjacent significant points by straight line segments.)
