Academic literature on the topic 'Polygonal chain simplification'

In this paper we present a novel nonparametric method for simplifying piecewise linear curves and we apply this method as a statistical approximation of structure within sequential data in the plane. Specifically, given a sequence P of n points in the plane that determine a simple polygonal chain consisting of n−1 segments, we describe algorithms for selecting a subsequence Q ⊂ P (including the first and last points of P) that determines a second polygonal chain to approximate P, such that the number of crossings between the two polygonal chains is maximized, and the cardinality of Q is minimized among all such maximizing subsets of P. Our algorithms have respective running times O(n2 log n) (respectively, [Formula: see text]) when P is monotonic and O(n2 log2 n) (respectively, [Formula: see text]) when P is any simple polygonal chain in the Real RAM model (respectively, in the Word RAM model).

Abstract This paper studies how biomechanical multibody models of scoliosis can neglect the changes of spinal length and yet be accurate in reconstructing spinal columns. As these models with fixed length comprise rigid links interconnected by rotary joints, they resemble polygonal chains that approximate spine curves with a finite number of line segments. In mathematics, using more segments with shorter lengths can result in more accurate curve approximations. This raises the question of whether more accurate spine curve approximations by increasing the number of links/joints can yield more accurate spinal column reconstructions. For this, the accuracy of spine curve approximation was improved consistently by increasing the number of links/joints, and its effects on the accuracy of spinal column reconstruction were assessed. Positive correlation was found between the accuracy of spine reconstruction and curve approximation. It was shown that while increasing the accuracy of curve approximations, the representation of scoliosis concavity and its side-to-side deviations were improved. Moreover, reconstruction errors of the spine regions separated by the inflection vertebrae had minimal impacts on each other. Overall, multibody scoliosis models with fixed spinal lengths can benefit from the extra rotational joints that contribute toward the accuracy of spine curve approximation. The outcome of this study leads to concurrent accuracy improvement and simplification of multibody models; joint-link configurations can be independently defined for the regions separated by the inflection vertebrae, enabling local optimization of the models for higher accuracy without unnecessary added complexity to the whole model.

We present a method for extracting contours from digital images, using techniques from computational geometry. Our approach is different from traditional pixel-based methods in image processing. Instead of working directly with pixels, we extract a set of oriented feature points from the input digital images, then apply classical geometric techniques, such as clustering, linking, and simplification, to find contours among these points. Experiments on synthetic and natural images show that our method can effectively extract contours, even from images with considerable noise; moreover, the extracted contours have a very compact representation.