REDUCED DATA FOR CURVE MODELING – APPLICATIONS IN GRAPHICS, COMPUTER VISION AND PHYSICS

Malgorzata Janik, Ryszard Kozera, Przemysław Kozioł
2013 Advances in Science and Technology Research Journal  
In this paper we consider the problem of modeling curves in R n via interpolation without a priori specified interpolation knots. We discuss two approaches to estimate missing knots {ti} m i=0 for nonparametric data (i.e. collection of points {qi} m i=0 , where qi ∈ R n ). The first approach (uniform evaluation) is based on blind guess in which knots {t i} m i=0 are chosen uniformly. The second approach (cumulative chord parameterization), incorporates the geometry of the distribution of data
more » ... tribution of data points. More precisely the differencet i+1 −ti is equal to the Euclidean distance between data points qi+1 and qi. The second method partially compensates for the loss of the information carried by the reduced data. We also present the application of the above schemes for fitting nonparametric data in computer graphics (light-source motion rendering), in computer vision (image segmentation) and in physics (high velocity particles trajectory modeling). Though experiments are conducted for points in R 2 and R 3 the entire method is equally applicable in R n . ABSTRACT In this paper we consider the problem of modeling curves in R n via interpolation without a priori specified interpolation knots. We discuss two approaches to estimate the missing knots m i=0 are chosen uniformly. The second approach (cumulative chord parameterization), incorporates the geometry of the distribution of data points. More precisely the differencet i+1 −ti is equal to the Euclidean distance between data points qi+1 and qi. The second method partially compensates for the loss of the information carried by the reduced data. We also present the application of the above schemes for fitting nonparametric data in computer graphics (light-source motion rendering), in computer vision (image segmentation) and in physics (high velocity particles trajectory modeling). Though experiments are conducted for points in R 2 and R 3 the entire method is equally applicable in R n . is equal to the Euclidean distance between data points q i+1 and q i . The second method partially compensates for the loss of the information carried by the reduced data. We also present the application of the above schemes for fitting non-parametric data in computer graphics (light-source motion rendering), in computer vision (image segmentation) and in physics (high velocity particles trajectory modeling). Though experiments are conducted for points in R 2 and R 3 the entire method is equally applicable in R n .
doi:10.5604/20804075.1049599 fatcat:kx5gg7vfvfayjoueawzvnqwq5m