Adaptive B-snake for planar curve approximation

An adaptive B-spline active contour model for planar curve approximation is proposed. Starting with an initial B-spline curve, the finite element method is adopted to make the active B-spline curve converge towards the target curve without the need of data points parameterization. A strategy of automatic control point insertion during the B-spline active contour deformation, adaptive to the shape of the planar curve, is also given. Experimental results show that this method is efficient and accurate in planar curve approximation.

PIECEWISE RATIONAL APPROXIMATIONS OF REAL ALGEBRAIC CURVES

We use a combination of both algebraic and numerical techniques to construct a C-1-continuous, piecewise (m, n) rational epsilon-approximation of a real algebraic plane curve of degree d. At singular points we use the classical Weierstrass Preparation Theorem and Newton power series factorizations, based on the technique of Hensel lifting. These, together with modified rational Pade approximations, are used to efficiently construct locally approximate, rational parametric representations for all real branches of an algebraic plane curve. Besides singular points we obtain an adaptive selection of simple points about which the curve approximations yield a small number of pieces yet achieve C-1 continuity between pieces. The simpler cases of C-1 and C-0 continuity are also handled in a similar manner. The computation of singularity, the approximation error bounds and details of the implementation of these algorithms are also provided.

KNOT PLACEMENT FOR B-SPLINE CURVE APPROXIMATION VIA l_(∞,1)-NORM AND DIFFERENTIAL EVOLUTION ALGORITHM

In this paper,we consider the knot placement problem in B-spline curve approximation.A novel two-stage framework is proposed for addressing this problem.In the first step,the l_(∞,1)-norm model is introduced for the sparse selection of candidate knots from an initial knot vector.By this step,the knot number is determined.In the second step,knot positions are formulated into a nonlinear optimization problem and optimized by a global optimization algorithm—the differential evolution algorithm(DE).The candidate knots selected in the first step are served for initial values of the DE algorithm.Since the candidate knots provide a good guess of knot positions,the DE algorithm can quickly converge.One advantage of the proposed algorithm is that the knot number and knot positions are determined automatically.Compared with the current existing algorithms,the proposed algorithm finds approximations with smaller fitting error when the knot number is fixed in advance.Furthermore,the proposed algorithm is robust to noisy data and can handle with few data points.We illustrate with some examples and applications.

Moving Multiple Curves/Surfaces Approximation of Mixed Point Clouds

We propose a local model called moving multiple curves/surfaces approximation to separate mixed scanning points received from a thin-wall object,where data from two sides of the object may be mixed due to measurement error.The cases of two curves(including plane curves and space curves)and two surfaces in one model are mainly elaborated,and a lot of examples are tested.