Medical images application of contour extraction based on Hermite splines contour model

Active Contour Model or Snake model is an efficient method by which the users can extract the object contour of Region Of Interest （ROI）. In this paper, we present an improved method combining Hermite splines curve and Snake model that can be used as a tool for fast and intuitive contour extraction. We choose Hermite splines curve as a basic function of Snake contour curve and present its energy function. The optimization of energy minimization is performed hy Dynamic Programming technique. The validation results are presented, comparing the traditional Snake model and the HSCM, showing the similar performance of the latter. We can find that HSCM can overcome the non-convex constraints efficiently. Several medical images applications illustrate that Hermite Splines Contour Model （HSCM） is more efficient than traditional Snake model.

C2 Continuous Quartic Hermite Spline Curves with Shape Parameters

In order to relieve the deficiency of the usual cubic Hermite spline curves,the quartic Hermite spline curves with shape parameters is further studied in this work. The interpolation error and estimator of the quartic Hermite spline curves are given. And the characteristics of the quartic Hermite spline curves are discussed.The quartic Hermite spline curves not only have the same interpolation and continuity properties of the usual cubic Hermite spline curves, but also can achieve local or global shape adjustment and C;continuity by the shape parameters when the interpolation conditions are fixed.

Numerical solution of Poisson equation with wavelet bases of Hermite cubic splines on the interval

A new wavelet-based finite element method is proposed for solving the Poisson equation. The wavelet bases of Hermite cubic splines on the interval are employed as the multi-scale interpolation basis in the finite element analysis. The lifting scheme of the wavelet-based finite element method is discussed in detail. For the orthogonal characteristics of the wavelet bases with respect to the given inner product, the corresponding multi-scale finite element equation can be decoupled across scales, totally or partially, and suited for nesting approximation. Numerical examples indicate that the proposed method has the higher efficiency and precision in solving the Poisson equation.

The Crank-Nicolson Hermite Cubic Orthogonal Spline Collocation Method for the Heat Equation with Nonlocal Boundary Conditions

We formulate and analyze the Crank-Nicolson Hermite cubic orthogonal spline collocation method for the solution of the heat equation in one space variable with nonlocal boundary conditions involving integrals of the unknown solution over the spatial interval.Using an extension of the analysis of Douglas and Dupont[23]for Dirichlet boundary conditions,we derive optimal order error estimates in the discrete maximum norm in time and the continuous maximum norm in space.We discuss the solution of the linear system arising at each time level via the capacitance matrix technique and the package COLROWfor solving almost block diagonal linear systems.We present numerical examples that confirm the theoretical global error estimates and exhibit superconvergence phenomena.

Storage-efficient reconstruction framework for planar contours

A storage-efficient reconstruction framework for cartographic planar contours is developed.With a smaller number of control points,we aim to calculate the area and perimeter as well as to reconstruct a smooth curve.The input data forms an oriented contour,each control point of which consists of three values:the Cartesian coordinates(x,y)and tangent angleθ.Two types of interpolation methods are developed,one of which is based on an arc spline while the other one is on a cubic Hermite spline.The arc spline-based method reconstructs a G1 continuous curve,with which the exact area and perimeter can be calculated.The benefit of using the Hermite spline-based method is that it can achieve G2 continuity on most control points and can obtain the exact area,whereas the resulting perimeter is approximate.In a numerical experiment for analytically defined curves,more accurate computation of the area and perimeter was achieved with a smaller number of control points.In another experiment using a digital elevation model data,the reconstructed contours were smoother than those by a conventional method.

Direct dynamic-simulation approach to trajectory optimization

This paper proposes a new direct method for an efficient trajectory optimization using the point that the dynamics of a deterministic system are uniquely determined by initial states and controls imposed over the time horizon of interest.To effectively implement this concept,the Hermite spline is adopted to interpolate the continuous controls and the system dynamics are integrated with corresponding control parameters in prior.As a result,the optimal control problem can be transcribed into a nonlinear programming problem which has no dynamic equality constraints and no intermediate states in its design variables.In addition,the paper proposes an efficient recursive Jacobian estimation technique and introduces a Jacobian transformation matrix to straightforwardly handle the general state constraints.Important properties of the present method are thoroughly investigated through its applications to the trajectory optimization for a soft lunar landing from a parking orbit,including the detailed analyses for the de-orbiting phase.The computed results are compared with those using the pseudo-spectral method to demonstrate an extreme outperformance of the proposed method in the aerospace applications over the traditional direct method.

UNIFORM SUPERCONVERGENCE OF GALERKIN METHODS FOR SINGULARLY PERTURBED PROBLEMS

In this paper, we are concerned with uniform superconvergence of Galerkin methods for singularly perturbed reaction-diffusion problems by using two Shishkin-type meshes. Based on an estimate of the error between spline interpolation of the exact solution and its numerical approximation, an interpolation post-processing technique is applied to the original numerical solution. This results in approximation exhibit superconvergence which is uniform in the weighted energy norm. Numerical examples are presented to demonstrate the effectiveness of the interpolation post-processing technique and to verify the theoretical results obtained in this paper.