Search

Contour extraction of image stacks is a basic task in medical modeling. The existing level-set methods usually suffer from some problems (e.g. serious errors around sharp features, incorrect split of topology and contour occlusions). This paper proposes a novel method of multi-constraint level-set evolution to avoid above-mentioned problems. Interpolation constraint and deviation constraint are added to evolution processin addition to existing constraints (such as edge points and areas). In order to prevent occlusions, it proposes a method of three-phase level-set evolution. The first phase obtains a rough contour according to selected edge points. The second phase applies an expanding LSE (level-set evolution). Missing edge points in the first phase are added when occlusions probably appear. In the third phase, occlusions are deleted and a refining evolution is implemented. As proved by final experiments, our method can steadily extract contours slice by slice when the shapes of previous contours (contours in the previous slice) are similar to current contours (contours in the current slice). Furthermore, there is no error propagation during the process of contour extraction.

ECT-spline curves for sequences of multiple knots are generated from different local ECT-systems via connection matrices. Under appropriate assumptions there is a basis of the space of ECT-splines consisting of functions having minimal compact supports, normalized to form a nonnegative partition of unity. The basic functions can be defined by generalized divided differences [24]. This definition reduces to the classical one in case of a Schoenberg space. Under suitable assumptions it leads to a recursive method for computing the ECT-B-splines that reduces to the de Boor–Mansion–Cox recursion in case of ordinary polynomial splines and to Lyche's recursion in case of Tchebycheff splines. For sequences of simple knots and connection matrices that are nonsingular, lower triangular and totally positive the spline weights are identified as Neville–Aitken weights of certain generalized interpolation problems. For multiple knots they are limits of Neville–Aitken weights. In many cases the spline weights can be computed easily by recurrence. Our approach covers the case of Bezier-ECT-splines as well. They are defined by different local ECT-systems on knot intervals of a finite partition of a compact interval [a,b] connected at inner knots all of multiplicities zero by full connection matrices A [i] that are nonsingular, lower triangular and totally positive. In case of ordinary polynomials of order n they reduce to the classical Bezier polynomials. We also present a recursive algorithm of de Boor type computing ECT-spline curves pointwise. Examples of polynomial and rational B-splines constructed from given knot sequences and given connection matrices are added. For some of them we give explicit formulas of the spline weights, for others we display the B-splines or the B-spline curves.

The classical de Casteljau algorithm for constructing Bezier curves can be generalized to sphere of arbitrary dimension by replacing line segments with shortest great circle arcs. The resulting spherical Bezier curve is C∞ and interpolates the endpoints of its control polygons. In this paper, a new method is proposed to construct spherical Bezier curves, which extends corner cutting method, introduced by Lane-Riesenfeld to sphere. The final curve created by this method converges to spherical Bezier curves named corner cutting spherical Bezier curves. The necessary and sufficient condition of G1 continuity for two spherical Bezier curves is presented. Finally, as a by-product geodesic can be created on free-form surfaces with presented approach.

Tube surfaces are the complicated surfaces generated by smoothly joining together several cylinders. Most kinds of industrial design models are tube surfaces in production. To meet the needs of composite materials in some industrial design, it is necessary to make the representation of the tube surfaces as simple as possible. Based on the theory of implicit surface modeling, the global modeling methods for the tube surfaces of elbow and Y-tube are presented, the influences of parameters on the blending surfaces are discussed and the concave-convex characteristics of the blending surfaces and control surfaces are studied in this paper. On VC++ software platform, using Open Gl, the tube surfaces of elbow and Y-tube are implemented with a computer by the steps of gathering the data points from the implicit expressions, forming triangular mesh and fairing the triangular surfaces. The research results are very important for craft and technique of the products.

In this paper, we present an automatic procedure for reconstructing a smooth parametric surfaces using T-Splines from a triangulation mesh .A key ingredient in our solution is a scheme for automatically constructing both T-mesh and a parameterization of the data points over T-mesh. We use the discrete conformal parameterization presented in as the solution of choice for mapping the 3D surface to a 2D domain, then using quad-tree subdivision in 2D domain to automatically constructing the T-mesh that we need for the reconstructing. By using least square approximation we can get the control point of the surface and finish our algorithm until the result is satisfactory. We use adaptive refinement of the T-mesh in order to satisfy user-specified error tolerances and demonstrate our method on real data.