Introduction 3D reconstruction of an object from its 2D cross-sections (slices) has many applications in different fields of sciences such as medical physics and biomedical engineering. In order to perform 3D reconstruction, at first, desired boundaries at each slice are detected and then using a correspondence between points of successive slices surface of desired object is reconstructed. Mate...

This paper describes a fast algorithm for scattered data interpolation and approximation. Multilevel B-splines are introduced to compute a C 2 -continuous surface through a set of irregularly spaced points. The algorithm makes use of a coarse-tofine hierarchy of control lattices to generate a sequence of bicubic B-spline functions whose sum approaches the desired interpolation function. Large p...

Glossary 5 Introduction 6 Definition of the Subject 7 Various Spline Spaces 8 The B-form Representation of Spline Functions 9 Dimension of Multivariate Spline Spaces 10 Approximation Power of Spline Spaces 11 Construction of Finite Elements 12 and Macro-Elements 13 Multivariate Splines for Scattered Data Fitting 14 Multivariate Splines for Numerical Solution 15 of Partial Differential Equations...

This paper provides a comparison of spline-based registration methods applied to register interventional Trans Rectal Ultrasound (TRUS) and pre-acquired Magnetic Resonance (MR) prostate images for needle guided prostate biopsy. B-splines and Thin-plate Splines (TPS) are the most prevalent spline-based approaches to achieve deformable registration. Pertaining to the strategic selection of corres...

This article describes a F0 curve estimation scheme based on a B-spline model1. We compare this model with more classical spline representation. The free parameters of both models are the number of knots and their location. An optimal location is proposed using a simulated annealing strategy. Experiments on real F0 curves confirm the adequacy and good performance of the B-spline approach, estim...

The famous de Boor conjecture states that the condition of the polynomial B-spline collocation matrix at the knot averages is bounded independently of the knot sequence, i.e., it depends only on the spline degree. For highly nonuniform knot meshes, like geometric meshes, the conjecture is known to be false. As an effort towards finding an answer for uniform meshes, we investigate the spectral c...

Boundary conditions are still an open question in the field of approximating subdivision since the problem of determining a general construction of the endpoint rules we need when subdividing a B-spline curve/surface with Bézier end conditions has not been solved yet. This consideration prompted us to present an efficient algorithm for the conversion between B-spline bases defined over differen...

We present an algorithm for bounding a piece of strip-shaped point cloud without self-intersections with an interval B-spline curve. Firstly we calculate the boundary points of the point cloud, and then bound it with an interval B-spline curve of which two pieces of boundary curves interpolate these boundary points. For the algorithm there are important applications in product shape verifying m...