We present a method for calculating the envelope surface of a parametric solid object swept along a path in threedimensional space. The boundary surface of the solid is the combination of parametric surfaces and an implicit surface where the Jacobian of the defining function has a rankdeficiency condition. Using this condition, we determine a set of square sub-Jacobian determinants that must al...

A nonlinear surface registration algorithm of thoracic/abdominal structures segmented from CT and PET volumes is presented. The aim of this work is to develop a method that can provide an initial estimate of the elastic deformation between the images, so that MI-based techniques can be successfully applied. To perform the matching, a Bspline Free Form Deformation (FFD) model has been chosen. Hi...

To determination the volume and weight of nonuniform bodies, such as in ore deposits evaluation for mining and rock cutting for construction, the methods of interpolation are usually used. The classic curves, which are frequently used to interpolate one-dimensional data are cubic spline, Bspline and Bezier curves. These methods have good efficiency for determination of geometric characteristics...

In cardiopulmonary bypass surgery, it is beneficial to avoid the use of a heart-lung machine and perform beating heart surgery instead. This is a difficult task even for the most skilled surgeons. To eliminate the risks associated with cardiopulmonary bypass on a beating heart, a motion compensation system can be used. We place markers on the heart surface, which we can use to track the complex...

In this paper we provide the guidelines for the direct degree elevation of NURBS curves. Through the analysis of linear equation systems of quartic and lower degree splines we derive a direct relation between the knot vector of a spline and the degree elevation coefficients. We also present a direct degree elevation scheme and several algorithms based on the discovered relation. Experimental re...

We propose an optimization method for estimating patientspecific muscle fiber arrangement from clinical CT. Our approach first computes the structure tensor field to estimate local orientation, then a geometric template representing fiber arrangement is fitted using a Bspline deformation by maximizing fitness of the local orientation using a smoothness penalty. The initialization is computed wi...

In this paper odd-order B-spline filters are proposed to reconstruct volumetric data sampled on an optimal Body-Centered Cubic (BCC) grid. To make these filters nearly interpolating, we adapt a previously published framework, which is based on a discrete frequency-domain prefiltering. It is shown that a BCC-sampled B-spline kernel is not invertible, therefore the interpolation constraint cannot...

Dimension reduction is helpful and often necessary in exploring nonlinear or nonparametric regression structures with a large number of predictors. We consider using the canonical variables from the design space whose correlations with a spline basis in the response space are significant. The method can be viewed as a variant of sliced inverse regression (SIR) with simple slicing replaced by Bs...

3D scanning technology has made enormous progress in the past 25 years (Blais, 2004); especially, the non-contact optical surface digitizers. These scanners or digitizers become more portable, affordable; and yet capturing points faster and more accurately. A hand-held laser scanner captures tens of thousands points per second with a level of accuracy around 40 m, and can cost as low as fifty ...

The representation of moving geometry entities is an important issue in the fields of CAD/CAM and robotics motion design. We present a method to interpolate the moving frame homogeneously using B-splines. By analysing the matrix representation of the moving frames, a simplified optimization functional is derived and a recursive iteration method is presented for approximating orthogonal frames a...