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2 2002

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Solving systems of algebraic equations

Kiciak P.

Machine Graphics and Vision

2002

Vol. 11, No. 4

455-473

Numerical procedutes of solving a system for algebraic equations usually consist of a part that localizes the solutions and a part that computers their accurate approximations. The localization is often based on the convex hull property of the Bernstein-Bezier representation of the equations. In the procedure described in this paper, the convex hull test is complemented with another, which significantly improves the efficiency of the procedures.

Non-rigid registration using hardware-accelerated free-form deformation

Soza G., Bauer M., Hastreiter P., Nimsky C., Greiner G.

Journal of Medical Informatics & Technologies

2002

Vol. 3

MI181--188

In this paper we introduce a new method for non-rigid voxel-based registration of medical images. There exist many applications where an alignment between two image datasets has to be established. Often a registration of a time-shifted medical image sequence with appearing deformation of soft tissue (e.g. pre- and intraoperative data) has to be conducted. Soft tissue deformations are usually highly non-linear. In our approach, for the handling of this phenomenon and for obtaining an optimal non-linear alignment of respective datasets we transform one of them using 3D Bézier functions, which provides some inherent smoothness as well as elasticity. In order to find the optimal transformation, many evaluations of this Bézier function are necessary. In order to make the method more efficient, graphics hardware is extensively used. We applied our non-rigid algorithm successfully to MR brain images in several clinical cases and showed its value.