Generating Bézier curves for medical image reconstruction

Abstract

The boundaries of medical images can be represented by a sequence of 2D curves from image slices taken from uncalibrated cameras. The 2D curves are used to reconstruct a 3D tissues volume in order to understand of anatomical functionality and morphological analysis. For that, new curves are needed to represent a sequence of 2D points sampled along the boundary. In this paper, we construct and analyse special types of Bézier curves for improving medical image reconstruction. The special types of Bézier curves are derived from the moving Frenet frames accompanying them. We describe and analysis of these curves in terms of their curvatures, torsions and control points. In addition, we introduce some important theories regarding the geometric properties of these curves. The thoughtful work represents the first attempt to deal with constructing such curves and might deliver fundamentals which are an important input in the algorithm for creating 3D surfaces. We provided an example with drawing as application, through which we demonstrate confirmation of our theoretical results.