Digital geometry and its applications to medical imaging

Abstract

Digital geometry is a modern discipline dealing with geometric properties of digital objects (also called digital pictures). These are usually modeled as sets of points with integer coordinates representing the pixels/voxels of the considered objects. Digital geometry is developed with the expectation that it would provide an adequate mathematical background for new advanced approaches and algorithms for various problems arising in image analysis and processing, computer graphics, medical imaging, and other areas of visual computing. In this chapter we first provide a brief discussion on the motivation, basic directions, and achievements of digital geometry. Then we consider typical examples of research problems and their solutions. We focus our attention on problems related to digital manifolds. The latter play an important role in computer graphics, 3D image analysis, volume modeling, process visualization, and so forth - in short, in all areas where discrete multidimensional data need to be represented, visualized, processed, or analyzed. The objects in these areas often represent surfaces and volumes of real objects. We discuss some applications of digital curves and surfaces to medical imaging, implied by theoretical results on digital manifolds.