INTRODUCTION - Fundamentals of Three-Dimensional Digital Image Processing - page 19

plex, deletability, path, and distance metric, and we will discuss their proper-
ties. We will also consider Euler numbers, connectivity indexes, and distance
functions as features of the topology of 3D digital shapes. Some specific algo-
rithms that compute these values also will be given.
Chapter 5 explains some processing algorithms that will probably be nec-
essary for 3D image analysis, such as labeling, axis thinning, surface thin-
ning, border tracing, distance transformation, skeleton extraction, and figure
restoration. Here our goal will be understanding not only the content of the
processing performed, but also the structure and design methodology of the
algorithm. We will make as clear as possible the required capabilities of such
processing, along with requirements that must be fulfilled (for example, topol-
ogy preservation, deletability testing, Euclid distance calculations, and figure
restorability), and give specific examples.
Whereas Chapter 5 is solely concernedwithshapeforms(andgeometric
properties), Chapter 6 discusses thinning, ridge line tracing, and gray weighted
distance transformations used on gray-scale images as examples of transfor-
mations required to incorporate density value information.
As described before, Chapter 7 describes display (rendering) algorithms
used as visualization tools for 3D gray-scale images. The discussion is not one
of computer graphics in general, but rather focuses on observation tools for
gray-scale data. Specifically, the use of ray casting for the generation of images
is discussed, for example, particular surface rendering and shading models, ray
tracing, volume rendering, and gradient shading.