INTRODUCTION - Fundamentals of Three-Dimensional Digital Image Processing - page 18

the cross section may be pruned so as to form a suciently isotropic true 3D
image. Some 3D processing algorithms can be applied even to images with
differing resolutions in each directional axis (images created from rectangu-
lar solid picture elements), taking such anisotropy into consideration without
modification of the source images (one example is the distance transform of
Section 5.5).
On the other hand, the construction of a 3D image by appropriately con-
necting a group of given shapes that depict cross-sectional forms is also im-
portant and has been studied extensively in the field of computer graphics
[Watt98]. Figure. 1.4 shows a schematic diagram. As can be predicted from
the figure, the inclusion of branchings or features running parallel to the cross
sections will make processing more dicult.
1.4 The contents of this topic
Of the types described above, this topic is a systematic explanation of the
fundamentals of processing true 3D digital images. Its content is divided into
two parts, the geometric characteristics of 3D digital forms (in other words,
the digital geometry of 3D forms), and fundamental algorithms for 3D image
processing. The latter is written assuming knowledge of the former. Methods
of visualization of 3D gray-scale images are also described, because, as dis-
cussed in Section 1.3.3, visualization is an indispensable tool not only with
regard to the development of processing methodologies for individual images,
but also for all aspects of the study and learning of digital geometry, as well
as the development and evaluation of algorithms.
Chapter 2 begins with a formal and precise definition of 3D digital image .
Next, image processing is defined algebraically as calculations on images ,or
as a mapping defined within an image space ,andthen compositions of image
calculations (both serial and parallel compositions) are defined. Additionally,
the executable form of a representative case of application to a digital image
is presented. From this, understanding and development of image processing
algorithms can be performed effectively.
Chapter 3 introduces localized processing of 3D gray-scale images, with
the focus on density value manipulations such as smoothing filters, difference
filters, Laplacians, and region expansion. Most of these methods can be di-
rectly expanded from 2D graphic processing equivalents, and so are relatively
easy to understand.
Chapters 4 and 5 are concerned with the geometric properties of 3D digital
images and the basic processing algorithms that are associated with them.
These chapters are the most important in the topic, from the standpoint that
they deal with those characteristics specific to 3D, and are what make the
topic a unique work.
First, in Chapter 4 we will discuss the fundamentals of what is referred to
as digital geometry, defining such terms as neighborhood, connectivity, sim-