Image Processing Reference
In-Depth Information
voxels , the 3D equivalent of pixels. An image that has been digitized in such a
manner is called a three-dimensional digital image , abbreviated as 3D image
in this topic. Chapter 2 will discuss the details of digitalization and the formal
expression of digital images.
Ideally, digital images should be created so that an original continuous
image is digitized with the same precision in the x , y ,and z axes in 3D space.
However, doing so is not always an easy task, given current image acquisition
technologies (imaging technologies). A common practice, as we will see in an
example below, is to create multiple 2D cross-sectional images that are parallel
to a given direction and separated by an appropriate spacing and to create
a 3D image by aligning and stacking those images. In such a situation, the
size of the pixels in the cross section, that is, the precision of digitalization,
and the spacing between cross sections are not necessarily the same. In most
cases, the spacing between cross sections will be larger. We will discuss the
details in Chapter 2; however, this topic will assume that, unless mentioned
otherwise, digitalization both between and within cross sections is at the same
resolution.
Remark 1.1. Common usage infers that an image refers to a 2D representa-
tion drawn on a plane. Our use of the term “3D image” probably gives readers
an impression somewhat different from the standard meaning of what “image
usually means.” It is not clear why that word is applied here. The term prob-
ably comes from the use in medical imaging and other applied fields of images
along with 2D images as a method of diagnostic imaging, and because humans
have been observed as a series of cross sections, in other words, a collection of
2D images, etc. Their 3D-ness is likely not particularly considered, and so the
term “image” is used naturally, without any particular sense of incongruity
Remark 1.2. Generally speaking, there are two ways to handle images in
which the spacing between cross sections is larger. One is to just treat it as
a 3D image, taking voxels not as cubes but as rectangular solids. The other
is to use some appropriate method to interpolate new cross sections between
the existing ones in a manner such that the sampling spacing becomes as
similar as possible in all three directions. In reality, the sampling distance
in each direction will not be at an integral ratio; thus, creating precisely
cubical elements (in other words, voxels that are exact cubes) will not be
possible. Some image processing algorithms can be directly applied to non-
cubic elements; however, the majority of processes cannot, and those will
be limited to approximating values within a given range of precision. When
measuring certain features on digital images, it therefore will be necessary to
verify the image acquisition process and then make any necessary corrections.
This is also related to the equipment and methods used for imaging and
digitalization. For example, when the imaging is performed on digital process-
ing equipment, the sampling distance will be determined by the capabilities of
the imaging device, and so the quality of the resulting image will depend on
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