Image Processing Reference
In-Depth Information
3.1.2 Classification by functions of filters
(a) Smoothing filter
This is a filter designed to suppress random variations of density values in
the neighborhood of an image called a
smoothing filter
. The basic policy of its
design is:
(i) To calculate a simple (or a weighted) average of density values in the
neighborhood.
(ii) To detect an outlier (a voxel of a density value extraordinarily different
from other voxel's density values) and suppress its value.
(b) Difference filter, edge extraction (detection) filter
This is a filter that calculates local differences in density values called a (
spa-
tial
)
difference filter
. These filters are used to detect parts of input images in
which the differences in local density values are relatively large and can be
used to define these differences.
(c) Local pattern matching (local template matching)
A typical pattern (or a density value distribution) in the subarea of a shape
and the size of the image neighborhood is used as a template, and the simi-
larity measure (or the degree of matching) between the subarea of an input
image and the template is calculated for each voxel of the input image.
(d) Local statistics filter
Various statistics of density values in the neighborhood area are calculated
for each voxel of an input image. An example of these statistics is as follows:
average, variance, median, maximum, minimum,
k
-th order statistics, range,
etc. Sometimes, a filter is denoted by the name of the calculated statistics,
such as a
median filter
and a
range filter
.
(e) Morphological filter
Morphological operations are performed on each voxel between subarea pat-
terns (template) defined beforehand and on subarea patterns of an input image
in the neighborhood.
3.1.3 Classification by the form of a local function
The concrete form of a local operation (or a filter) discussed here is determined
by the local function
φ
in Eq. 3.1. Filters also are classified by the local function
φ
.
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