Image Processing Reference
In-Depth Information
17
Region and Boundary Descriptors
In this chapter we discuss images consisting of two colors (or gray values), so called
binary images
. Such images are typically the result of a computer processing, e.g.,
applying a threshold, but they can also be semiautomatically or manually produced
by humans in artistic activities, e.g., graphics with regions having the same color,
such as logos or cartoon images. First, we introduce some general tools from mathe-
matical morphology that can be useful in binary image processing. Then we elaborate
on how to label the regions with the purpose to identify them for further processing.
This will be done within the framework of morphological filtering. Subsequently,
we describe elementary shape features of a region, assuming that the regions have
been individually labelled. In the final two sections we present a more systematic ap-
proach to describe the shape of a region with possibility to increase the description
power systematically, i.e., complex moments for regions and Fourier descriptors for
boundaries.
17.1 Morphological Filtering of Regions
A binary image is an image which has only two colors in it. Without loss of generality
we call these as 0 and 1 respectively.
We start with continuous morphological operations and then focus on binary ver-
sions of them, as this has some pedagogical benefits. The functions max(
f
) and
min(
f
) correspond to the largest and smallest value of the image
f
within the re-
gion, where the image is defined as the basic operators in this theory. In applications,
typically
f
is a local image, which means that max and min will be applied to all
points of a local image, producing a (nonlinearly) filtered image. In consequence,
there is a
neighborhood function
,
g
(
r
), also called a
morphological filter
,or
struc-
ture element
, associated with such uses of max and min, delivering the result after
a pointwise product with the original function. To mark the filtering aspect that ne-
cessitates the filter
g
in their use, these operators are called
dilation
and
erosion
,
respectively, and are defined as:
