20-08-2012, 04:02 PM
Binary Images. Simple Geometrical Properties
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INTRODUCTION
The simplest type of image which is used widely in a variety of industrial and medical
applications is binary, i.e. a black-and-white or silhouette image.
Advantages
-Easy to acquire: simple digital cameras; thresholding may be applied to grey-level
images.
-Low storage: no more than 1 bit/pixel, often this can be reduced by compression (e.g. runlength
coding).
-Simple and fast processing: the algorithms are in most cases much simpler than those
applied to grey-level images.
Disadvantages
-Limited application: application is restricted to tasks where internal detail is not required
as a distinguishing characteristic.
-Does not extend to 3D: the 3D nature of objects can rarely be represented by silhouettes.
-Specialized lighting is required to obtain reliable binary images without restricting the
environment.
THRESHOLDING
In the simplest case, an image may consist of a single object or several separated objects
of relatively high intensity, viewed against a background of relatively low intensity.
This allows figure/ground separation by thresholding.
The goal of thresholding is to segment an image into regions of interest and to remove all other
regions deemed inessential. The simplest thresholding methods use a single threshold in order to
isolate objects of interest. In many cases, however, no single threshold provides a good
segmentation result over an entire image. In such cases variable and multilevel threshold
techniques based on various statistical measures are used.
Variable Thresholding
• Variable thresholding allows different threshold levels to
be applied to different regions of an image.
• Let f(x,y) be the source image and let d(x,y) denote the
local (region) threshold value associated with each point in
the image, that is d(x,y) is the threshold value associated
with the region in which point (x,y) lies.
Otsu’s Thresholding Method (1979)
• Find the threshold that minimizes the weighted withinclass
variance which turns out to be the same as
maximizing the between-class variance.
• Operates directly on the gray level histogram [e.g. 256
numbers, P(i)], so it’s fast (once the histogram is
computed).
• Histogram (and the image) are bimodal.
• Assumes uniform illumination (implicitly), so the
bimodal brightness behavior arises from object
appearance differences only.
Run-Length coding (3)
• The vertical projection is obtained by adding up all picture cell values in
one column of the image.
• It is difficult to compute vertical projection directly from the run lengths.
Consider instead the first difference of the vertical projection:
• The first difference of the vertical projection can be obtained by
projecting not the image data, but the first horizontal differences of the
image data:
• The first difference has the advantage over bi,j itself that is nonzero
only at the beginning of each run. It equals +1 where the data change
from 0 to a 1, and –1 where the data change from a 1 to a 0.