Thresholding of Medical Images - Medical Image Processing: Advanced Fuzzy Set Theoretic Techniques - page 111

2. If an image consists of distinct objects and background, the histo-
gram will contain peaks and valleys. If the histogram is bimodal,
the threshold is selected at the valley of the two peaks, that is, at the
minima. If the histogram is multimodal, more thresholds may be
determined at minima between any two maxima.
3. Another technique that constructs a grey-level histogram consists
of border pixels and the histogram thus making the histogram uni-
modal. The threshold is chosen at the peak of the histogram, and the
peak corresponds to the grey levels bordering between the object
and the background.
4. For obtaining distinct peaks and valleys, one can weigh the histo-
gram by suppressing the pixels with a high gradient. In such cases,
the histogram will contain the grey levels that belong mostly to the
object and the background and may not consider the border pixels
having a high pixel gradient.
6.2.2 Iterative Thresholding
In this method, the threshold is selected iteratively:
1. Select an initial estimate of the threshold T , which may be the mean.
2. Using the threshold or the mean, partition the image into regions as
R 1 and R 2 .
3. Calculate the mean of the intensities of the two regions as μ 1 and μ 2 .
4. Compute the new threshold as T = (μ 1 + μ 2 )/2 .
5. Repeat steps 2-4 until the mean values μ 1 and μ 2 do not change in the
successive iterations.
6.2.3 Optimal Thresholding
In many images, histogram peaks are not clearly separable and it happens
when the object is flat with no colour variation and no discernible texture and
colour. Peaks may overlap and choosing a threshold in overlapping peaks
will not classify the pixels in correct regions. So, many pixels will be incor-
rectly classified. Optimal thresholding uses a criterion function that yields a
measure of separation between two regions. A criterion function may be cal-
culated in many ways that may be Shannon's entropy, cross entropy, diver-
gence or any other measure. There are many thresholding techniques that
use the optimal method to select a threshold [19,20].
6.2.4 Locally Adaptive Thresholding
Till now, global thresholding methods are discussed. Global threshold selects
only one threshold for the entire image. But in some images, especially in medi-
cal images where there is a variation in grey-level intensity throughout the