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9.2. HISTOGRAM PREPROCESSING
109
Figure 9.7: Result of High-Pass Filtering on Figure 9.6
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110
CHAPTER 9. HISTOGRAM-BASED SEGMENTATION
but the peaks are shorter and the valleys are lled.
Figure 9.8: The Result of Smoothing the Histogram Given in Figure 9.2
Smoothing a histogram is an easy operation. It replaces each point with
the average ofit and itstwoneighbors. Listing9.1shows thesmooth
histogram
function that performs this operation.
9.3 Thresholding and Region Growing
There are two more topics common to all the methods of image segmenta-
tion: image thresholding and region growing. Image thresholding sets the
pixels in the image to one or zero. Listing 9.2 shows all the subroutines
used in this chapter’s segmentation techniques. It begins with the routine
threshold
image
array that accomplishes this task.
The dicult task is region growing. Figure 9.9 shows the result of thresh-
olding Figure 9.1 correctly. The \object" in Figure 9.9 is a happy face. It
comprises three dierent regions (two eyes and the smile). Region growing
takes this image, groups the pixels in each separate region, and gives them
unique labels. Figure 9.10 shows the result of region growing performed on
Figure 9.9. Region growing grouped and labeled one eye as region 1, the
other eye as region 2, and the smile as region 3.
Figure 9.11 shows the algorithm for region growing. It begins with an
image array g comprising zeros and pixels set toa value. The algorithm loops
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9.3. THRESHOLDING AND REGION GROWING
111
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00001100000000100000
00011111000011110000
00001111100111000000
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Figure 9.9: The Result of Correctly Thresholding Figure 9.1
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112
CHAPTER 9. HISTOGRAM-BASED SEGMENTATION
00000000000000000000
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00111100000000200000
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00033333000033330000
00003333300333000000
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00000000330000000000
00000000000000000000
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Figure 9.10: The Result of Region Growing Performed on Figure 9.9
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9.4. HISTOGRAM-BASED TECHNIQUES
113
through the image array looking for a g(i,j) == value. When it nds such a
pixel, it calls the label
and
check
neighbor routine. label
and
check
neighbor
sets the pixel to g
label (the region label) and examines the pixel’s eight
neighbors. If any of the neighbors equal value, they are pushed onto a stack.
When control returnsto the main algorithm, each pixel on thestackispopped
and sent to label
and
check
neighbor. All the points on the stack equaled
value, so set them and check their neighbors. After setting all the pixels in
the rst region, increment g
label and begin looking for the next region.
Listing 9.2 next shows the functions that implement region growing with
grow being the primary routine. grow runs through the region-growing algo-
rithm and calls label
and
check
neighbor (shown next in Listing 9.2). The
grow and label
and
check
neighbor functions follow the region- growing al-
gorithm step for step.
9.4 Histogram-Based Techniques
Thefollowing pages presentfoursegmentation techniques: manual technique,
histogram peak technique, histogram valley technique, and adaptive tech-
nique.
9.4.1 Manual Technique
In the manual technique the user inspects an image and its histogram man-
ually. Trial and error comes into play and the result is as good as you want
it to be.
Figure 9.12 is the input for all the segmentation examples. Figures 9.13,
9.14, and 9.15 show the result of segmentation using three dierent thresh-
olds. The result in Figure 9.14 used a high of 255 and a low of 125. The
segmentation included the white gravel roads as well as the house trailers
and sidewalks. The result in Figure 9.14 used a high of 255 and a low of
175. The gravel roads begin to disappear, but the house trailers and side-
walks remain. Figure 9.15 shows the result using a high of 255 and a low of
225. This segmentation only nds the four dominant house trailers. Which
answer is correct? That depends on what you wanted to nd.
Note that all image segmentations will appear rough. It is possible to
perform additional processing to make the result more pleasing to the eye
(see chapter 11 for erosion and dilation techniques), but that is not the
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114
CHAPTER 9. HISTOGRAM-BASED SEGMENTATION
1. Given an image g with m rows and n columns
g(i,j) for i=1,m j=1,n
g(i,j) = value for object
= 0 for background
2. set g_label=2 this is the label value
3.
for (i=0; i<m; i++)
scan ith row
for (j=0; j<n; j++)
check jth element
stack_empty = true
if g(i,j) == value
label_and_check_neighbor(g(i,j),g_label)
while stack_empty = false do
pop element (i,j) off the stack
label_and_check_neighbor(g(i,j),g_label)
end while
g_label = g_label + 1
end of checking jth element
end of scanning ith row
4. The End
---------------------------------------
procedure label_and_check_neighbor(g(r,e), g_label)
g(r,e) = g_label
for (R=r-1; r<=r+1; R++)
for (E=e-1; e<=e+1; e++)
if g(R,E) == value then
push (R,E) onto the stack
stack_empty = false
end if
end loop over E
end loop over R
end procedure label_and_check_neighbor
Figure 9.11: Pseudocode for Region Growing
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9.4. HISTOGRAM-BASED TECHNIQUES
115
Figure 9.12: Input Image for Segmentation Examples
Figure 9.13: Threshold of Figure 9.12 with High=255 and Low=125
116
CHAPTER 9. HISTOGRAM-BASED SEGMENTATION
Figure 9.14: Threshold of Figure 9.12 with High=255 and Low=175
Figure 9.15: Threshold of Figure 9.12 with High=255 and Low=225
9.4. HISTOGRAM-BASED TECHNIQUES
117
purpose of segmentation. The purpose is to break the image into pieces
so later computer processing can interpret their meaning. The output is
for computer not human consumption. Also note how dicult it is for the
computer, even with manual aid, to nd objects that are trivial for humans
to see. Anyone could trace over the input image and outline the objects
better than the segmentation process.
Listing 9.2 next shows the code that implements manual segmentation.
The function manual
threshold
segmentation has the same form as the other
subroutines.
manual
threshold
segmentation has the usual inputs as well as the high
and low threshold values and the value and segment parameters. The value
parameter species the value at which to set a pixel if it falls between the
high and low thresholds. value is usually one since those pixels outside the
high-low range are set to zero. The segment parameter species whether or
not to grow regions after thresholding. Sometimes you only want tothreshold
an image and not grow regions. The two operations are identical except for
the last step. If segment == 1, manual
threshold
segmentation calls the
region-growing routines.
Manual segmentation is good for ne tuning and understanding the op-
eration. Its trial-and-error nature, however, makes it time consuming and
impractical for many applications. We need techniques that examine the
histogram and select threshold values automatically.
9.4.2 Histogram Peak Technique
The rst technique to examine the histogram and select threshold values
automatically uses the peaks of the histogram. This technique nds the two
peaks in the histogram corresponding to the background and object of the
image. It sets the threshold halfway between the two peaks. Look back at
the smoothed histogram in Figure 9.8. The background peak is at two and
the object peak is at seven. The midpoint is four, so the low threshold value
is four and the high is nine.
The peak technique is straightforward except for two items. In the his-
togram in Figure 9.8, you’ll note the peak at seven is the fourth highest peak.
The peaks at one and three are higher, but they are part of the background
mountain of the histogram and do not correspond to the object. Searching
the histogram for peaks requires peak spacing to ensure the highest peaks
are separated. If the peak technique does not, then it would choose two as
118
CHAPTER 9. HISTOGRAM-BASED SEGMENTATION
----------*----*----
-------*--**--*--*--
--------------------
*--------*-------*--
------------------*-
-*-----*------------
--**------*-----*---
-*--*--*-----------*
----------------*---
-*------------------
-----------------*-*
--*-----------------
--------------*--*--
------------*-*-----
----*-*-------------
--*-------*----*-**-
-*-------*--*------*
----*-*-------------
-*--------*------*--
Figure 9.16: Result of Incorrect Peak Separation
the background peak and one as the object peak. Figure 9.16 shows the
disastrous eect of this.
Thesecond item to watch carefully is determiningwhich peak corresponds
to the background and which corresponds to the object. Suppose an image
had the histogram shown in Figure 9.17. Which peak corresponds to the
background? The peak for gray level eight is the highest, but it corresponds
to the object not the background. The reason is the mountain surrounding
the peak at gray level two has a much greater area than that next to gray
level eight. Therefore, gray levels zero through six occupy the vast majority
of the image, and they are the background.
Listing 9.2 next shows the source code to implement the peak technique.
peak
threshold
segmentation is theprimary function. Next, it calls new func-
tions to nd the histogram peaks and determine the high and low threshold
values. Finally, it thresholds the image, performs region growing if desired,
and writes the result image to the output le.
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