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Electronic Letters on Computer Vision and Image Analysis 20(1):42-54, 2021
Adaptive Window Selection for Non-uniform Lighting Image
Thresholding
Tapaswini Pattnaik∗ and Priyadarshi Kanungo+
∗
+
Department of Electronics and Telecommunication, C. V. Raman Global University, Bhubaneswar, India
Department of Electronics and Telecommunication, C. V. Raman Global University, Bhubaneswar,India
Received 26th of August2020; accepted 13th of January 2021
Abstract
Selection of appropriate size of windows or subimages is the most important step for thresholding images
with non-uniform lighting. In this paper, a novel criteria function is developed to partition images into
different size of sub images appropriate for thresholding. After the partitioning, each subimage is segmented
by Otsu’s thresholding approaches. The performance of the proposed method is validated on benchmark
test images with different degree of uneven lighting. Based on the qualitative and quantitative measures, the
proposed method is fully automatic, fast and efficient in comparison to many landmark approaches.
Key Words: Image segmentation, Thresholding, Non-uniform Lighting, Local thresholding, Bimodal distribution
1
Introduction
Image segmentation is a technique of partitioning an image into homogenous regions. Among all the image
segmentation techniques, thresholding is the most popular image segmentation technique for real time application. In thresholding of a two class images, the pixels are divided into two groups at the threshold point.
Thresholding techniques [1–4] are broadly classified into two types such as (i) global thresholding and (ii) local thesholding. In global thresholding [5] a single threshold is used to divide all the pixels into two groups.
Whereas in local thresholding, the image is divided into sub-images and for each sub-image a threshold is
evaluated to binarize the corresponding subimage. Histogram of an image is commonly used for the bi-level or
multi-level thresholding evaluation. In histogram based thresholding, Otsu’s [6] threshold is one of the landmark global thresholding approach for image binarization. Otsu thresholding is one of the most popular and
widely used approach for global thresholding due to its roboustness,simplicity and adaptability. Otsu method
is better than most of the other global thresholding because of its high performance on segmenting real images
as the calculation of threshold values depends on 1D intensity data. Another advantage of Otsu approach is
its simple and strong criteria function [7]. The criteria function maximizing between class variance and minimizing the within class variance produced an efficient segmentation result with low complexity [7–11]. The
Correspondence to: <tapaswini.n@gmail.com>
Recommended for acceptance by Angel D. Sappa
https://doi.org/10.5565/rev/elcvia.1301
ELCVIA ISSN:1577-5097
Published by Computer Vision Center / Universitat Autònoma de Barcelona, Barcelona, Spain
Tapaswini Pattnaik et al. / Electronic Letters on Computer Vision and Image Analysis 20(1):42-54; 2021
43
performance of global thresholding methods decrease in images with non-uniform lighting and poor resolution [12]. In last few decades many literatures [13–22] developed different approaches to binarize images with
non-uniform lighting. Niblack [13] used mean and standard deviation to find out the threshold for each pixel
in a particular local window. Bradley [16] considered the integral image for the binarization of each pixels.
Threshold for each pixel in the integral image is evaluated based on the mean of the neighbouring pixels in
a 15 × 15 window. Huang’s method [17], used the Lorentz information measure as a feature for selection
of window size adaptively and then Otsu’s thresholding is used to binarize each local window. However, the
performance of this method is highly dependent on the initial small size of window. Zheng [18], designed the
principle of adaptively adjustment of the local window size. The number of edge pixels in a local window
determined the optimal size of the window over a pixel. After getting the optimal window size the range constrained Otsu’s thresholding method is applied on window to binarize the center pixel of that window. As this
method evaluated threshold for each pixel, the time complexity of this method is very high. High sensitivity
to noise and high complexity are the two major drawbacks of this method. Kanungo et al. [19], developed an
entropy base window merging and growing process to partition the image into subimages. Further, each subimages is binarized based on the PGA and MMSE based algorithms. The performance of this method is sensitive
to the choice of initial window size in both merging and growing process. Zhao [20], evaluated the posterior
probability of each center pixel in a 3 × 3 or 5 × 5 window. Considering the posterior probability and Bayesian
criteria the binary map is generated. This method is effective to deal the noise, however the performance of this
method is highly depend on the size of the user defined neighbourhood.
Recently Zheng et al. [21], developed an adaptive segmentation based on fuzzy c-means with spatial information (FCMS). The complexity of this method is very high as each pixel is binarized based on the information
of different local window. Bogiatzis [23], proposed the local thresholding technique in which pixel is binarized
based on fuzzy inclusion and entropy criteria from the fuzzy subset hood of the neighbourhood M × N of
pixel. This method is not automatic as it depends on the optimal choice of the user defined window size. It is
observed from the recent literatures that, the performance of all these adaptive thresholding methods is highly
sensitive to the partitioning process to generate optimal size of subimages or window size. The objective of the
partition process is to find subimages with clearly bimodal gray level or feature distributions.
The review of the literature revels that, the performance of any adaptive thresholding largly depends on
the selection of the window size and the bimodal testing criteria function. This motivates us to, develop simple partitioning process which does not need any initial size of window. The second novelty of the proposed
method is its non parametric bimodality test criteria function followed by exhaustive experimental evaluation
for the selection of threshold for the above criteria function. The criteria function does not need any parameter
estimation. Therefore the complexity of the entire process is within the range of real-time application. Experimental results depicts that the proposed method is faster and efficient in comparison to landmark thresholding
methods for images with non-uniform lighting. The organisation of this paper is as follows: the formulation
of the proposed method (materials and methods) is presented in Section 2. The proposed NMDM algorithm
based adaptive image partitioning for thresholding is presented in Section 3. The simulations and discussions
are presented in Section 4 followed by the conclusion in Section 5.
2
Materials and methods
The major problem of thresholding any images with non-uniform lighting is the development of a criterion
function for partitioning the image into optimal size of subimages. To address this problem, in this section a
normalized mean difference measure (NMDM) criteria is developed to partition the images with non-uniform
lighting images into optimal size of subimages such that the gray level distribution of each sub image satisfy
the bimodality property.
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2.1
Tapaswini Pattnaik et al. / Electronic Letters on Computer Vision and Image Analysis 20(1):42-54; 2021
Normalized mean difference measure (NMDM)
In two class images, the histogram of an image represents the gray level distribution. In thresholding, histogram
plays a major role to evaluate the optimal threshold. The histogram of a two class image can be model as a two
class Gaussian mixture model. For uniform lighting image there is a clear valley between the distributions of
object and background class. However the valley between the distributions of object and background vanished
in the non-uniform lighting conditions.
(a)
(b)
(c)
(d)
Figure 1: Simulated two class Gaussian Mixture PDF using (2) w1 = w2 = 0.5, and σ1 = σ2 = 30, with four
different combination of µ1 and µ2 :(a)µ1 = µ2 = 128, (b)µ1 = 100 and µ2 = 180,(c)µ1 = 80 and µ2 = 200,
(d)µ1 = 60 and µ2 = 250
f (g) = w1 P (g | C1 ) + w2 P (g | C2 )
(1)
Therefore two class image histogram can be modeled as f(g) in (1). Where, P (g | C1 ) and P (g | C2 ) represent
Gaussian distribution of class C1 and class C2 respectively. The gray level distribution f (g) is represented as
2
2
w1
w2
− (g − µ1 )
− (g − µ2 )
p
f (g) = p
+
e
e
2σ12
2σ22
2πσ12
2πσ22
(2)
where w1 and w2 are class probabilities, σ1 and σ2 are the standard deviation, µ1 and µ2 are the mean of the
class C1 and class C2 respectively. If the two parameters, µ and σ of C1 and C2 are equal, then these two
distributions are identical distributions with 100% overlapping. The µ1 and µ2 are the two key parameters
which are responsible for the overlapping of the two distributions. Using (1), four different two-class gray
level distribution are synthesized and placed in Fig. 1. These four distributions, are synthesized based on
w1 = w2 = 0.5, σ1 = σ2 = 30, whereas the µ1 and µ2 are different. Considering µ1 = µ2 = 128, the
distribution is a uni-modal and 100% overlapping as shown in Fig. 1(a). In Fig. 1(b), the µ1 = 100 and
µ2 = 180, where there is a reduction in the overlapping of the two distributions in comparison with µ1 = µ2 as
shown in Fig. 1(a). Further reduction in overlapping between the two distributions is observed with µ1 = 80
and µ2 = 200 as shown in Fig. 1(c). Considering µ1 = 60 and µ2 = 250 the overlapping is almost negligible
as shown in Fig. 1(d). Let consider the absolute mean difference is d, which is defined as d = |µ2 − µ1 |.
Keeping σ1 and σ2 constant, it is observed that, as d increasing the overlapping between the two distributions
is decreasing. Let define the normalized mean difference measure (NMDM) as follows.
dµ =
d
(Gmax − Gmin )
(3)
where Gmax is the maximum and Gmin is the minimum gray value of the image. From (3) it is expected that
if dµ is 0 i.e µ1 = µ2 then the maximum overlapping between the two distributions. Similarly if µ1 = Gmin
and µ2 = Gmax then dµ = 1 which represents the minimum overlapping between the two distribution. The
condition, dµ = 1 is an ideal condition for any two class real image. Based on this NMD measure and the
standard deviation of the entire image a criterion function is developed in Section 2.2 to measure the bimodal
characteristics of the graylevel distribution with acceptable overlapping.
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Tapaswini Pattnaik et al. / Electronic Letters on Computer Vision and Image Analysis 20(1):42-54; 2021
(a)
(b)
Figure 2: PE vs dµ plot considering with different σ1 and σ2 (a) w1 = w2 = 0.5 and (b)w1 = 0.2, w2 = 0.8
2.2
Bimodality Criteria function
As per Bayes rule, the minimum error partitioning threshold of any two class GMM is the intersection point of
these two distributions. Let consider the intersection point of these two distributions in the probability density
function(PDF) is at k th gray level. Then at k th gray value the equality condition is.
w1 P (k|C1 ) = w2 P (k|C2 )
(4)
The probability of error due to the threshold at k th gray value can be evaluated as
P E = w1
k
X
g=1
P (g|C1 ) + w2
255
X
P (g|C2 )
(5)
g=k+1
The probability error, ”PE ”, increases with the increase in overlapping of class distributions. The effect of dµ
and the standard deviation of the image on PE at different sets of (w1 , w2 ) and (σ1 , σ2 ) are presented in Fig.
2(a) and 2(b). All the five plots in Fig. 2(a) are with equal class probability condition i.e w1 = w2 = 0.5.
Similarly the five plots in Fig. 2(b) are with unequal class probability condition i.e w1 = 0.2 and w2 =
0.8. The five sets of (σ1 ,σ2 ) considered for simulation are (10 10), (20 20), (30 30), (40 40) and (60 60) for
both Fig. 2(a) and Fig. 2(b). It is observed from the considered non uniform light image database that the
minimum standard deviation is 25 and the maximum standard deviation is 60. Therefore we have considered
the maximum standard deviation as 60. The dµ is varied by varying µ1 and µ2 , (µ2 ≥ µ1 ), of the C1 and C2
distributions. Initial value of µ1 and µ2 is considered as 128 and 128 respectively, which results a dµ = 0.
Further, the dµ is varied from 0 to 1 with 128 steps by incrementing µ2 by one unit and decrementing µ1 by
one unit at each step.It is clearly observed from PE vs dµ plots in Fig. 2(a) and (b) that for a particular value
of dµ the PE is increasing with increase in standard deviation σ1 and σ2 . In Fig. 2(a) at dµ = 0.5, for σ1 =
σ2 = 10 and σ1 = σ2 = 20. It is observed from Fig. 2(a) that PE values for σ1 = σ2 = 10 and σ1 = σ2 = 20
curve at dµ = 0.5 are almost zero. It is also observed that, for σ1 = σ2 = 30 the PE is 0.01, σ1 = σ2 = 40
the PE is 0.04, and for σ1 = σ2 = 60 the PE is 0.1. Similarly in Fig. 2(b) there is an increasing trend in the
PE with increase in the σ1 and σ2 values for a particular dµ . However it is clearly observed that for unequal
weighted distribution in Fig. 2(b) the PE is very less than the equal weighted distribution case in Fig. 2(a). For
example, considering the σ1 = σ2 = 60 , the PE value for dµ = 0.5 in Fig. 2(b) is half of the PE value for
dµ = 0.5 in Fig. 2(a). It is also observed that for dµ > 0.5 the PE is almost less than 0.1 for both the conditions
in Fig. 2(a) and 2(b). Based on the above observations, it is considered that if dµ > 0.5 and the standard
deviation of the images σI < 60, then the gray level distribution of the image depicts the bimodal charaterstics
with a maximum overlapping error of 10%. The above criteria function is considered for the adaptive image
partitioning for threshold in section 3. The criteria of bimodality is
1 if (dµ > 0.5 && σI < 60)
CI =
(6)
0
otherwise
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Tapaswini Pattnaik et al. / Electronic Letters on Computer Vision and Image Analysis 20(1):42-54; 2021
Where CI = 1 represents the clear bimodality characteristics of an image. The proposed criteria function is
based on the parameter dµ and σI . Evaluation of dµ needs the estimation of parameters µ1 and µ2 of a two
class GMM. The parameter estimation using EM algorithm will increase the overall complexity of the proposed
adaptive thresholding approach. Therefore simple method using Otsu’s thresholding approach is developed to
estimate value of µ1 and µ2 . The proposed parameter estimation algorithm is as follows.
Algorithm for evaluating the CI :
Step 1 Evaluate the normalized histogram h(g) and Otsu’s [6] global threshold ‘T ’ of the input image I
Step 2. Evaluate the max gray value (Gmax ) and minimum gray value (Gmin ) of the input at step-1
Step3. Evaluate the µ1 and µ2 as follows
P
µ1 = Tg=0 g × h(g)
P
and µ2 = 255
g=T +1 g × h(g)
where g is the variable represents the gray value.
|µ2 −µ1 |
Step4. Evaluate the dµ = (Gmax
−Gmin )
Step5. Evaluate σI =
nP
255
g=1 [g −
Step6. Evaluate CI =
3
o1
2 h(g) 2
g
×
h(g)]
g=1
P255
1 if (dµ > 0.5 && σI < 60)
0
otherwise
Adaptive Image Partitioning for thresholding
Figure 3: Image Partitioning Process
The proposed partitioning process is a non overlapping partitioning process. To avoid the overpartition and
reduce the complexity the minimum size of window is set to 32 × 32. As the input images are of different
spatial resolution, it is necessary to resize the image in such a way that the image could be partitioned evenly
upto 32×32 windows. The test images collected from database [24] and [25] are less than 256×256 resolutions
and greater than 64 × 64 resolutions. Therefore, the images are resized to the higher resolution i.e 256 × 256
(a)
(b)
(c)
(d)
Figure 4: (a) histogram of input Rice image at stage-I; (b) Four partition at stage-II; (c) 16 partitions in stage-III
(d) 28 partition in stage-IV
Tapaswini Pattnaik et al. / Electronic Letters on Computer Vision and Image Analysis 20(1):42-54; 2021
(a)
(b)
47
(c)
Figure 5: (a) dµ of fig. 4(d) and (b) the corresponding sigma(σ) value (c) Otsu’s threshold value for each
subimages in Fig. 5(c)
(a)
(b)
Figure 6: (a) Segmentation of subimages (b) Final Segmentation results of Rice image
spatial resolution to satisfy the proposed criteria and make the partitioning process more convenient. The
proposed image partitioning approach is presented in Fig. 3. In this process, all the images are resized into
256 × 256 spatial resolutions. The resizing also reduced the overall non-linear lighting effect of an image. To
avoid the overpartition and reduced the complexity the minimum size of window is set to 32 × 32. Therefore
the proposed partitioning process has maximum of four stages. In (stage-I), the proposed NMD Criteria in (6)
is applied on input gray image, If the CI = 1, then it is binarized using Otsu’s thresholding method. Otherwise,
the image is partitioned in to four subimages as shown in stage-II. Further the criteria function is applied on each
subimages at stage-II. The subimages in the stage-II satisfying the criteria function are not further partitioned
in the stage-III. Any subimage in stage-II does not satisfied the criterion function are partitioned into four parts
in stage-III. The process described for stage-II applied to the subimages in stage-III and stage IV. The minimum
size of subimages in stage-IV is 32 × 32 and the maximum size may be 256 × 256. If the minimum size of
subimages(32 × 32) resolution at stage-IV does not satisfy CI = 1 then the threshold value of that subimage is
evaluated based on the average of the neighbouring subimages.
The proposed partitioning process and binarization of Rice image demonstrated in Fig. 4. As the histogram(gray level distribution) of Rice image in Fig. 4(a) is not clearly bimodal, the criteria function does not
satisfy at stage-I. Therefore the rice image is partitioned into four parts in stage-II. The histogram of these four
subimage at stage-II are placed in Fig. 4(b). It is clearly observed that all these histograms are not clearly
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Tapaswini Pattnaik et al. / Electronic Letters on Computer Vision and Image Analysis 20(1):42-54; 2021
bimodal. Therefore each subimages at stage-II are not satisfying the criteria function. Therefore all these
subimages are partitioned into four equal parts at stage-III. There are 16 subimages at stage-III. It is observed
form Fig. 4(c) that the histograms of 1st column subimages at stage-III are not following clear bimodality.
However the histograms of last three column subimages are exhibiting the bimodality. Therefore, these twelve
subimages in last three columns not allowed to partition at the stage-IV. However, each subimage in 1st column
of stage-III are divided into equal size subimages at stage-IV as shown in Fig. 4(d). The histograms of all these
subimages in 1st and 2nd column of Fig. 4(d) depicts bimodality. In the partitioning process of rice image, all
the subimages at stage-IV satisfied the criteria function. Therefore the partitioning process stopped at stage-IV.
Otsu’s thresholding is applied to each subimages at the stage-IV. The corresponding dµ , the window standard
deviation σI and threshold for each subimage are presented in Fig. 5(a), (b) and (c) respectively. The segmented
result of each subimage are placed in Fig. 6(a). It is clearly observed from Fig. 6(b) that the proposed method
segmented the non-uniform lighted Rice image efficiently.
Table 1: Miss classification error rate (ER ) in % age
BRAD FIE
LIAW GMM ADRCO
Image
Proposed
[16]
[23]
[17]
[20]
[18]
Plane
1.11
0.77
2.05
1.50
4.34
1.50
Swan
81.48
82.47 1.53
4.95
58.03
1.72
DOC
8.59
19.62 23.14 18.00 21.37
4.1
Fish
11.92
20.34 3.53
8.06
3.07
3.93
Hex2
56.39
60.68 8.51
43.21 46.09
1.34
Block
59.64
63.21 0.51
17.15 63.7
0.27
Sept
23.68
27.2
1.17
24.56 18.11
1.41
Rice5
29.62
62.82 8.68
15.39 36.97
1.41
Hex
51.15
52.44 8.49
27.99 31.61
1.46
Hand
48.7
53.4
3.74
15.23 30.97
2.31
Flower
18.5
21.2
7.45
0.01
18.13
3.68
Coin1
52.8
57.92 3.48
0.29
35.26
3.47
86016
2.44
23.48 4.43
2.14
5.17
2.84
311068
44.4
67.05 8.21
3.8
18.0
2.82
Tree
3.12
15.31 2.15
39.48 14.29
1.86
pins1
6.19
12.56 2.71
1.15
4.47
2.1
pins2
3.55
11.47 9.97
3.87
22.2
0.05
partree
15.85
27.58 15.04 1.41
3.64
0.50
Bandage
24.89
27.58 2.00
1.51
4.34
2.17
star
16.12
27.81 37.04 53.29 10.91
7.7
synthetic1
67.93
63.81 9.97
5.87
51.07
0.05
flower1
61.38
79.89 6.25
2.15
64.09
0.6
Erget
75.7
77.11 2.68
2.3
29.75
1.9
ninety eight 15.94
29.83 3.06
3.69
15.29
3.6
coin2
29.17
40.39 1.7
1.96
16.65
1.0
flower2
56.70
65.75 3.19
3.88
27.80
0.81
fingerprint
5.29
40.03 1.5
6.75
4.58
2.1
Swan2
65.92
77.16 1.9
1.5
14.02
1.8
AVG ER
31.3
43.17 6.57
10.23 24.02
2.08
Tapaswini Pattnaik et al. / Electronic Letters on Computer Vision and Image Analysis 20(1):42-54; 2021
Image
GT
BRAD
FIE
LIAW
GMM
ADRCO
Proposed
Plane
Swan
DOC
Fish
Hex2
Block
Sept
Rice5
Hex
Hand
Flower
Coin1
86016
311068
Figure 7: Segmentation results of test images From left column to right column :original test images, Corresponding groundtruth(GT), BRAD [16], FIE [23], LIAW [17], GMM [20], ADRCO [18], and Proposed method
49
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Tapaswini Pattnaik et al. / Electronic Letters on Computer Vision and Image Analysis 20(1):42-54; 2021
Image
GT
BRAD
FIE
LIAW
GMM
ADRCO
Proposed
Tree
Pins1
pins2
Partree
Bandage
star
synthetic1
flower1
erget
ninetyeight
coin2
flower2
fngerprint
swan2
Figure 8: Segmentation results of test images with added illumination From left column to right column :original test images, Corresponding groundtruth(GT), BRAD [16], FIE [23], LIAW [17], GMM [20], ADRCO [18],
and Proposed method
Tapaswini Pattnaik et al. / Electronic Letters on Computer Vision and Image Analysis 20(1):42-54; 2021
Image
Plane
Swan
Doc
Fish
Hex2
Block
Sept
Rice5
Hex
Hand
Flower
Coin1
86016
311068
Tree
pin1
pin2
partree
Bandage
star
synthetic1
flower1
Erget
ninety eight
coin2
flower2
fingerprint
swan2
Avg Tc
4
Table 2: Time Complexity(Tc ) in Seconds
BRAD FIE
LIAW GMM ADRCO
[16]
[23]
[17]
[20]
[18]
0.12
29.37 0.023 4.03
722.4
0.13
28.7
0.025 3.64
299
0.16
29.10 1.62
3.7
71.7
0.14
29.15 0.023 3.75
355.3
0.13
29
0.80
3.72
148.2
0.16
28.9
0.08
4.02
36.12
0.18
28.97 0.037 3.7
86.6
0.18
28.6
0.033 3.77
26.10
0.15
30.43 0.053 3.78
210.8
0.14
29.3
0.036 3.7
94.3
0.17
28.53 0.823 3.80
600
0.15
29.12 0.10
4.12
62.3
0.16
29.2
0.023 4.4
40.09
0.16
29.9
0.026 3.75
69.85
0.29
29.33 0.048 3.67
106.8
0.15
32.02 0.043 3.62
377.5
0.13
30.91 0.067 3.71
153.0
0.18
32.71 0.044 3.57
157.9
0.18
30.70 0.030 3.62
63.38
0.19
27.81 0.036 3.63
9.14
0.16
31.28 0.035 3.77
78.5
0.13
30.25 0.044 3.74
206.8
0.13
30.42 0.035 3.76
175.0
0.13
29.83 0.025 4.14
4.88
0.13
29.71 0.037 4.06
101.5
0.20
31.95 0.05
5.98
134.85
0.24
36.48 0.032 4.53
58.72
0.20
30.76 0.031 3.85
337.04
0.16
30.08 0.15
3.75
170.9
51
Proposed
0.28
0.30
0.30
0.31
0.26
0.40
0.41
0.26
0.25
0.24
0.42
0.14
0.33
0.028
0.42
0.62
0.48
1.37
0.47
0.86
0.7
0.25
0.31
0.31
3.34
0.65
0.68
0.63
0.53
Simulations and discussions
The proposed adaptive thresholding is simulated in MatLab 9.5 with an Intel core i5, 4 MB L2 cache, 8GB
RAM and 2.4 GHz speed machine. twenty eight test images with different degree of non-uniform lighting
are considered for validation of the proposed method. The proposed algorithm is validated with five landmark
methods such as BRAD [16], FIE [23], LIAW [17], GMM [20], and ADRCO [18]. The misclassification error
rate (ER ) and the time complexity(Tc ) are the two measures we considered to measure the strength of the
thresholding algorithms. The misclassification error rate is evaluated as follows
T
S
T
#(OGT OS ) #(BGT BS )
S
× 100
(7)
ER = 1 −
#(OGT BGT )
where, OGT and Os represent the object region in the GT and segmented image respectively. Similarly BGT and
BS represent the background region in the GT and segmented images respectively. The symbol 0 #0 represents
the cardinality of a set. The time complexity is evaluated based on time elapsed between the starting and to the
end of the algorithm. The twenty eight test images are divided into two groups. In the first group, fourteen non
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Tapaswini Pattnaik et al. / Electronic Letters on Computer Vision and Image Analysis 20(1):42-54; 2021
uniform test images are collected from internet source, Weizmann dataset [24] and Berkeley dataset [25]. The
1st group test images along with the corresponding binary images generated by different methods are placed
in Fig. 7. In the second group, fourteen non-uniform test images are synthesized by adding illumination. Non
uniform lighting images collected from weizmann dataset [24]. The 2nd group of test images along with the
corresponding binary images generated by different methods are placed in Fig. 8. In Fig. 7 and Fig. 8 the
non uniform lighted gray level test images are placed in column 1, the corresponding groundtruth images are
placed in column 2 and the corresponding binarized images generated by BRAD [16], FIE [23], LIAW [17],
GMM [20], ADRCO [18] and proposed method are placed in column 3 to column 8 respectively. Based on the
visual perceptions, it is observed from Fig. 7 and Fig. 8 that the proposed NMD method binarized most of the
test images efficiently in comparison to other five methods. It is observed from the Fig. 7 that the performance
of the proposed method slightly degrades in the presence of multilevel background like sky in plane image,
multilevel object in ”coin1” test image, textured background in ”86016” test image and highly non uniform
light conditition as in flower test image. Similarly it is observed from Fig. 8. that the performance of the
proposed method slightly degrades in the presence of light reflection from a metal body as in ”pins1” test
image, the low contrast image as in ”Bandage” test image. Apart from the above qualitative measures the
quantitative measures ER and Tc are evaluated for all the methods and tabulated in Table 1 and Table 2. It is
observed that in seventeen test images the proposed method has lowest ER . The performance of the proposed
method in other eleven images is the 2nd lowest ER , due to the textured background, background is sky, low
contrast image, and reflection of light as discussed in visual result analysis from Fig. 7 and Fig. 8. It is clearly
observed that the ER measure for the proposed NMD method is the lowest among all the methods for most
of the test images. Therefore the average ER of the proposed approach is 2.08% which is lowest among all
the methods. However for adaptive thresholding methods, ADRCO has the highest time complexity among all
the other methods for most of test images. Observing the average time, it is lowest in LIAW Method i.e 0.15
second. However the proposed method has an average computation time of 0.53, the third lowest computation
time with avg ER of 2.08%. In overall, considering qualitative, quantitative and time complexity measures the
proposed NMD outperformed the other methods.
5
Conclusion
In this paper, an efficient adaptive image partitioning based thresholding technique is developed to segment
images with non-uniform lighting. A normalized mean difference measure is formulated to test the bimodality
of the image. Otsu’s method is used to evaluate the normalized mean difference value of an image. Further
the bimodal criteria parameter CI is determined through an exhaustive experimental results. Based on the
normalized mean difference criterion function an algorithm is developed to partition the image into optimum
number of sub-images. The proposed method has the lowest average misclassification error rate (Avg. ER ) in
comparison with BRAD, FIE, LIAW, GMM and ADRCO. The average CPU time is 0.53 sec/image, which is
suitable for real time application. The proposed method outperforms other landmark methods on different bench
mark test images with non-uniform lighting in terms of qualitative and quantitative measures. The proposed
approach is suitable for gray levels images only. Performance of proposed method slightly decreases on the
textured background images and low contrast images affected by illumination. Further to address this issue
textural feature can also be gainfully employed which can taken up as a future extension of the paper.
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