# Maximum Entropy Threshold Segmentation for Target Matching Using Speeded-Up Robust Features

Authors: Mu Zhou; Xia Hong; Zengshan Tian; Huining Dong; Mingchun Wang; Kunjie Xu
Journal: Journal of Electrical and Computer Engineering
 (2014)

---

## Abstract

This paper proposes a 2-dimensional (2D) maximum entropy threshold segmentation (2DMETS) based speeded-up robust features (SURF) approach for image target matching. First of all, based on the gray level of each pixel and the average gray level of its neighboring pixels, we construct a 2D gray histogram. Second, by the target and background segmentation, we localize the feature points at the interest points which have the local extremum of box filter responses. Third, from the 2D Haar wavelet responses, we generate the 64-dimensional (64D) feature point descriptor vectors. Finally, we perform the target matching according to the comparisons of the 64D feature point descriptor vectors. Experimental results show that our proposed approach can effectively enhance the target matching performance, as well as preserving the real-time capacity.


---

## Body

## 1. Introduction

In recent decades, the image target matching not only plays a significant role in many research fields, like the computer vision and digital image processing [1], but also has been widely used in a variety of military and civil applications [2], such as the image target detection, autonomous navigation, 3-dimensional reconstruction, target and scene recognition, and visual positioning and tracking. The image target matching involves two main categories of matching algorithms: gray correlation-based algorithm [3] and feature-based algorithm [4]. Gray correlation-based algorithm is based on the calculation of image similarities and the searching for the extreme values of similarities by using the optimal parameters in transformation model. However, feature-based algorithm mainly relies on the matching of the feature parameters extracted from images (e.g., the points, lines, and surfaces in images). In the condition of slight distortion of gray and geometry, although a large amount of computation cost is required by gray correlation-based algorithm, it normally outperforms feature-based algorithm, in terms of accuracy, robustness, and antinoise ability. However, in the serious distortion condition, feature-based algorithm is much preferred due to the lower false matching rates and better robustness for gray changes, image deformation, and occlusion.The basic motivation of addressing 2DMETS based SURF in this paper is to improve the cost efficiency and matching accuracy further. In concrete terms, due to the smaller sizes of descriptors in integral images (e.g., each descriptor in SURF only contains 64 bins which is half the size of the descriptor in SIFT), 2DMETS based SURF requires lower computation cost for the detecting and matching of feature points compared to the conventional SIFT [5]. There are two main steps involved in 2DMETS based SURF: (i) performing 2DMETS to construct 2D gray histogram and (ii) conducting feature point searching and target matching by SURF.The rest of this paper is structured as follows. In Section2, we give some related works. In Section 3, the detailed steps of 2DMETS based SURF are discussed. Experimental results are provided in Section 4. Finally, Section 5 concludes this paper and presents some future directions.


## 2. Related Work

As the first representative work on image target matching, the authors in [6] proposed the cross correlation algorithm to conduct the target matching in remote multispectral and multitemporal images by using the fast Fourier transform. The sequential similarity detection algorithm (SSDA) addressed in [6] can not only effectively eliminate the unmatched points, but also remarkably save the cost for image matching. Rosenfeld and Kak in [7] used a new concept of cross-correlation-based target matching which relies on the similarities of the gray areas in different templates. Harris operator which was introduced in [8] can extract the angular feature points with good performance in computation cost and stability. Harris and Stephens in [8] illustrated the four main factors involved in image target matching: feature spaces, searching spaces, searching strategies, and similarity measures. Considering medical image deformation property, Collignon et al. in [9] and Viola and Wells in [10] analyzed the mutual information-based medical image target matching. By conducting normalization of rotation and translation to obtain the affine invariant, SIFT [11] was proved to perform well with respect to image rotation, transformation, and zooming [12]. One of the most popular ways to represent local features as the histogram of gradient locations and orientations was introduced in [13].In recent decades, many institutes and universities proposed a variety of enhanced approaches for image target matching, like the principle component analysis-based SIFT (PCA-SIFT), Harris-SIFT, affine SIFT (ASIFT), shape SIFT (SSIFT), and speeded-up robust features (SURF). The descriptors in PCA-SIFT can effectively reduce the number and dimensions of feature points. In concrete terms, the descriptors in PCA-SIFT encode salient aspect of image gradients into the neighborhood of feature points and then normalize the gradient patches by using the PCA approach [14]. Harris-SIFT relies on the Harris operators to extract feature points and calculate descriptors [5]. There are two camera axis parameters, latitude angle and longitude angle, considered in ASIFT [15]. Based on the global shape context, SSIFT was applied to recognize the Chinese characters in the images contaminated by complex circumstance in [16]. By using the integral images for the image convolution, SURF only requires a small number of histograms to quantize the gradient orientations [17]. Sergieh et al. in [18] studied the way to reduce the number of required features by SURF, while preserving the high correct matching performance. Zhang and Hu in [3] invented the Fast-Hessian detectors for SURF from accelerated segment test (FAST) corner detector. Kai et al. in [19] proposed the normalized SURF to reduce the influence of huge difference on target matching. Juan and Gwun in [20] focused on panorama image stitching by the integration of SURF and multiband blending.The abovementioned algorithms fail to carefully consider the interference of background noise and edge pixels on image target matching. To fix this problem, we propose the 2DMETS based SURF in this paper. 2DMETS based SURF can be simply recognized as an integration of 2DMETS and SURF.


## 3. Steps of 2DMETS of SURF

### 3.1. Flow Chart

In 2DMETS based SURF, we first construct a 2D gray histogram based on the gray level of each pixel and the average gray level of its 8 neighboring pixels (orneighborhood). Then, we conduct image segmentation for the sake of mitigating the interference from background noise and edge pixels. Finally, we use SURF to conduct the target matching. The flow chart of 2DMETS based SURF for image matching is shown in Figure 1.Figure 1
Flow chart of 2DMETS based SURF.


### 3.2. Gray Histogram Construction

For each raw imageI (with gray levels L), the gray level of each pixel i(i=0,…,L-1) and the average gray level of its neighborhood j(j=0,…,L-1) form a pair of gray levels [i,j]. We can calculate the probability of each gray level pair p(i,j)(0≤p(i,j)≤1) by
(1)p(i,j)=r(i,j)M×N,∑i=0L-1∑j=0L-1p(i,j)=1,
where r(i,j) denotes the frequency of pair [i,j]; M and N stand for the number of pixels in horizontal direction and in vertical direction, respectively, in the raw image. Then, the gray histogram to be constructed in this paper can be recognized as a 2D histogram consisting of the frequencies of gray level pairs.


### 3.3. Optimization of Maximum Entropy Threshold

If we set the maximum entropy threshold at gray level pair[s,t], the segmented regions which contain the pairs [i′,j′](i′=0,…,s;j′=0,…,t) and [i′′,j′′](i′′=s+1,…,L-1;j′′=t+1,…,L-1), respectively, stand for the target and background regions. The normalization entropy with respect to target (H1) and background (H2) is calculated by
(2)H1=∑i=0s∑j=0tp(i,j)p1(s,t)lgp1(i,j)p(s,t)=lgp1(s,t)+h1(s,t)p1(s,t),p1(s,t)=∑i=0s∑j=0tp(i,j),h1(s,t)=-∑i=0s∑j=0tp(i,j)lgp(i,j),H2=∑i=s+1L-1∑j=t+1L-1p(i,j)p2(s,t)lgp2(i,j)p(s,t)=lgp2(s,t)+h2(s,t)p2(s,t),p2(s,t)=∑i=s+1L-1∑j=t+1L-1p(i,j),h2(s,t)=-∑i=s+1L-1∑j=t+1L-1p(i,j)lgp(i,j).The total entropy (H(s,t)) for the target and background regions can be obtained by
(3)H(s,t)=lgp1(s,t)p2(s,t)+h1(s,t)p1(s,t)+h2(s,t)p2(s,t).We select the pair[s*,t*] which results in the largest total entropy as the optimal maximum entropy threshold, such that
(4)[s*,t*]=argmax⁡0≤s≤L-1;0≤t≤L-1H(s,t).


### 3.4. Feature Point Determination

The three main steps involved in the determination of feature points are as follows: integral image construction, interest point detection, and Gaussian scale approximation.After the Gaussian scales have been approximated, all the interested points can be detected. As the final step of the feature point determination, we compare each interested point with its 26 neighboring pixels in a3×3 region at the current and adjacent scales by the nonmaximum suppression approach and then localize the feature points at the interest points which have the local maximum or minimum values of box filter responses.


### 3.5. Calculation of SURF Descriptor

To guarantee the rotation invariance, each feature point is assigned by a reproducible orientation. By assuming that a feature point is found at scales, Haar wavelet responses with the size 4s can be obtained for the neighboring pixels with radius 6s. The Haar wavelet responses are weighted by the Gaussian scale with σ=2s and then represented as the points in a space centered at the feature point. The longest orientation vector is selected as the dominant orientation to be assigned to the descriptor.


### 3.6. Target Matching

We adopt the Euclidean distance to evaluate the similarity of every two normalized SURF descriptors (Di,j), as described in
(5)Di,j=∑k=064(Xi-Xj)2,
where Xi and Xj stand for the ith and jth normalized SURF descriptors in two different images. We calculate the Euclidean distances from each feature point in one of the two images to its first nearest neighbor (1st NN) and second nearest neighbor (2nd NN) in another image. The matching occurs when the ratio (1stNN)/(2ndNN) is larger than a given threshold. In our experiments, we set the threshold as 0.75. The larger threshold could result in the smaller number of matching points between these two images.


## 3.1. Flow Chart

In 2DMETS based SURF, we first construct a 2D gray histogram based on the gray level of each pixel and the average gray level of its 8 neighboring pixels (orneighborhood). Then, we conduct image segmentation for the sake of mitigating the interference from background noise and edge pixels. Finally, we use SURF to conduct the target matching. The flow chart of 2DMETS based SURF for image matching is shown in Figure 1.Figure 1
Flow chart of 2DMETS based SURF.


## 3.2. Gray Histogram Construction

For each raw imageI (with gray levels L), the gray level of each pixel i(i=0,…,L-1) and the average gray level of its neighborhood j(j=0,…,L-1) form a pair of gray levels [i,j]. We can calculate the probability of each gray level pair p(i,j)(0≤p(i,j)≤1) by
(1)p(i,j)=r(i,j)M×N,∑i=0L-1∑j=0L-1p(i,j)=1,
where r(i,j) denotes the frequency of pair [i,j]; M and N stand for the number of pixels in horizontal direction and in vertical direction, respectively, in the raw image. Then, the gray histogram to be constructed in this paper can be recognized as a 2D histogram consisting of the frequencies of gray level pairs.


## 3.3. Optimization of Maximum Entropy Threshold

If we set the maximum entropy threshold at gray level pair[s,t], the segmented regions which contain the pairs [i′,j′](i′=0,…,s;j′=0,…,t) and [i′′,j′′](i′′=s+1,…,L-1;j′′=t+1,…,L-1), respectively, stand for the target and background regions. The normalization entropy with respect to target (H1) and background (H2) is calculated by
(2)H1=∑i=0s∑j=0tp(i,j)p1(s,t)lgp1(i,j)p(s,t)=lgp1(s,t)+h1(s,t)p1(s,t),p1(s,t)=∑i=0s∑j=0tp(i,j),h1(s,t)=-∑i=0s∑j=0tp(i,j)lgp(i,j),H2=∑i=s+1L-1∑j=t+1L-1p(i,j)p2(s,t)lgp2(i,j)p(s,t)=lgp2(s,t)+h2(s,t)p2(s,t),p2(s,t)=∑i=s+1L-1∑j=t+1L-1p(i,j),h2(s,t)=-∑i=s+1L-1∑j=t+1L-1p(i,j)lgp(i,j).The total entropy (H(s,t)) for the target and background regions can be obtained by
(3)H(s,t)=lgp1(s,t)p2(s,t)+h1(s,t)p1(s,t)+h2(s,t)p2(s,t).We select the pair[s*,t*] which results in the largest total entropy as the optimal maximum entropy threshold, such that
(4)[s*,t*]=argmax⁡0≤s≤L-1;0≤t≤L-1H(s,t).


## 3.4. Feature Point Determination

The three main steps involved in the determination of feature points are as follows: integral image construction, interest point detection, and Gaussian scale approximation.After the Gaussian scales have been approximated, all the interested points can be detected. As the final step of the feature point determination, we compare each interested point with its 26 neighboring pixels in a3×3 region at the current and adjacent scales by the nonmaximum suppression approach and then localize the feature points at the interest points which have the local maximum or minimum values of box filter responses.


## 3.5. Calculation of SURF Descriptor

To guarantee the rotation invariance, each feature point is assigned by a reproducible orientation. By assuming that a feature point is found at scales, Haar wavelet responses with the size 4s can be obtained for the neighboring pixels with radius 6s. The Haar wavelet responses are weighted by the Gaussian scale with σ=2s and then represented as the points in a space centered at the feature point. The longest orientation vector is selected as the dominant orientation to be assigned to the descriptor.


## 3.6. Target Matching

We adopt the Euclidean distance to evaluate the similarity of every two normalized SURF descriptors (Di,j), as described in
(5)Di,j=∑k=064(Xi-Xj)2,
where Xi and Xj stand for the ith and jth normalized SURF descriptors in two different images. We calculate the Euclidean distances from each feature point in one of the two images to its first nearest neighbor (1st NN) and second nearest neighbor (2nd NN) in another image. The matching occurs when the ratio (1stNN)/(2ndNN) is larger than a given threshold. In our experiments, we set the threshold as 0.75. The larger threshold could result in the smaller number of matching points between these two images.


## 4. Experimental Results

### 4.1. Image Description

There are four groups of images selected for the testing: (i) group 1 (in Figure2): indoor short-distance images containing one target and with slight difference of illumination intensity and angle rotation; (ii) group 2 (in Figure 3): indoor short-distance images containing multiple targets and with similar illumination intensity, but slight difference of angle rotation; (iii) group 3 (in Figure 4): outdoor long-distance images with great difference of angle rotation; this group of images is also used in [13, 14]; and (iv) group 4 (in Figure 5): image 1 is from the SOSO street view [21], while image 2 is taken by a SONY L26i cellphone. The interference of background noise in this group of images is more significant compared to the previous three groups of images (e.g., the passing pedestrians).(a) Otsu segmentation on images in group 1. (b) 2DMETS on images in group 1.
(a)
(b)(a) Otsu segmentation on images in group 2. (b) 2DMETS on images in group 2.
(a)
(b)(a) Otsu segmentation on images in group 3. (b) 2DMETS on images in group 3.
(a)
(b)(a) Otsu segmentation on images in group 4. (b) 2DMETS on images in group 4.
(a)
(b)


### 4.2. Matching Results

First of all, we apply Otsu segmentation and 2DMETS to transform the raw images into black-and-white images in a uniform gray scale to mitigate the interference from background noise and edge pixels, as shown in Figures2–5. By setting L=16, we have 256 pairs of gray levels, as represented at horizontal coordinates in gray histogram, while the vertical coordinates stand for the frequencies of gray level pairs. Figures 2(a), 3(a), 4(a), and 5(a) show the segmentation results by Otsu, while Figures 2(b), 3(b), 4(b), and 5(b) show the results by 2DMETS.Second, Figures6, 7, 8, and 9 show the results of target matching by using SIFT, SURF, Otsu based SIFT, Otsu based SURF, 2DMETS based SIFT, and 2DMETS based SURF for each group of images. Last, the matching performance is compared in Tables 1, 2, 3, and 4.Table 1
Matching performance for images in group 1.
Parameters
SIFT
SURF
Otsu based SIFT
Otsu based SURF
2DMETS based SIFT
2DMETS based SURF
Number of feature points (left/right images)
84/88
60/69
223/169
82/83
698/321
116/89
Number of correct matches
10
18
21
25
21
22
Number of incorrect matches
1
3
3
2
1
1Table 2
Matching performance for images in group 2.
Parameters
SIFT
SURF
Otsu based SIFT
Otsu based SURF
2DMETS based SIFT
2DMETS based SURF
Number of feature points (left/right images)
151/86
210/161
152/169
175/144
478/508
221/189
Number of correct matches
56
99
46
80
136
144
Number of incorrect matches
2
2
5
2
1
0Table 3
Matching performance for images in group 3.
Parameters
SIFT
SURF
Otsu based SIFT
Otsu based SURF
2DMETS based SIFT
2DMETS based SURF
Number of feature points (left/right images)
827/796
406/429
1570/1211
418/430
1756/1522
378/414
Number of correct matches
2
4
6
8
4
11
Number of incorrect matches
0
0
2
3
0
0Table 4
Matching performance for images in group 4.
Parameters
SIFT
SURF
Otsu based SIFT
Otsu based SURF
2DMETS based SIFT
2DMETS based SURF
Number of feature points (left/right images)
342/182
316/296
339/458
328/269
355/407
296/322
Number of correct matches
11
56
1
40
8
62
Number of incorrect matches
3
0
0
4
0
0Target matching for images in group 1.
(a)
SIFT
(b)
SURF
(c)
Otsu based SIFT
(d)
Otsu based SURF
(e)
2DMETS based SIFT
(f)
2DMETS based SURFTarget matching for images in group 2.
(a)
SIFT
(b)
SURF
(c)
Otsu based SIFT
(d)
Otsu based SURF
(e)
2DMETS based SIFT
(f)
2DMETS based SURFTarget matching for images in group 3.
(a)
SIFT
(b)
SURF
(c)
Otsu based SIFT
(d)
Otsu based SURF
(e)
2DMETS based SIFT
(f)
2DMETS based SURFTarget matching for images in group 4.
(a)
SIFT
(b)
SURF
(c)
Otsu based SIFT
(d)
Otsu based SURF
(e)
2DMETS based SIFT
(f)
2DMETS based SURF


### 4.3. Result Discussion

#### 4.3.1. Repeatability

After the affine transformation, if there is a pair of feature points located at the same target in the two different images, acorrespondence occurs. Then, we defineRepeatability as the ratio between the number ofcorrespondence and the minimal number of feature points (min⁡(featureimg1,featureimg2)):
(6)Repeatability=Numberofcorrespondencemin⁡(featureimg1,featureimg2),
where featureimg1 and featureimg2 stand for the numbers of feature points in the two different images, respectively. The higher value ofRepeatability indicates that the targets are more likely to be matched.


#### 4.3.2. Match Score

Match Score is defined as the ratio between the number ofcorrect matches and the value min⁡(featureimg1,featureimg2). Obviously, the higherMatch Score means that the targets are more likely to be matched correctly:
(7)MatchScore=Numberofcorrectmatchesmin⁡(featureimg1,featureimg2).


#### 4.3.3. Correct Matching Rate

We useCorrect Matching Rate to examine the probability of the targets to be matched.Correct Matching Rate is defined as the ratio between the number ofcorrect matches and the number oftotal matches. The higherCorrect Matching Rate will result in the higher probability for correct matching:
(8)CorrectMatchingRate=NumberofcorrectmatchesNumberoftotalmatches.


#### 4.3.4. Matching Time

The matching time determines the real-time capacity of our proposed approach. We define it as the time cost for feature point searching and target matching. TheRepeatability,Match Score,Correct Matching Rate, and the matching time for each group of images are shown in Figure 10.Repeatability,Match Score, Correct Matching Rate, and matching time for each group of images.
(a)
Repeatability
(b)
Match Score
(c)
Correct Matching Rate
(d)
Matching timeAs can be seen from Figure10, we can find that (i) the targets are very likely to be matched by 2DMETS based SURF due to the highRepeatability achieved; (ii) there is slight influence onMatch Score by using the SURF with and without 2DMETS; (iii) our proposed 2DMETS based SURF performs best in terms ofCorrect Matching Rate; and (iv) although a little extra time cost is required by 2DMETS processing, the real-time capacity can also be guaranteed by the proposed 2DMETS based SURF.


## 4.1. Image Description

There are four groups of images selected for the testing: (i) group 1 (in Figure2): indoor short-distance images containing one target and with slight difference of illumination intensity and angle rotation; (ii) group 2 (in Figure 3): indoor short-distance images containing multiple targets and with similar illumination intensity, but slight difference of angle rotation; (iii) group 3 (in Figure 4): outdoor long-distance images with great difference of angle rotation; this group of images is also used in [13, 14]; and (iv) group 4 (in Figure 5): image 1 is from the SOSO street view [21], while image 2 is taken by a SONY L26i cellphone. The interference of background noise in this group of images is more significant compared to the previous three groups of images (e.g., the passing pedestrians).(a) Otsu segmentation on images in group 1. (b) 2DMETS on images in group 1.
(a)
(b)(a) Otsu segmentation on images in group 2. (b) 2DMETS on images in group 2.
(a)
(b)(a) Otsu segmentation on images in group 3. (b) 2DMETS on images in group 3.
(a)
(b)(a) Otsu segmentation on images in group 4. (b) 2DMETS on images in group 4.
(a)
(b)


## 4.2. Matching Results

First of all, we apply Otsu segmentation and 2DMETS to transform the raw images into black-and-white images in a uniform gray scale to mitigate the interference from background noise and edge pixels, as shown in Figures2–5. By setting L=16, we have 256 pairs of gray levels, as represented at horizontal coordinates in gray histogram, while the vertical coordinates stand for the frequencies of gray level pairs. Figures 2(a), 3(a), 4(a), and 5(a) show the segmentation results by Otsu, while Figures 2(b), 3(b), 4(b), and 5(b) show the results by 2DMETS.Second, Figures6, 7, 8, and 9 show the results of target matching by using SIFT, SURF, Otsu based SIFT, Otsu based SURF, 2DMETS based SIFT, and 2DMETS based SURF for each group of images. Last, the matching performance is compared in Tables 1, 2, 3, and 4.Table 1
Matching performance for images in group 1.
Parameters
SIFT
SURF
Otsu based SIFT
Otsu based SURF
2DMETS based SIFT
2DMETS based SURF
Number of feature points (left/right images)
84/88
60/69
223/169
82/83
698/321
116/89
Number of correct matches
10
18
21
25
21
22
Number of incorrect matches
1
3
3
2
1
1Table 2
Matching performance for images in group 2.
Parameters
SIFT
SURF
Otsu based SIFT
Otsu based SURF
2DMETS based SIFT
2DMETS based SURF
Number of feature points (left/right images)
151/86
210/161
152/169
175/144
478/508
221/189
Number of correct matches
56
99
46
80
136
144
Number of incorrect matches
2
2
5
2
1
0Table 3
Matching performance for images in group 3.
Parameters
SIFT
SURF
Otsu based SIFT
Otsu based SURF
2DMETS based SIFT
2DMETS based SURF
Number of feature points (left/right images)
827/796
406/429
1570/1211
418/430
1756/1522
378/414
Number of correct matches
2
4
6
8
4
11
Number of incorrect matches
0
0
2
3
0
0Table 4
Matching performance for images in group 4.
Parameters
SIFT
SURF
Otsu based SIFT
Otsu based SURF
2DMETS based SIFT
2DMETS based SURF
Number of feature points (left/right images)
342/182
316/296
339/458
328/269
355/407
296/322
Number of correct matches
11
56
1
40
8
62
Number of incorrect matches
3
0
0
4
0
0Target matching for images in group 1.
(a)
SIFT
(b)
SURF
(c)
Otsu based SIFT
(d)
Otsu based SURF
(e)
2DMETS based SIFT
(f)
2DMETS based SURFTarget matching for images in group 2.
(a)
SIFT
(b)
SURF
(c)
Otsu based SIFT
(d)
Otsu based SURF
(e)
2DMETS based SIFT
(f)
2DMETS based SURFTarget matching for images in group 3.
(a)
SIFT
(b)
SURF
(c)
Otsu based SIFT
(d)
Otsu based SURF
(e)
2DMETS based SIFT
(f)
2DMETS based SURFTarget matching for images in group 4.
(a)
SIFT
(b)
SURF
(c)
Otsu based SIFT
(d)
Otsu based SURF
(e)
2DMETS based SIFT
(f)
2DMETS based SURF


## 4.3. Result Discussion

### 4.3.1. Repeatability

After the affine transformation, if there is a pair of feature points located at the same target in the two different images, acorrespondence occurs. Then, we defineRepeatability as the ratio between the number ofcorrespondence and the minimal number of feature points (min⁡(featureimg1,featureimg2)):
(6)Repeatability=Numberofcorrespondencemin⁡(featureimg1,featureimg2),
where featureimg1 and featureimg2 stand for the numbers of feature points in the two different images, respectively. The higher value ofRepeatability indicates that the targets are more likely to be matched.


### 4.3.2. Match Score

Match Score is defined as the ratio between the number ofcorrect matches and the value min⁡(featureimg1,featureimg2). Obviously, the higherMatch Score means that the targets are more likely to be matched correctly:
(7)MatchScore=Numberofcorrectmatchesmin⁡(featureimg1,featureimg2).


### 4.3.3. Correct Matching Rate

We useCorrect Matching Rate to examine the probability of the targets to be matched.Correct Matching Rate is defined as the ratio between the number ofcorrect matches and the number oftotal matches. The higherCorrect Matching Rate will result in the higher probability for correct matching:
(8)CorrectMatchingRate=NumberofcorrectmatchesNumberoftotalmatches.


### 4.3.4. Matching Time

The matching time determines the real-time capacity of our proposed approach. We define it as the time cost for feature point searching and target matching. TheRepeatability,Match Score,Correct Matching Rate, and the matching time for each group of images are shown in Figure 10.Repeatability,Match Score, Correct Matching Rate, and matching time for each group of images.
(a)
Repeatability
(b)
Match Score
(c)
Correct Matching Rate
(d)
Matching timeAs can be seen from Figure10, we can find that (i) the targets are very likely to be matched by 2DMETS based SURF due to the highRepeatability achieved; (ii) there is slight influence onMatch Score by using the SURF with and without 2DMETS; (iii) our proposed 2DMETS based SURF performs best in terms ofCorrect Matching Rate; and (iv) although a little extra time cost is required by 2DMETS processing, the real-time capacity can also be guaranteed by the proposed 2DMETS based SURF.


## 4.3.1. Repeatability

After the affine transformation, if there is a pair of feature points located at the same target in the two different images, acorrespondence occurs. Then, we defineRepeatability as the ratio between the number ofcorrespondence and the minimal number of feature points (min⁡(featureimg1,featureimg2)):
(6)Repeatability=Numberofcorrespondencemin⁡(featureimg1,featureimg2),
where featureimg1 and featureimg2 stand for the numbers of feature points in the two different images, respectively. The higher value ofRepeatability indicates that the targets are more likely to be matched.


## 4.3.2. Match Score

Match Score is defined as the ratio between the number ofcorrect matches and the value min⁡(featureimg1,featureimg2). Obviously, the higherMatch Score means that the targets are more likely to be matched correctly:
(7)MatchScore=Numberofcorrectmatchesmin⁡(featureimg1,featureimg2).


## 4.3.3. Correct Matching Rate

We useCorrect Matching Rate to examine the probability of the targets to be matched.Correct Matching Rate is defined as the ratio between the number ofcorrect matches and the number oftotal matches. The higherCorrect Matching Rate will result in the higher probability for correct matching:
(8)CorrectMatchingRate=NumberofcorrectmatchesNumberoftotalmatches.


## 4.3.4. Matching Time

The matching time determines the real-time capacity of our proposed approach. We define it as the time cost for feature point searching and target matching. TheRepeatability,Match Score,Correct Matching Rate, and the matching time for each group of images are shown in Figure 10.Repeatability,Match Score, Correct Matching Rate, and matching time for each group of images.
(a)
Repeatability
(b)
Match Score
(c)
Correct Matching Rate
(d)
Matching timeAs can be seen from Figure10, we can find that (i) the targets are very likely to be matched by 2DMETS based SURF due to the highRepeatability achieved; (ii) there is slight influence onMatch Score by using the SURF with and without 2DMETS; (iii) our proposed 2DMETS based SURF performs best in terms ofCorrect Matching Rate; and (iv) although a little extra time cost is required by 2DMETS processing, the real-time capacity can also be guaranteed by the proposed 2DMETS based SURF.


## 5. Conclusion

A novel 2DMETS based SURF proposed in this paper is proved to perform well in accuracy and computation cost for image target matching. Compared to the conventional SIFT, SURF, Otsu based SIFT, Otsu based SURF, and the enhanced 2DMETS based SIFT, an effective improvement ofCorrect Matching Rate without significant loss in real-time capacity is possible, which indicates an important advantage for the time-efficient image processing applications. However, this paper mainly focuses on the target matching between gray images. We will pay more attention to the design of the accurate and cost-efficient image target matching approaches for color images in future.



---

*Source: 768519-2014-08-26.xml*