Journal of Ambient Intelligence and Humanized Computing https://doi.org/10.1007/s12652-018-0833-0

ORIGINAL RESEARCH

Image matching algorithm of defects on navel orange surface based on compressed sensing Xin Xie1 · Songlin Ge1 · Mingye Xie2 · Fengping Hu3 · Nan Jiang1 · Tijian Cai1 · Bo Li1 Received: 26 July 2016 / Accepted: 3 May 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018

Abstract The surface defect of navel orange is one of the significant factors that affects its price. At present, most of surface defect detection algorithms for navel orange have disadvantages of slow speed, massive calculation and low efficiency, making it difficult to meet the needs of automated detection. This article proposes an improved image matching method on navel orange surface defect detection which combines wavelet transform (WT) and speeded up robust features (SURF) based on compressed sensing (CS). Firstly, do some pre-treatment on the navel orange images such as de-noising, compression and so on, then decompose the image by wavelet transform based on compressed sensing technology, and obtain the low frequency sub-image and extract SURF features of the image, next compare the extracted SURF feature with feature library, search for the maximum matching value of the similarity measurement values, and output the recognition results. The algorithm ensures better recognition accuracy and efficiency, and achieves rapid identification of navel orange defects. Keywords  Compressed sensing · Wavelet transform · SURF features · Surface defect · Similarity measure

1 Introduction

* Xin Xie [email protected] Songlin Ge [email protected] Mingye Xie [email protected] Fengping Hu [email protected] Nan Jiang [email protected] Tijian Cai [email protected] Bo Li [email protected] 1



School of Information Engineering, East China Jiaotong University, Nanchang, People’s Republic of China

2



School of Information Science Technology, East China Normal University, Shanghai, People’s Republic of China

3

School of Civil Engineering, East China Jiaotong University, Nanchang, People’s Republic of China



The defects on fruit surface can directly reflect its quality, and it is an important factor that affects its price. Navel orange is a kind of significant economic fruit, there are kinds of common defects, for example: thrips fruit, ulcers fruit, lacerations fruit, anthracnose fruit, sunburn fruit, drug injury fruit, wind damage fruit, insect injury fruit, scale insects fruit, different color stripes fruit, rotting fruit and so on. The traditional method of manual sorting has many problems, such as slow detection speed and unsatisfactory classification results. In the internet era, with the rapid development of machine vision technology and multimedia technology, image recognition  (Wang and Zhang 2007; Burger and Burge 2016) has become a popular research direction in computer image processing. Many scholars and researchers have done a lot of research on the detection of fruit surface defects by using machine vision technology, and proposed a lot of related detection methods. Surface defect identification (Li et al. 2011; Rong et al. 2017a) for navel orange has also become an important research area. The current studies on navel orange surface defect detection are mostly based on static images, using complex algorithm to identify fruit surface defects, primarily focusing on one of single characteristic for classification with less

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characteristic information, the result of categorization is not very ideal. Although these methods can realize the detection of surface defects, there are still a lot of shortcomings, especially in defect matching and identification. In recent years, lots of algorithms of image matching have been proposed (Man et al. 2001; Ge et al. 2014). The image matching method based on content is gradually replacing traditional retrieval method as the main method of image retrieval technology. A variety of methods of fruit surface defect detection (LI et al. 2012; Rong et al. 2017b) and automatic fruit grading  (Wang et al. 2014; Thendral and Suhasini 2016) have been proposed. Baranowski et al. (2012) combined with principal component analysis and minimum noise separation analysis method to analyze apple surface defect. Yogitha and Sakthivel (2014) developed a computer machine vision system based on synchronized trigger events, and it can be used for automatic high-speed fruit sorting and grading. Bhatt and Pant (2015) described a new apple classification system based on machine vision and artificial neural network (ANN), which classifies apple in real time on the basis of physical parameters of apple such as size, color and external defects. In 2004, (Lowe 2004) formally put forward feature points matching algorithm named SIFT (Scale Invariant Feature Transform), which can keep rotation, scale and affine unchanged, and widely be used in image matching (Tan 2013; Xu et al. 2013; Cao 2012). Although this method could maintain stability to a certain extent, it has the problem of image mismatch when the feature points are too many. Afterwards, Bay et al. (2006) proposed SURF algorithm  (Xuanmin 2010; Wu et al. 2014) based on SIFT. The method improved the speed and performance greatly, and widely be used in image matching, which is superior in processing in severe blurring and rotation of image. The two methods above can only be used in some specific conditions in image matching, thus, it remains to be further improved in complex environment. In Yao et al. (2014), used Euclidean nearest neighbor distance ratio method to match the extracted SURF features roughly, and obtain neighborhood gray statistics of corresponding feature point scale. Then, matching pairs with strong robustness with Pearson correlation coefficient. The method can effectively improve the matching accuracy and meet real-time requirements. But it takes too much time, which is not ideal for large image. In the same year, Hu et al. (2014) used mathematical morphological method to separate navel orange from background. And the features of bulk, surface defect, color and texture were extracted as the input feature vectors of the support vector machine (SVM), which is used for training. The trained classifier was used to detect the navel orange. However, this method is slow, and the correct recognition rate is not high. In view of the disadvantages of the methods above, this paper introduces the compressed sensing and wavelet

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transform technology to find a fast SURF image matching algorithm, which can make matching for feature point more accurate and faster to achieve a better visual effect. Firstly, describing spatial signal’s changes through compressed sensing on the basis of WT’s multi-resolution feature. Then do some pre-treatments on the navel orange images. Secondly, using wavelet multi-scale decomposition with compressed sensing technology on the image, which can obtain the low-frequency sub-image, then extracting SURF features of the image. Lastly, comparing the extracted SURF feature points with feature library, and searching maximum matching value of the similarity measure value.

2 Theory of compressed sensing Compressed sensing (Donoho 2006) is a kind of technology that uses compressible signal to achieve signal reconstruction when acquires signal, compressing the data appropriately at the same time to reduce sampling data and save storage space, but it still contains a sufficient amount of information, thus it can use signal compression value as its characteristic value. In image monitoring, compressed sensing technology can be carried out on the image compression effectively, which is advantageous to storage, as there is almost no distortion after extracting the information, ensuring the requirement of the small storage space and high accuracy. The theory of compressed sensing has made a new revolution in signal coding and decoding. The theory indicates that signal sampling and compression can occur at the same time. The signals are no-adaptively encoded and measured at a rate much lower than the Nyquist sampling rate. The decoding process is not a simple encoding inverse process, but a signal reconstruction algorithm based on sparse signal decomposition. It can reconstruct the signal at a certain level. The number of measurements required for decoding is far less than the number required for traditional methods. Literature (Donoho 2006; Shi et al. 2009) points out that: if the signal X ∈ RN on an orthogonal basis or tight frame Ψ is compressible, then linear combination of N × 1-dimen{ }the N sion basic vector 𝜓i i=1 could be used to express any signal of RN space. For arbitrary signal X ∈ RN  , the transformation { }N coefficient vector under the orthogonal basis Ψ = 𝜓i i=1 can be expressed as: (1) Θ = ΨT X where Ψ is the transform matrix composed by orthogonal transform bases, Θ is Ψ ’s equivalent or approximate sparse representation. The original signal X (if it is sparse by itself) or the transform basis Ψ (if the signal is sparse in transform domain) can be projected to a set of irrelevant observation matrices Φ with

Image matching algorithm of defects on navel orange surface based on compressed sensing

a size of smooth M × N(M ≪ N) dimensions, and observations on Θ to get the set of observations as vector Y = ΦΘ or Y = ΦΨT Θ . that is, X conducts adaptive observation by matrix ACS. (2) Y = ACS X where ACS is a CS information operator; Y is an observation set of M × 1 dimensions. Since Y includes specific information of every signal, each of the different signal values of Y is various. In the case that signal is an image, compressed data Y can be regarded as the representation of image features. Therefore, the use of compression perception technology can quickly and accurately extract the image feature.

3 Image representation based on CS The wavelet transform (Yan et al. 2011; Wang et al. 2012) is a local transformation of space (time) and frequency, which can obtain effective information from the signal, and analysis the signal by stretching and translating it in detailed multi-scale. Wavelet transform also has the characteristics of multi-level resolution analysis, which can decompose different scales of different signals, and then obtain the general and detail information of different levels of the target image. For the simple and single texture image, it will reduce the image matching rate when extracted the feature points excessively. Wavelet transform can decompose an image into components of location, size and orientation, and the image will be divided into the high-frequency and low-frequency part, high-frequency part maintains the details characteristics of the image and the low-frequency part maintains the overall characteristics of the image (Luo 2012; Cen et al. 2010). The low-frequency sub-image contains most of the information of the original image, and its scale space keeps the overall characteristics of the original image. Although it reduces its internal details, it also reduces the unnecessary features extraction while maintaining the basic characteristics of the image.

3.1 Wavelet multi‑scale representation of image Suppose 𝛿(x, y) is a separable two-dimensional scaling function, then 𝛿(x, y) can be separated into the product of two onedimensional scaling function: (3) if 𝜑(x) is the corresponding wavelet function, we can define three two-dimensional orthogonal wavelet functions:

𝛿(x, y) = 𝛿(x) ⋅ 𝛿(y)

𝜑1 (x, y) = 𝛿(x) ⋅ 𝜑(y) 𝜑2 (x, y) = 𝛿(y) ⋅ 𝜑(x) 𝜑3 (x, y) = 𝜑(x) ⋅ 𝜑(y)

Suppose f(x, y) is the image signal to be matched, its twodimensional discrete signal f (m, n) ’s approximation image is: ∑ ∑ 1 f (x, y) = am,n (j)𝜙m,n (j) + dm,n (k)𝜑1m,n (k) m,n

+

∑ m,n

m,n

2 dm,n (k)𝜑2m,n (k)

+

∑

3 dm,n (k)𝜑3m,n (k)

(5)

m,n

where, the right-hand side of the first term is image wavelet transform low frequency approximation part, the rest are the details of the signal. Next we need to decompose the image by two-dimensional wavelet transform (Wang and Zhang 2011), then do one-dimensional filtering on rows and columns of the image. In each transformation layer, do the operation of convolution on original image with a wavelet image, and take samples of the image, which at twice intervals on the x and y directions after convolution, after that, we can obtain four equal-sized sub-image, as is shown in Fig. 1. Wavelet transform, with the characteristic of multi-resolution analysis, can conduct different decompositions for different signals to obtain contours and details of different levels. The image can be divided into high-frequency parts which keep the detailed features and low-frequency parts which keep the general features.

3.2 CS representation of image based on wavelet multi‑scale decomposition The main idea of compressed sensing representation of image based on wavelet multi-scale decomposition is measuring a sparse image coefficient in the wavelet transform domain 𝜂 by using a random measurement matrix 𝜌 , which can obtain measurement coefficients in size of M × N  . These measurement coefficients contain sufficient information to reconstruct the image, which can solve the corresponding optimization problem by a certain model of decoding linear or nonlinear. As is shown in Fig. 2. We can obtain a sparse matrix after wavelet multi-scale decomposition, which contains low frequency and high frequency parts. Then by using translating and scaling wavelet function 𝜃(t) with band-pass characteristics and

(4)

Fig. 1  Wavelet decomposition of image

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4 SURF algorithm SURF operator (Peng et al. 2010; Oliveira et al. 2016) is a kind of local image feature descriptor based on scale space, which maintains invariance after image scaling, rotation and even affine transformations. SURF algorithm uses Pyramid and Gauss kernel filter to find the extreme points in the scale space, then extracts the feature points of the image to match the local feature points, SURF algorithm process is as follow.

Fig. 2  Image representation of compressed sensing

4.1 Feature point extraction

Fig. 3  Process of SURF algorithm

translation of scaling function 𝜅(t) with low-pass characteristics to represent the decomposition of signal X (Fig. 3):

( ) 𝜃J,P(t) ≡ 2−J∕2 𝜃 2−J t − P 𝜃J0 ,P(t) ≡ 2

−J∕2

(

𝜃 2

−J0

t−P

(6)

)

(7)

Then the signal X can be expressed as multi-scale decomposition:

x(t) =

∑

uP 𝜃J0 ,P (t) +

P

J0 ∑ ∑

vJ,P 𝜅J,P (t)

(8)

J=+∞ P

∗ dt . J represents where,uP = ∫ z(t)𝜃J∗ ,P (t)dt , vJ,P = ∫ x(t)𝜅J,P 0

the scale; The larger the scale, the lower the resolution and the lower frequency component. J0 represents the highest resolution of the corresponding components, which is the high frequency component; P is the translation component.

SURF algorithm and SIFT algorithm are both based on the scale space, image feature points are extracted by using the Hessian matrix of integral graph. For a certain point x(x, y) in the image I of scale 𝜎 , the Hessian matrix is defined as: ] [ Lxx (x, 𝜎) Lxy (x, 𝜎) H(x, 𝜎) = (9) Lxy (x, 𝜎) Lyy (x, 𝜎) where, Lxx (x, 𝜎) , Lxy (x, 𝜎) and Lyy (x, 𝜎) is the two-dimensional convolution of Gauss second-order partial derivative in point x. In order to improve the calculation speed of Gauss convolution, SURF operator uses the scale box filter to approximate the second-order Gauss filter, which constructs a Fast-Hessian matrix. For example as the 9 × 9 box filter, set the scale value s = 𝜎 = 1.5, the approximation of the second-order partial derivative of the Gauss convolution kernel is shown in Fig. 4. In the original image, we can form different scales of image Pyramids by expanding the size of the box filter, and accelerate the image convolution by using integral image. The approximation process of the Hessian matrix determinant is shown in Eq. (10).

ΔH=Dxx (x)Dyy (x) − (0.9Dxy (x))2

Fig. 4  Template of box filter

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(10)

Image matching algorithm of defects on navel orange surface based on compressed sensing

where ΔH is the response value of box filter in point x(x, y), use Δ to detect the extreme points of the image. Dxx , Dyy and Dxy represent the convolution results of a approximated template in Fig. 4 with the image. The value 0.9 is a weight coefficient which is mainly for balancing the approximation error. It has no significant effect on experimental results. In the scale space, the value of ΔH of each point is compared with the adjacent position of 26 neighboring areas, which can obtain the chosen local maximum points, then we can calculate the stable feature points by interpolating the image.

4.2 Feature point detection Coefficients of Haar wavelet responses are calculated in the x and y directions within a circular neighborhood of 6 𝜎 radius around the feature point, 𝜎 is the scale at which the feature point is detected. Then, response values within the scope of 60 are summed up to form a new vector. The direction of the longest vector as the main direction of feature point is selected after the entire circular area that is traversed.

Fig. 5  SURF feature point description

4.3 Feature point description The coordinate axis will rotates into the main direction of feature point to ensure rotation invariance. The square region within the range of 20𝜎 is regularly split into smaller 4 × 4 square sub-regions. Haar wavelet responses are computed at 5 × 5 regularly spaced sample points for each sub-region. dx is assumed to represent Haar wavelet response in horizontal direction and dy represents in vertical direction. Each sub∑ ∑ ∑ ∑� � region can be described as V = ( dx , ��dx ��, dy , �dy �) . � � All these vectors of sub-regions are concatenated to obtain a descriptor vector of 64 dimensions. Finally, in order to maintain the invariance of the illumination, the vector is normalized, and finally obtained the feature descriptor. As is shown in Fig. 5. Fig. 6  Technical route

4.4 Feature point matching The similarity criterion (Zhang et al. 2016) of the algorithm is based on the Euclidean distance between two feature points. Suppose the descriptors of feature point a and feature point b are x and y, then the distance is:

d=

n ∑ ( )2 xi − yi

(11)

i−1

So the ratios of the nearest neighbor to second nearest neighbor are calculated. If the ratios are less than the preset threshold, the nearest neighbor is considered as a good match.

5 The improved image matching algorithm The technical route flow chart of this paper is shown in Fig. 6. The technical route process includes obtaining lowfrequency sub-images by wavelet multi-scale decomposition of the image from the database to extract the SURF features of the low-frequency sub-images which can form the SURF feature vector database. Do wavelet multi-scale decomposition on image to be detected in the same way, then extract its SURF features, do the similarity measure through comparing SURF feature points with the SURF

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feature vector database, and finally output the results. The improved image matching algorithm is shown in Fig. 7. The specific steps of the algorithm are as follows: Step 1 Image preprocessing. Images can affect by noise, in order to avoid the influence of these factors, images in the database and the images which need to be matched were preprocessed by filtering, de-noising, enhancement and so on. Step 2 Selection of random observation matrix. Sparse coefficient matrix is obtained after doing wavelet transform to preprocessed images, to obtain observation value M (M ≪ N) whose data size is far smaller than the original signal or image dimension N based on observation of properly designed random observation matrix P. According to reference (Cen et al. 2010), P is defined as:

Pij =

√

⎧1 ⎪ s×⎨0 ⎪ −1 ⎩

probability i s 1∕2s probability i s 1 − 1∕s probability i s 1∕2s

(12)

where s ranges from 2 to 4, therefore we can obtain the feature of image and compress it quickly and accurately with compressed sensing, and get low-frequency sub-images through wavelet multi-scale decomposition. Step 3 Search for the feature points. Establish the SURF feature vector database by processing the image database and form SURF feature set A. Process the image S with wavelet transform, which can get low-frequency sub image T, then extract SURF features of T, and form set B of the feature point, using KD-Tree to establish the index

Fig. 7  Technical route

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for all elements of the B. Based on Euclidean distance, using BBF(Best Bin First) search algorithm to obtain each element approximation nearest neighbor feature point p ′ and p ′′ on the KD-Tree, then determine whether matching according to the value of d1/d2. Step 4 Image matching. Calculate the number of matched feature points and output the results.

6 Algorithm simulation and results analysis In order to verify feasibility of the algorithm, we use sym4 wavelet function to extract the features of low-frequency sub-images, then obtain the feature point’s distribution map of the original image and the sub-images by SURF. As is shown in Fig. 8. In Fig. 8a, b, which are the original image feature points distribution, the number of feature points are 185 and 79, and in Fig. 8c, d, which are the feature points distribution processed by wavelet transform, the number of feature points are 163 and 56. By contrast, the number of feature points has been reduced under guaranteeing the integrity of the information at the same time, which is processed by wavelet transform. And it also has reduced the time to search and improved the processing efficiency of a single image of navel orange. The four images are matched by the traditional SURF algorithm and the paper algorithm, and the results are shown in Figs. 9 and 10 It can be seen that the number of matched feature points is reduced by using paper algorithm. Error matching contrast between traditional SURF algorithm and paper algorithm is shown in Fig. 11. In the figure below, the error of paper algorithm keeps below 0.15, while the error of traditional SURF algorithm stays about 0.48. In order to verify the accuracy and efficiency of paper algorithm, we use 15 navel orange images with rotation, stretching transformation to establish an image retrieval database. The result is shown in Fig. 12. The paper also contrasts two algorithms in detection number of feature point, matching point number and times, as is shown in Table 1. From Table 1, it could be found that both the number of feature point and matching point in the proposed algorithm are less than the traditional SURF algorithm, what’s more, the proposed algorithm also spends less time. In order to demonstrate the superiority of the improved method better, this method is compared with the most commonly used support vector machine (SVM) for navel orange detection. The contrast result is shown in Fig. 13. All the data tells that the paper algorithm based on compressed sensing has higher matching efficiency and accuracy, and faster speed on defect detection of navel orange.

Image matching algorithm of defects on navel orange surface based on compressed sensing

Fig. 8  The original image and the image processed by wavelet transform feature points distribution

0.5 0.45

Image error matching

0.4

Paper algorithm The traditional SURF algorithm

0.35 0.3 0.25 0.2 0.15 0.1 0.05 0

0

50

100 Time/s

150

200

Fig. 11  Error contrast of two algorithms Fig. 9  Image defects matching by traditional SURF algorithm

Fig. 10  Image defects matching by paper algorithm

Fig. 12  The result of retrieval

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Table 1  The contrast of two algorithms Name

Number of feature point

The traditional 79 SURF algorithm Paper algorithm 56

Number of Matching

Matching time(s)

64

1.536

52

1.028

accuracy of the matching algorithm in dynamic navel orange defect image needs further research. Acknowledgements  This work is supported by the National Natural Science Foundation, under Grant Nos. 61762037, 61640217, 61462028, Science and Technology Support Program of Jiangxi Province, under Grant No. 20151BBE50055, and Science and Technology Project supported by education department of Jiangxi Province, under Grant No. GJJ150541, and Nanchang City Knowledge Innovation Team, under Grant No. 2016T75.

120

References

100

Detection speed

80 Paper algorithm SVM

60

40

20

0 0

20

40

60

80

100 Time/s

120

140

160

180

200

Fig. 13  The contrast result of decision speed

7 Conclusion and prospect In view of the shortcomings of the traditional SURF algorithm in extracting the feature points of the image with slow speed, this paper proposes a new algorithm of navel orange defect detection based on compressed sensing (Zhang et al. 2012; Wang and Xiang 2014) and wavelet transform combined with SURF algorithm. The sampling rate required by the CS theory is much lower than the traditional Nyquist sampling. Therefore, the feature extraction of the defect image requires less feature points and the speed of extraction improved greatly. The algorithm not only reduces feature point irrelevant with image matching greatly but also makes feature point matching more accurately. At the same time, based on the wavelet transform, the compression sensing technology is integrated, which greatly improves the detection efficiency of navel orange defect. Simulation experiment shows that the paper algorithm obtains satisfying results both in accuracy and time which meets real-time request in machine vision system. The research in this paper is based on the static navel orange defect image, if the navel orange images contain fruit stems and fruit calyx, the number of error matching will increase. Considering these, how to improve the

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