# Fast Extraction Algorithm for Local Edge Features of Super-Resolution Image

Authors: Feng Chen; Botao Yang
Journal: Security and Communication Networks
 (2022)

---

## Abstract

Image super-resolution is getting popularity these days in diverse fields, such as medical applications and industrial applications. The accuracy is imperative on image super-resolution. The traditional approaches for local edge feature point extraction algorithms are merely based on edge points for super-resolution images. The traditional algorithms are used to calculate the geometric center of gravity of the edge line when it is near, resulting in a low feature recall rate and unreliable results. In order to overcome these problems of lower accuracy in the existing system, an attempt is made in this research work to propose a new fast extraction algorithm for local edge features of super-resolution images. This paper primarily focuses on the super-resolution image reconstruction model, which is utilized to extract the super-resolution image. The edge contour of the super-resolution image feature is extracted based on the Chamfer distance function. Then, the geometric center of gravity of the closed edge line and the nonclosed edge line are calculated. The algorithm emphasizes on polarizing the edge points with the center of gravity to determine the local extreme points of the upper edge of the amplitude-diameter curve and to determine the feature points of the edges of the super-resolution image. The experimental results show that the proposed algorithm consumes 0.02 seconds to extract the local edge features of super-resolution images with an accuracy of up to 96.3%. The experimental results show that our proposed algorithm is an efficient method for the extraction of local edge features from the super-resolution images.


---

## Body

## 1. Introduction

The super-resolution technology of images is a technique for obtaining high-resolution images corresponding to scenes by using an existing method for low-resolution images without changing the image observation system [1]. Image super-resolution technology is improving day by day due to the huge demand in computer science and aligned fields [2]. It is widely used in medical imaging, video surveillance and transmission, generation of satellite remote sensing images, and HDTV [3]. In order to process images and to draw meaningful inferences, it is necessary to extract the edge’s local features of super-resolution images [4]. In this paper, the features of super-resolution images are extracted fast from the point of view of local feature points. Since the points are the primitives that constitute the super-resolution image, the points constituting the image vary widely. Therefore, it needs to extract some specific features that can represent the image attributes and can assist in image feature extraction and recognition. Feature extraction is also important to identify and track the target according to different needs and to construct a three-dimensional target surface [5, 6]. In the past research endeavours, many feature point extraction algorithms are proposed and deployed, which are mainly divided into two categories. One is the curvature-based local edge feature extraction algorithm of super-resolution image, and the other is the grey gradient-based algorithm. Both algorithms have disadvantages. The first type of algorithm has a large amount of calculation, and the second type of algorithm has low accuracy. At present, there is a feature point extraction algorithm based on edge points. Compared with the performance of the first two types of algorithms, the algorithm is simple and convenient to implement, but it has the following problems: first, only the edge line is considered. It is closed and does not conform to the actual situation. Secondly, the obtained local edge features of the super-resolution image are only the convex curvature with large curvature on the edge line, and the description of the shape of the target is incomplete [7].In [8], the authors have introduced a novel method for extracting transform characteristics from pictures or video frames. These characteristics are used to represent the local visual content of image and video frames. The projected method, such as Shot Boundary Detection (SBD), is measured using conventional methods utilizing the standard procedure. The experimental results reveal that the proposed method outperforms previous methods in terms of computational cost. In [9], the authors have investigated various picture feature extraction analysis techniques. By aggregating low-level characteristics to explore various feature data representations, this technique obtains more expressive and productive high-level information content. In [10], the authors have suggested a random deep neural network-based picture feature extraction technique. The goal of this strategy is to detect more consistent features by eliminating duplicate feature points. In [11], the authors have introduced a novel approach based on Bidimensional Empirical Mode Decomposition. This method was used to extract self-adaptive characteristics from pictures. In [12], the authors have designed a video summarization framework based on frame choice to determine only significant frames. As there are various drawbacks in the existing systems, we aim to produce an efficient algorithm to solve the above problems, which is fast and efficient than the previous approaches for local edge feature extraction of super-resolution images. The proposed algorithm will accurately reflect the shape contour of the target feature, which has important significance to extract the super-resolution image features.The contribution of the work is as follows:(i)
In this paper, a new fast extraction algorithm for local edge features of super-resolution images is proposed(ii)
The algorithm mainly focuses on the super-resolution image reconstruction model, which is used to obtain the super-resolution image(iii)
The algorithm puts emphasis on polarizing the edge points with the center of gravity as the pole to find the local extreme points of the upper edge of the amplitude-diameter curve and determine the feature points of the edge of the super-resolution image(iv)
The algorithm is compared using a super-resolution image reconstruction model and local edge feature extraction of a super-resolution image on the basis of which we calculate the geometric center of gravity and polarization of edges(v)
So, the proposed algorithm produces efficient output than the existing traditional approaches when compared using the RPC curve and keepingF-measure as a calculatory parameter(vi)
The proposed algorithm gives an efficiency of around 99% that surpasses the traditional approaches with a great margin, which was about 75% and 64%, respectivelyFurther, the paper is divided into five sections:(1)
Section1 gives an introduction about the existing approaches and shows the drawbacks of existing approaches(2)
Section2 shows the various approaches to the image reconstruction model and local edge feature extraction model and the changes to be made in them to make them efficient(3)
Section3 shows us the comparative result analysis of various algorithms with respect to the proposed system(4)
Section4 is the discussion of results and the various approaches made to make the algorithm efficient(5)
Section5 tells us about the obtained results and how much efficient our approach is with respect to others


## 2. Material and Methods

### 2.1. Super-Resolution Image Reconstruction Model

Degraded models for super-resolution image reconstruction can be expressed as follows:(1)yk=DWkFkX+ηk,where yk is the degraded kth frame image, X is the high-resolution image, D and Wk are the downsampling matrix and motion matrix, Fk is the fuzzy matrix, and ηk is the noise.Let the low-resolution image beY and the corresponding high-resolution image be X. The problem that the super-resolution reconstruction needs to solve is to find the optimal approximate solution X under the condition of known Y. The common method for solving this problem is Maximum Posterior Probability (MAP) under low-resolution range image conditions. MAP estimates can be represented by(2)x^=argmaxXPX|Y1,…,YN.According to the Bayesian estimation criterion, (2) can be rewritten as follows:(3)x^=argmaxXPY1=y1,…,YN=yN|X=xPX=x.In (3), it is assumed that the noise is independent Gaussian white noise [10] and the variance is σ2. Then, (4) is expressed as follows:(4)PY1=y1,…,YN=yN|X=x=12πσ2N1N2×exp−∑k=1Nyk−DWkFkX222σ2.According to the Markov random field model, the prior probabilityPX=x of the high-resolution range image is obtained, and the equivalence between MRF and Gibbs is used. The Gibbs distribution is used to explicitly describe the Markov distribution; that is, the prior probability of X can be expressed by(5)PX=x=1Zexp−1T∑c∈CXVcxx.The energy function takes the form of Li, as follows:(6)∑c∈CXVcxx=∑i=1L1∑j=1L24γ−γexp−xi,j−xi,j−12γ−γexp−xi,j−xi,j+12γ−γexp−xi,j−xi−1,j2γ−γexp−xi,j−xi+1,j2γ.Here,Z is a normalized constant, T is the temperature parameter, and Vcxx is the potential function of the connected group; the potential function describes the interaction of a set of neighbouring pixels, and different potential functions determine the different MRF models. From (4) and (5), (3) can be rewritten as follows:(7)x^=argminX∑k=1Nyk−DWkFkX22+∑c∈CXVcxx.Since the energy function of the prior distribution of the DAMRF model is a nonconvex function when solving the optimal solution of the objective function, it is easy to fall into the local minimization problem, and the optimal approximate solution of the reconstructed image cannot be obtained [7, 11]. Therefore, the graduated nonconvexity (GNC) optimization algorithm is used to optimize the objective function to obtain the optimal solution of the reconstruction result.


### 2.2. Local Edge Feature Extraction of Super-Resolution Image

#### 2.2.1. Chamfer Matching Metrics

The Chamfer distance is used to measure the similarity of the two-edge figures. The match between the template mapT and the image to be matched E is achieved by searching for their minimum Chamfer distance. The main steps are as follows:Step 1.
Calculate the Chamfer distance map of the image to be matched.Step 2.
Superimpose the template on the distance map. Calculate the Chamfer distance between the template and the image to be matched as follows:(8)DChamfer=1n∑i=1nvi.
Here,n is the number of edges of the template and vi is the distance value at which the template is superimposed.Step 3.
The template is translated on the distance map to obtain the Chamfer distance value distribution functionSp of the template on the image to be matched, and the position vector p of the minimum value Sp is the best matching point. In practical applications, image features are extracted by determining whether the minimum value Sp is less than a set threshold θ.


#### 2.2.2. Local Edge Contour Feature Function Based on Class Chamfer Distance

The local edge features used in this paper are defined by a rectangular window, that is,r=x,y,w,h. Each local edge r is represented by two positional parameters x,y and two scaled parameters w,h, which, respectively, represent the width and height of the rectangle. The local edge feature Fr is defined on the Chamfer distance map I of the image, concerning (8), and the eigenvalue calculation is as follows:(9)FrI=1w×h∑i=xx+w∑j=yy+hvi,j,where vi,j is the value of the Chamfer distance at the corresponding point in the image.This paper implements the fast calculation of (9) by establishing the integrated image of the Chamfer distance map. For the distance graph I, as shown in Figure 1, the integral image value at a pixel x,y is defined as iix,y=∑x1≤x,y1≤yix1,y1, that is, the sum of all the pixel values of the shaded portion. Once the integral image is established, the local edge feature values of any parameters can be obtained by only 4 table lookups and simple operations.Figure 1
Integral image value at the pointx,y.The super-resolution feature extracted by the above method is the feature edge contour, so the geometric center of gravity of the feature contour needs to be calculated to determine the feature points that meet the requirements.


### 2.3. Geometric Center of Gravity Calculation

The geometric center of gravity is obtained by weighting the points in the Grassmannian space and adding them; then it is divided by the sum of ownership. There are many state-of-the-art approaches that deal with calculation of geometric center of gravity [13, 14]. The pixel points of the image have greyscale properties, but the feature points extracted in this paper are on the edge contour line, and the edge image is a binary plane image, which is independent of the grey level of the image. Therefore, the edge image can be considered as a uniform substance. So, the geometric center of gravity of the edge contour is the geometric center.Considering whether the extracted edge lines are closed, the edge contours can be divided into two categories: closed contours and nonclosed contours, and their centres of gravity are calculated below.(1)
Calculation for the Geometric Center of Gravity of the Closed Contour.For a closed irregular planar figure, let the coordinates of the edge points bexi,yi and 1≤i≤n be the number of edge points. The geometric center coordinate x0,y0 is calculated by(10)x0=1n∑i=1nxi,y0=1n∑i=1nyi.The geometric center of gravity, thus, obtained is unique. The experimental results are shown in Figure2(a). In the figure, the circle represents the center of gravity of the geometry, and the contour of the feature extraction is closed.(2)
Calculation for the Geometric Center of Gravity of the Unclosed Contour.Figure 2
The geometric barycenter of the contour line of an object. (a) Closing the center of gravity of a contour line. (b) The center of gravity after a closed contour line is segmented.
(a)(b)Since the three points that are not collinear on the plane are linearly independent, the coordinates for the center of gravity of the triangle are uniquely defined [15, 16]. Therefore, for a convex or concave curve, it can first form a triangle consisting of the two ends of the edge line and the middle point and then find the geometric center of gravity. If an edge line is not single convex or single concave, then it is segmented. The experimental results are shown in Figure 2(b). In the figure, the curve AC⌢ is divided into segments from point B, and the geometric centers of gravity of the arcs AC⌢ and BC⌢ are, respectively, obtained. The solid line is the outline of the feature extraction, which is nonclosed, and the circle represents the center of gravity of the geometry.


### 2.4. Polarization of Edge Points

To conveniently calculate the length and position of each point on the edge from the geometric center of gravity, it is necessary to polarize the edge point. Taking the geometric center of gravity as the pole, as shown in Figure3, the conversion equation is as follows:(11)ρi=xi−x02+yi−y02θi=arctanyi−y0xi−x0.Figure 3
Polar coordinates of edge points.In Figure3, the origin of the coordinates is represented by x0,y0, and the points in polar coordinates are represented by xi,yi.The polarized edge points form a polar-amplitude curve, as shown in Figure4. In Figure 4, the abscissa is the edge point angle, and the unit is the arc degree; the ordinate is the polar diameter of the edge point, and the unit is taken in micrometres (μm). The horizontal and vertical coordinates’ contents in Figures 5 to 8 are the same as those in Figure 4.Figure 4
Polar diameter curve.Figure 5
Polar diameter and amplitude curves of local maximum points.Figure 6
The polar diameter curve of the local minimum point.Figure 7
The maximum diameter curve of the maximum diameter (small) value.Figure 8
The polar diameter curve diagram of the edge local feature points.


### 2.5. Determination of the Local Feature Points of the Image Edge

Polarization simplifies the problem, making it easy to find extreme points locally and then further identifying the feature points [17, 18]. The extraction process of extreme points and feature points is described below.


#### 2.5.1. Determination of the Extreme Point

If the maximum point in the rangeθ1,θ2 is represented by Pmax, then Pmax can be described by(12)Pmax=maxθ∈θ1,θ2ρ.Similarly, if the minimum value point in the rangeθ1,θ2 is represented by Pmin, then Pmin can be represented by(13)Pmin=minθ∈θ1,θ2ρ.The curves of the local maximum point and the minimum point on the polar-amplitude curve are shown in Figures5 and 6, respectively, and the interval between the two figures is 10°, that is, 1/18π. In Figure 5, the maximum value of the local maximum point is about 140 μm, and the minimum value is about 20 μm. In Figure 6, the maximum value of the local maximum point is about 110 μm, and the minimum value is about 15 μm.


#### 2.5.2. Determination of Feature Points

The final feature points are obtained based on the principle of nonmaximum (small) value suppression in the local area [19, 20]. Therefore, the maximum (small) value point of each interval and the maximum (small) value point in the adjacent interval are compared, and if the polar diameter of the maximum (minimum) value point is larger (smaller) than that of the maximum (minimum) value point in the two adjacent intervals, it is considered to be a feature point. The argument-polar radius curves of the two feature points further extracted from the maximum and minimum values of Figures 5 and 6 are shown in Figure 7, and the finally extracted feature points are as shown in Figure 8 in Figure 7; the argument-polar radius curve of the maximum value curve is always above the argument-polar radius curve of the minimum value curve; the distribution of the last extracted effective feature points and the argument-polar radius curve of the feature points can be seen in Figure 7. In Figure 8, it can be observed obviously that the polar diameter curve diagram of the edge local feature points varies from the range of −4/3πto 4/3π, representing the values of maximum value curve points and the minimum value curve points on the y-axis ranging from 0 to 150.


## 2.1. Super-Resolution Image Reconstruction Model

Degraded models for super-resolution image reconstruction can be expressed as follows:(1)yk=DWkFkX+ηk,where yk is the degraded kth frame image, X is the high-resolution image, D and Wk are the downsampling matrix and motion matrix, Fk is the fuzzy matrix, and ηk is the noise.Let the low-resolution image beY and the corresponding high-resolution image be X. The problem that the super-resolution reconstruction needs to solve is to find the optimal approximate solution X under the condition of known Y. The common method for solving this problem is Maximum Posterior Probability (MAP) under low-resolution range image conditions. MAP estimates can be represented by(2)x^=argmaxXPX|Y1,…,YN.According to the Bayesian estimation criterion, (2) can be rewritten as follows:(3)x^=argmaxXPY1=y1,…,YN=yN|X=xPX=x.In (3), it is assumed that the noise is independent Gaussian white noise [10] and the variance is σ2. Then, (4) is expressed as follows:(4)PY1=y1,…,YN=yN|X=x=12πσ2N1N2×exp−∑k=1Nyk−DWkFkX222σ2.According to the Markov random field model, the prior probabilityPX=x of the high-resolution range image is obtained, and the equivalence between MRF and Gibbs is used. The Gibbs distribution is used to explicitly describe the Markov distribution; that is, the prior probability of X can be expressed by(5)PX=x=1Zexp−1T∑c∈CXVcxx.The energy function takes the form of Li, as follows:(6)∑c∈CXVcxx=∑i=1L1∑j=1L24γ−γexp−xi,j−xi,j−12γ−γexp−xi,j−xi,j+12γ−γexp−xi,j−xi−1,j2γ−γexp−xi,j−xi+1,j2γ.Here,Z is a normalized constant, T is the temperature parameter, and Vcxx is the potential function of the connected group; the potential function describes the interaction of a set of neighbouring pixels, and different potential functions determine the different MRF models. From (4) and (5), (3) can be rewritten as follows:(7)x^=argminX∑k=1Nyk−DWkFkX22+∑c∈CXVcxx.Since the energy function of the prior distribution of the DAMRF model is a nonconvex function when solving the optimal solution of the objective function, it is easy to fall into the local minimization problem, and the optimal approximate solution of the reconstructed image cannot be obtained [7, 11]. Therefore, the graduated nonconvexity (GNC) optimization algorithm is used to optimize the objective function to obtain the optimal solution of the reconstruction result.


## 2.2. Local Edge Feature Extraction of Super-Resolution Image

### 2.2.1. Chamfer Matching Metrics

The Chamfer distance is used to measure the similarity of the two-edge figures. The match between the template mapT and the image to be matched E is achieved by searching for their minimum Chamfer distance. The main steps are as follows:Step 1.
Calculate the Chamfer distance map of the image to be matched.Step 2.
Superimpose the template on the distance map. Calculate the Chamfer distance between the template and the image to be matched as follows:(8)DChamfer=1n∑i=1nvi.
Here,n is the number of edges of the template and vi is the distance value at which the template is superimposed.Step 3.
The template is translated on the distance map to obtain the Chamfer distance value distribution functionSp of the template on the image to be matched, and the position vector p of the minimum value Sp is the best matching point. In practical applications, image features are extracted by determining whether the minimum value Sp is less than a set threshold θ.


### 2.2.2. Local Edge Contour Feature Function Based on Class Chamfer Distance

The local edge features used in this paper are defined by a rectangular window, that is,r=x,y,w,h. Each local edge r is represented by two positional parameters x,y and two scaled parameters w,h, which, respectively, represent the width and height of the rectangle. The local edge feature Fr is defined on the Chamfer distance map I of the image, concerning (8), and the eigenvalue calculation is as follows:(9)FrI=1w×h∑i=xx+w∑j=yy+hvi,j,where vi,j is the value of the Chamfer distance at the corresponding point in the image.This paper implements the fast calculation of (9) by establishing the integrated image of the Chamfer distance map. For the distance graph I, as shown in Figure 1, the integral image value at a pixel x,y is defined as iix,y=∑x1≤x,y1≤yix1,y1, that is, the sum of all the pixel values of the shaded portion. Once the integral image is established, the local edge feature values of any parameters can be obtained by only 4 table lookups and simple operations.Figure 1
Integral image value at the pointx,y.The super-resolution feature extracted by the above method is the feature edge contour, so the geometric center of gravity of the feature contour needs to be calculated to determine the feature points that meet the requirements.


## 2.2.1. Chamfer Matching Metrics

The Chamfer distance is used to measure the similarity of the two-edge figures. The match between the template mapT and the image to be matched E is achieved by searching for their minimum Chamfer distance. The main steps are as follows:Step 1.
Calculate the Chamfer distance map of the image to be matched.Step 2.
Superimpose the template on the distance map. Calculate the Chamfer distance between the template and the image to be matched as follows:(8)DChamfer=1n∑i=1nvi.
Here,n is the number of edges of the template and vi is the distance value at which the template is superimposed.Step 3.
The template is translated on the distance map to obtain the Chamfer distance value distribution functionSp of the template on the image to be matched, and the position vector p of the minimum value Sp is the best matching point. In practical applications, image features are extracted by determining whether the minimum value Sp is less than a set threshold θ.


## 2.2.2. Local Edge Contour Feature Function Based on Class Chamfer Distance

The local edge features used in this paper are defined by a rectangular window, that is,r=x,y,w,h. Each local edge r is represented by two positional parameters x,y and two scaled parameters w,h, which, respectively, represent the width and height of the rectangle. The local edge feature Fr is defined on the Chamfer distance map I of the image, concerning (8), and the eigenvalue calculation is as follows:(9)FrI=1w×h∑i=xx+w∑j=yy+hvi,j,where vi,j is the value of the Chamfer distance at the corresponding point in the image.This paper implements the fast calculation of (9) by establishing the integrated image of the Chamfer distance map. For the distance graph I, as shown in Figure 1, the integral image value at a pixel x,y is defined as iix,y=∑x1≤x,y1≤yix1,y1, that is, the sum of all the pixel values of the shaded portion. Once the integral image is established, the local edge feature values of any parameters can be obtained by only 4 table lookups and simple operations.Figure 1
Integral image value at the pointx,y.The super-resolution feature extracted by the above method is the feature edge contour, so the geometric center of gravity of the feature contour needs to be calculated to determine the feature points that meet the requirements.


## 2.3. Geometric Center of Gravity Calculation

The geometric center of gravity is obtained by weighting the points in the Grassmannian space and adding them; then it is divided by the sum of ownership. There are many state-of-the-art approaches that deal with calculation of geometric center of gravity [13, 14]. The pixel points of the image have greyscale properties, but the feature points extracted in this paper are on the edge contour line, and the edge image is a binary plane image, which is independent of the grey level of the image. Therefore, the edge image can be considered as a uniform substance. So, the geometric center of gravity of the edge contour is the geometric center.Considering whether the extracted edge lines are closed, the edge contours can be divided into two categories: closed contours and nonclosed contours, and their centres of gravity are calculated below.(1)
Calculation for the Geometric Center of Gravity of the Closed Contour.For a closed irregular planar figure, let the coordinates of the edge points bexi,yi and 1≤i≤n be the number of edge points. The geometric center coordinate x0,y0 is calculated by(10)x0=1n∑i=1nxi,y0=1n∑i=1nyi.The geometric center of gravity, thus, obtained is unique. The experimental results are shown in Figure2(a). In the figure, the circle represents the center of gravity of the geometry, and the contour of the feature extraction is closed.(2)
Calculation for the Geometric Center of Gravity of the Unclosed Contour.Figure 2
The geometric barycenter of the contour line of an object. (a) Closing the center of gravity of a contour line. (b) The center of gravity after a closed contour line is segmented.
(a)(b)Since the three points that are not collinear on the plane are linearly independent, the coordinates for the center of gravity of the triangle are uniquely defined [15, 16]. Therefore, for a convex or concave curve, it can first form a triangle consisting of the two ends of the edge line and the middle point and then find the geometric center of gravity. If an edge line is not single convex or single concave, then it is segmented. The experimental results are shown in Figure 2(b). In the figure, the curve AC⌢ is divided into segments from point B, and the geometric centers of gravity of the arcs AC⌢ and BC⌢ are, respectively, obtained. The solid line is the outline of the feature extraction, which is nonclosed, and the circle represents the center of gravity of the geometry.


## 2.4. Polarization of Edge Points

To conveniently calculate the length and position of each point on the edge from the geometric center of gravity, it is necessary to polarize the edge point. Taking the geometric center of gravity as the pole, as shown in Figure3, the conversion equation is as follows:(11)ρi=xi−x02+yi−y02θi=arctanyi−y0xi−x0.Figure 3
Polar coordinates of edge points.In Figure3, the origin of the coordinates is represented by x0,y0, and the points in polar coordinates are represented by xi,yi.The polarized edge points form a polar-amplitude curve, as shown in Figure4. In Figure 4, the abscissa is the edge point angle, and the unit is the arc degree; the ordinate is the polar diameter of the edge point, and the unit is taken in micrometres (μm). The horizontal and vertical coordinates’ contents in Figures 5 to 8 are the same as those in Figure 4.Figure 4
Polar diameter curve.Figure 5
Polar diameter and amplitude curves of local maximum points.Figure 6
The polar diameter curve of the local minimum point.Figure 7
The maximum diameter curve of the maximum diameter (small) value.Figure 8
The polar diameter curve diagram of the edge local feature points.


## 2.5. Determination of the Local Feature Points of the Image Edge

Polarization simplifies the problem, making it easy to find extreme points locally and then further identifying the feature points [17, 18]. The extraction process of extreme points and feature points is described below.


### 2.5.1. Determination of the Extreme Point

If the maximum point in the rangeθ1,θ2 is represented by Pmax, then Pmax can be described by(12)Pmax=maxθ∈θ1,θ2ρ.Similarly, if the minimum value point in the rangeθ1,θ2 is represented by Pmin, then Pmin can be represented by(13)Pmin=minθ∈θ1,θ2ρ.The curves of the local maximum point and the minimum point on the polar-amplitude curve are shown in Figures5 and 6, respectively, and the interval between the two figures is 10°, that is, 1/18π. In Figure 5, the maximum value of the local maximum point is about 140 μm, and the minimum value is about 20 μm. In Figure 6, the maximum value of the local maximum point is about 110 μm, and the minimum value is about 15 μm.


### 2.5.2. Determination of Feature Points

The final feature points are obtained based on the principle of nonmaximum (small) value suppression in the local area [19, 20]. Therefore, the maximum (small) value point of each interval and the maximum (small) value point in the adjacent interval are compared, and if the polar diameter of the maximum (minimum) value point is larger (smaller) than that of the maximum (minimum) value point in the two adjacent intervals, it is considered to be a feature point. The argument-polar radius curves of the two feature points further extracted from the maximum and minimum values of Figures 5 and 6 are shown in Figure 7, and the finally extracted feature points are as shown in Figure 8 in Figure 7; the argument-polar radius curve of the maximum value curve is always above the argument-polar radius curve of the minimum value curve; the distribution of the last extracted effective feature points and the argument-polar radius curve of the feature points can be seen in Figure 7. In Figure 8, it can be observed obviously that the polar diameter curve diagram of the edge local feature points varies from the range of −4/3πto 4/3π, representing the values of maximum value curve points and the minimum value curve points on the y-axis ranging from 0 to 150.


## 2.5.1. Determination of the Extreme Point

If the maximum point in the rangeθ1,θ2 is represented by Pmax, then Pmax can be described by(12)Pmax=maxθ∈θ1,θ2ρ.Similarly, if the minimum value point in the rangeθ1,θ2 is represented by Pmin, then Pmin can be represented by(13)Pmin=minθ∈θ1,θ2ρ.The curves of the local maximum point and the minimum point on the polar-amplitude curve are shown in Figures5 and 6, respectively, and the interval between the two figures is 10°, that is, 1/18π. In Figure 5, the maximum value of the local maximum point is about 140 μm, and the minimum value is about 20 μm. In Figure 6, the maximum value of the local maximum point is about 110 μm, and the minimum value is about 15 μm.


## 2.5.2. Determination of Feature Points

The final feature points are obtained based on the principle of nonmaximum (small) value suppression in the local area [19, 20]. Therefore, the maximum (small) value point of each interval and the maximum (small) value point in the adjacent interval are compared, and if the polar diameter of the maximum (minimum) value point is larger (smaller) than that of the maximum (minimum) value point in the two adjacent intervals, it is considered to be a feature point. The argument-polar radius curves of the two feature points further extracted from the maximum and minimum values of Figures 5 and 6 are shown in Figure 7, and the finally extracted feature points are as shown in Figure 8 in Figure 7; the argument-polar radius curve of the maximum value curve is always above the argument-polar radius curve of the minimum value curve; the distribution of the last extracted effective feature points and the argument-polar radius curve of the feature points can be seen in Figure 7. In Figure 8, it can be observed obviously that the polar diameter curve diagram of the edge local feature points varies from the range of −4/3πto 4/3π, representing the values of maximum value curve points and the minimum value curve points on the y-axis ranging from 0 to 150.


## 3. Results

### 3.1. Algorithm Validation

To verify the effectiveness of the proposed algorithm, the expansion feature extraction test of a single super-resolution image is selected. Figure9 is the local edge feature result of the super-resolution image extracted by the proposed algorithm. It can be seen from the analysis of Figure 9 that the algorithm not only extracts the feature points of the super-resolution image convex, but also the feature points of the concave point can be detected. The connection of these feature points can reflect the edge contour shape of the target, which verifies the validity of the local edge features extraction by the proposed algorithm.Figure 9
The feature points extracted by this algorithm.To verify the effectiveness of the proposed algorithm, the advantages of the proposed algorithm are highlighted. The super-resolution image of the valve pressure gauge is used as the object and 10% noise is added. The proposed algorithm, method given in paper [4], and method given in paper [5] are used to extract local edge features of the image. The original super-resolution image of the pressure meter with 10% noise is shown in Figure 10(a), and the result of feature extraction is shown in Figures 10(b)–10(d).Figure 10
Local edge feature extraction results from noisy super-resolution images.
(a)(b)(c)(d)Figure10(b) is the result of the method given in paper [4] extracting the local edge features of the super-resolution image, and Figure 10(c) is the extraction result of the method given in paper [5]. Due to the feature points extracted by the two algorithms being unclear, they are circled with red lines.


### 3.2. Comparison of RPC Performance andF-Measure Performance of Different Algorithms

#### 3.2.1. Testing Set

To highlight the advantages of the proposed algorithm, it is compared with the method given in paper [4] and the method given in paper [5]. The experiment uses the super-resolution image database of vehicles in UIUC. The database consists of a training set and a testing set. The training set includes 550 positive samples with size of 100 × 40. The experiment does not increase the number of positive samples in the training set (usually, increasing the number of training samples can improve the accuracy of the classifier), and the testing set consists of two subsets, denoted by TI and TII, respectively. TI contains 170 super-resolution images with a total of 200 vehicles. The scale of vehicle imaging is the same as the training set. TII contains 108 super-resolution images with 139 vehicles. The scale of vehicle imaging is different from the TI testing set. The range is between 0.8 and 2 times. Some testing images contain complex backgrounds. Some images also have partial occlusion and image blur. In general, the feature extraction of testing set TII is more difficult than that of testing set TI. The training set also includes 50,517 negative samples, each of which is 100 × 40 in size.The experiment uses the recall rate, precision rate, andF-measure to evaluate the performance of the algorithm. The calculation method of the evaluation index is as follows:(1)
The recall-precision curve (RPC) is defined as follows:(14)recall=PTPn,(15)precision=PTPT+PF.In the equation,PT, PF, and Pn, respectively, indicate the number of correct extraction of features, the number of error extractions, and the total number of features.(2)
TheF-measure (F−measure) is defined as (16), which can be considered as an equal error measure:(16)F−measure=2recall×precisionrecall+precision.


#### 3.2.2. Analysis of Experimental Results

During the experiment, some feature extraction results of the proposed algorithm are shown in Figures11(a)–11(c).Figure 11
Part of the feature extraction results of the algorithm.
(a)(b)(c)It can be seen from Figures11(a)–11(c) that the result of using the algorithm of this paper to extract the vehicle in the super-resolution image can identify the vehicle in the image in the case of obstacle occlusion and verify the effectiveness of the algorithm.The feature extraction and RPC fold line comparison of the three algorithms in the testing setTI are shown in Table 1 and Figure 12, respectively. The feature extraction and RPC fold line comparison of the three algorithms in the testing set TII are shown in Table 2 and Figure 13, respectively.Table 1
Feature extraction of different algorithms on the test setT.
AlgorithmNumber of base classifiersF-measure (%)Average feature extraction time (s)Test platformMethod of paper [4]80082.20.0951.86 GHz Core 2 DuoMethod of paper [5]405075.20.0561.86 GHz Core 2 DuoProposed method185096.30.021.86 GHz Core 2 DuoFigure 12
Comparison of RPC curves of three algorithms onTI.Table 2
Feature extraction performance of different algorithms on the test setTII.
AlgorithmF-measure (%)Average feature extraction time (s)Method in paper [4]440.35Method in paper [5]80.10.22Proposed method95.60.031Figure 13
Comparison of RPC algorithms for three algorithms on the test setTII.In Table1, the equal error measure of the proposed algorithm is 96.3%, which is 14.1% higher than that of the method given in paper [4] and 21.1% higher than that of the method given in paper [5]. The average feature extraction time of the proposed algorithm is 0.02 s, which saves 0.075 s compared with the method given in paper [4] and 0.036 s compared with the method given in paper [5].In Figure12, the RPC polyline arrangement of the proposed algorithm, method given in paper [4], and the method given in paper [5] can be seen. The RPC polyline of the proposed algorithm is located at the top of the line graph. The initial value of the algorithm is 60%. The rate rises linearly, the stability is about 97% in the later period, and the maximum precision is 99%; the initial value of the method given in paper [4] and the method given in paper [5] is about 8%. The maximum precision of the method given in paper [4] is about 75% and that of the method given in paper [5] is approximately 64%. From this, we can clearly state that our proposed algorithm is better in terms of precision compared to the method given in paper [4] and the method given in paper [5] as our algorithm has the maximum of 99% precision rate at its best case and the other algorithms method given in paper [4] and method given in paper [5] are having a maximum of 75% and 64% approximately as our proposed algorithm outcasts them in case of RPC curves.It can be seen from Table2 that the F-measure value of the proposed algorithm is higher, and the average feature extraction time is less. Compared with the case of Table 1, the proposed algorithm saves feature extraction time and has high efficiency while maintaining the highest accuracy and high precision.In Figure13, the RPC polyline of the proposed algorithm on the testing set TII is located at the top of the image, indicating that the RPC performance of the proposed algorithm is the strongest. Like the testing set TI, the initial value of the proposed algorithm is 60%, which is larger than that of the method given in paper [4] of 51% and the method given in paper [5], respectively; the highest precision of the proposed algorithm is 99%, and the highest precision of the method in paper [4] and the method in paper [5] is 82% and 68%, respectively. Comparing the three groups of data, the RPC performance of the proposed algorithm is superior to similar algorithms and has significant advantages.


## 3.1. Algorithm Validation

To verify the effectiveness of the proposed algorithm, the expansion feature extraction test of a single super-resolution image is selected. Figure9 is the local edge feature result of the super-resolution image extracted by the proposed algorithm. It can be seen from the analysis of Figure 9 that the algorithm not only extracts the feature points of the super-resolution image convex, but also the feature points of the concave point can be detected. The connection of these feature points can reflect the edge contour shape of the target, which verifies the validity of the local edge features extraction by the proposed algorithm.Figure 9
The feature points extracted by this algorithm.To verify the effectiveness of the proposed algorithm, the advantages of the proposed algorithm are highlighted. The super-resolution image of the valve pressure gauge is used as the object and 10% noise is added. The proposed algorithm, method given in paper [4], and method given in paper [5] are used to extract local edge features of the image. The original super-resolution image of the pressure meter with 10% noise is shown in Figure 10(a), and the result of feature extraction is shown in Figures 10(b)–10(d).Figure 10
Local edge feature extraction results from noisy super-resolution images.
(a)(b)(c)(d)Figure10(b) is the result of the method given in paper [4] extracting the local edge features of the super-resolution image, and Figure 10(c) is the extraction result of the method given in paper [5]. Due to the feature points extracted by the two algorithms being unclear, they are circled with red lines.


## 3.2. Comparison of RPC Performance andF-Measure Performance of Different Algorithms

### 3.2.1. Testing Set

To highlight the advantages of the proposed algorithm, it is compared with the method given in paper [4] and the method given in paper [5]. The experiment uses the super-resolution image database of vehicles in UIUC. The database consists of a training set and a testing set. The training set includes 550 positive samples with size of 100 × 40. The experiment does not increase the number of positive samples in the training set (usually, increasing the number of training samples can improve the accuracy of the classifier), and the testing set consists of two subsets, denoted by TI and TII, respectively. TI contains 170 super-resolution images with a total of 200 vehicles. The scale of vehicle imaging is the same as the training set. TII contains 108 super-resolution images with 139 vehicles. The scale of vehicle imaging is different from the TI testing set. The range is between 0.8 and 2 times. Some testing images contain complex backgrounds. Some images also have partial occlusion and image blur. In general, the feature extraction of testing set TII is more difficult than that of testing set TI. The training set also includes 50,517 negative samples, each of which is 100 × 40 in size.The experiment uses the recall rate, precision rate, andF-measure to evaluate the performance of the algorithm. The calculation method of the evaluation index is as follows:(1)
The recall-precision curve (RPC) is defined as follows:(14)recall=PTPn,(15)precision=PTPT+PF.In the equation,PT, PF, and Pn, respectively, indicate the number of correct extraction of features, the number of error extractions, and the total number of features.(2)
TheF-measure (F−measure) is defined as (16), which can be considered as an equal error measure:(16)F−measure=2recall×precisionrecall+precision.


### 3.2.2. Analysis of Experimental Results

During the experiment, some feature extraction results of the proposed algorithm are shown in Figures11(a)–11(c).Figure 11
Part of the feature extraction results of the algorithm.
(a)(b)(c)It can be seen from Figures11(a)–11(c) that the result of using the algorithm of this paper to extract the vehicle in the super-resolution image can identify the vehicle in the image in the case of obstacle occlusion and verify the effectiveness of the algorithm.The feature extraction and RPC fold line comparison of the three algorithms in the testing setTI are shown in Table 1 and Figure 12, respectively. The feature extraction and RPC fold line comparison of the three algorithms in the testing set TII are shown in Table 2 and Figure 13, respectively.Table 1
Feature extraction of different algorithms on the test setT.
AlgorithmNumber of base classifiersF-measure (%)Average feature extraction time (s)Test platformMethod of paper [4]80082.20.0951.86 GHz Core 2 DuoMethod of paper [5]405075.20.0561.86 GHz Core 2 DuoProposed method185096.30.021.86 GHz Core 2 DuoFigure 12
Comparison of RPC curves of three algorithms onTI.Table 2
Feature extraction performance of different algorithms on the test setTII.
AlgorithmF-measure (%)Average feature extraction time (s)Method in paper [4]440.35Method in paper [5]80.10.22Proposed method95.60.031Figure 13
Comparison of RPC algorithms for three algorithms on the test setTII.In Table1, the equal error measure of the proposed algorithm is 96.3%, which is 14.1% higher than that of the method given in paper [4] and 21.1% higher than that of the method given in paper [5]. The average feature extraction time of the proposed algorithm is 0.02 s, which saves 0.075 s compared with the method given in paper [4] and 0.036 s compared with the method given in paper [5].In Figure12, the RPC polyline arrangement of the proposed algorithm, method given in paper [4], and the method given in paper [5] can be seen. The RPC polyline of the proposed algorithm is located at the top of the line graph. The initial value of the algorithm is 60%. The rate rises linearly, the stability is about 97% in the later period, and the maximum precision is 99%; the initial value of the method given in paper [4] and the method given in paper [5] is about 8%. The maximum precision of the method given in paper [4] is about 75% and that of the method given in paper [5] is approximately 64%. From this, we can clearly state that our proposed algorithm is better in terms of precision compared to the method given in paper [4] and the method given in paper [5] as our algorithm has the maximum of 99% precision rate at its best case and the other algorithms method given in paper [4] and method given in paper [5] are having a maximum of 75% and 64% approximately as our proposed algorithm outcasts them in case of RPC curves.It can be seen from Table2 that the F-measure value of the proposed algorithm is higher, and the average feature extraction time is less. Compared with the case of Table 1, the proposed algorithm saves feature extraction time and has high efficiency while maintaining the highest accuracy and high precision.In Figure13, the RPC polyline of the proposed algorithm on the testing set TII is located at the top of the image, indicating that the RPC performance of the proposed algorithm is the strongest. Like the testing set TI, the initial value of the proposed algorithm is 60%, which is larger than that of the method given in paper [4] of 51% and the method given in paper [5], respectively; the highest precision of the proposed algorithm is 99%, and the highest precision of the method in paper [4] and the method in paper [5] is 82% and 68%, respectively. Comparing the three groups of data, the RPC performance of the proposed algorithm is superior to similar algorithms and has significant advantages.


## 3.2.1. Testing Set

To highlight the advantages of the proposed algorithm, it is compared with the method given in paper [4] and the method given in paper [5]. The experiment uses the super-resolution image database of vehicles in UIUC. The database consists of a training set and a testing set. The training set includes 550 positive samples with size of 100 × 40. The experiment does not increase the number of positive samples in the training set (usually, increasing the number of training samples can improve the accuracy of the classifier), and the testing set consists of two subsets, denoted by TI and TII, respectively. TI contains 170 super-resolution images with a total of 200 vehicles. The scale of vehicle imaging is the same as the training set. TII contains 108 super-resolution images with 139 vehicles. The scale of vehicle imaging is different from the TI testing set. The range is between 0.8 and 2 times. Some testing images contain complex backgrounds. Some images also have partial occlusion and image blur. In general, the feature extraction of testing set TII is more difficult than that of testing set TI. The training set also includes 50,517 negative samples, each of which is 100 × 40 in size.The experiment uses the recall rate, precision rate, andF-measure to evaluate the performance of the algorithm. The calculation method of the evaluation index is as follows:(1)
The recall-precision curve (RPC) is defined as follows:(14)recall=PTPn,(15)precision=PTPT+PF.In the equation,PT, PF, and Pn, respectively, indicate the number of correct extraction of features, the number of error extractions, and the total number of features.(2)
TheF-measure (F−measure) is defined as (16), which can be considered as an equal error measure:(16)F−measure=2recall×precisionrecall+precision.


## 3.2.2. Analysis of Experimental Results

During the experiment, some feature extraction results of the proposed algorithm are shown in Figures11(a)–11(c).Figure 11
Part of the feature extraction results of the algorithm.
(a)(b)(c)It can be seen from Figures11(a)–11(c) that the result of using the algorithm of this paper to extract the vehicle in the super-resolution image can identify the vehicle in the image in the case of obstacle occlusion and verify the effectiveness of the algorithm.The feature extraction and RPC fold line comparison of the three algorithms in the testing setTI are shown in Table 1 and Figure 12, respectively. The feature extraction and RPC fold line comparison of the three algorithms in the testing set TII are shown in Table 2 and Figure 13, respectively.Table 1
Feature extraction of different algorithms on the test setT.
AlgorithmNumber of base classifiersF-measure (%)Average feature extraction time (s)Test platformMethod of paper [4]80082.20.0951.86 GHz Core 2 DuoMethod of paper [5]405075.20.0561.86 GHz Core 2 DuoProposed method185096.30.021.86 GHz Core 2 DuoFigure 12
Comparison of RPC curves of three algorithms onTI.Table 2
Feature extraction performance of different algorithms on the test setTII.
AlgorithmF-measure (%)Average feature extraction time (s)Method in paper [4]440.35Method in paper [5]80.10.22Proposed method95.60.031Figure 13
Comparison of RPC algorithms for three algorithms on the test setTII.In Table1, the equal error measure of the proposed algorithm is 96.3%, which is 14.1% higher than that of the method given in paper [4] and 21.1% higher than that of the method given in paper [5]. The average feature extraction time of the proposed algorithm is 0.02 s, which saves 0.075 s compared with the method given in paper [4] and 0.036 s compared with the method given in paper [5].In Figure12, the RPC polyline arrangement of the proposed algorithm, method given in paper [4], and the method given in paper [5] can be seen. The RPC polyline of the proposed algorithm is located at the top of the line graph. The initial value of the algorithm is 60%. The rate rises linearly, the stability is about 97% in the later period, and the maximum precision is 99%; the initial value of the method given in paper [4] and the method given in paper [5] is about 8%. The maximum precision of the method given in paper [4] is about 75% and that of the method given in paper [5] is approximately 64%. From this, we can clearly state that our proposed algorithm is better in terms of precision compared to the method given in paper [4] and the method given in paper [5] as our algorithm has the maximum of 99% precision rate at its best case and the other algorithms method given in paper [4] and method given in paper [5] are having a maximum of 75% and 64% approximately as our proposed algorithm outcasts them in case of RPC curves.It can be seen from Table2 that the F-measure value of the proposed algorithm is higher, and the average feature extraction time is less. Compared with the case of Table 1, the proposed algorithm saves feature extraction time and has high efficiency while maintaining the highest accuracy and high precision.In Figure13, the RPC polyline of the proposed algorithm on the testing set TII is located at the top of the image, indicating that the RPC performance of the proposed algorithm is the strongest. Like the testing set TI, the initial value of the proposed algorithm is 60%, which is larger than that of the method given in paper [4] of 51% and the method given in paper [5], respectively; the highest precision of the proposed algorithm is 99%, and the highest precision of the method in paper [4] and the method in paper [5] is 82% and 68%, respectively. Comparing the three groups of data, the RPC performance of the proposed algorithm is superior to similar algorithms and has significant advantages.


## 4. Discussion

In Figure10, the feature points extracted by the method given in paper [4] and the method given in paper [5] have a commonality: fuzzy, unclear, and large fragment points; it is difficult to effectively restore the local edge features of super-resolution images, affecting the image analysis effect; relatively speaking, the feature points extracted by the proposed algorithm in Figure 10(d) are clear and significant. The pointers and meter scales of the pressure gauge are clear and complete, and there are only weak blur points at the edge of the instrument, which does not affect the overall image restoration effect. In summary, the proposed algorithm can effectively extract the feature points of a super-resolution image with 10% noise, and the acquired local edges features are clear, continuous, and complete.Based on the obtained local features of the super-resolution image, the proposed algorithm calculates the geometric center of gravity of the closed contour line and the nonclosed contour line to further determine the effective feature points. Firstly, the edge points are polarized, which is convenient for calculating the length and position of each point on the edge point from the geometric center of gravity, searching for local extremum points, and further determining the feature points so that the feature points of the obtained super-resolution image are effective and reliable. The final feature points are obtained on the principle of nonmaximum (minimum) value suppression in the local area.In Table1, the equal error measure of the proposed algorithm is 96.3%, which is 14.1% higher than that of the method given in paper [4] and 21.1% higher than that of the method given in paper [5]. The equal error measure indicates the accuracy of feature extraction, which indicates the accuracy of the proposed algorithm to extract the local edge features of the super-resolution image is high; the average feature extraction time of the proposed algorithm is 0.02 s, which saves 0.075 s compared with the method given in paper [4] and 0.036 s compared with the method given in paper [5]. It can be seen that the average time of extracting features by using the proposed algorithm is less. In summary, compared with similar algorithms, the proposed algorithm extracts feature with the shortest time while maintaining the highest accuracy and achieves fast feature extraction with high efficiency and high precision.In Figure12, the RPC polyline of the proposed algorithm is located at the top of the line graph, indicating that the recall rate and precision are higher. The initial value of the proposed algorithm is 60%. The recall rate in the previous stage rises linearly and is stable in the later stage, being about 97%, and the maximum precision is 99%; the initial value of the method given in paper [4] and the method given in paper [5] is about 8%, the maximum precision of the method given in paper [4] is about 75%, and the maximum precision of the method given in paper [5] is about 64%. The recall rate and precision of the three algorithms are compared, indicating that the RPC performance of the proposed algorithm is better. In the process of local edge feature extraction of super-resolution images, the proposed algorithm has a high recall rate and high accuracy. Similar to the testing set TI, the feature extraction result obtained by the algorithm on TII has a high recall rate and high precision, which has advantages.It can be seen from Tables1 and 2 that in the process of local edge feature extraction of super-resolution images when the proposed algorithm maintains the highest accuracy, the feature extraction time is the shortest. The reason why the algorithm has good RPC performance and F-measure performance is because the algorithm uses the Chamfer matching metric to extract the local edge features of super-resolution images. Chamfer’s distance is used to measure the similarity of two-edge graphics and search for similar graphics. The Chamfer distance matching is realized by searching the minimum Chamfer distance of similar graphics. Finally, the local edge features of super-resolution images are extracted based on the local edge feature function of class Chamfer distance. The obtained features are comprehensive and accurate, which provide favourable conditions for extracting the final feature points and prevent feature points from loss.


## 5. Conclusions

In super-resolution image processing technology, feature extraction algorithms have attracted a great attention as a potential area of interest. The feature point extraction algorithm for the local edge of super-resolution image based on edge point has been proposed. The proposed method considers the case where the edge line is closed. The obtained local edge feature points of the super-resolution image are lone convex points with large curvature on the edge line. The problem proposes a new fast extraction algorithm for extracting local edge features of super-resolution images. The experimental results show that the proposed algorithm can not only detect the points with large curvature on the edges of the image but also locate them accurately for refined extraction of the features. The equal error measure for extracting the local features of the super-resolution image is 96.3%, and the average time taken by the algorithm to produce the results is 0.02 seconds. In the final results, it shows a precision of 98% where our method outperforms the existing approaches, which shows accuracy of 75% and 64%, respectively, during comparative study. The proposed method is of great significance for the recognition of objects in the super-resolution image and for the reconstruction of the three-dimensional surfaces where accurate extraction of features plays a noteworthy role.



---

*Source: 8801978-2022-01-05.xml*