A Fast Corner Detection Method Based on the Ratio of Symmetric Contour Center Distances

Abstract

The present invention proposes a fast corner detection method based on the ratio of symmetric contour center distances to solve the technical problems of large computational complexity and low detection speed in existing corner detection methods. The steps of the present invention are as follows: convert a color image into a grayscale image; use a Canny edge detection sub-module to extract the contour of the grayscale image, and select the curve in the contour as the target contour; use a Gaussian function to smooth the target contour to obtain a smooth curve; arbitrarily select a point on the smooth curve, and calculate the discrete curvature of the smooth curve at this point using the ratio of symmetric contour center distances; mark the points on the smooth curve where the discrete curvature reaches a local maximum and the value is greater than the curvature threshold as corner points. The present invention only needs to calculate the Euclidean distance twice to estimate the discrete curvature of each point on the contour, with faster speed; it has a high corner resolution and strong robustness to noise and local contour changes; the simulation experiment results verify its effectiveness and efficiency.

Description

Technical Field

[0001] The present invention relates to the technical field of corner detection, and in particular, to a fast corner detection method based on the ratio of the distances from the centers of symmetric contours. Background Art

[0002] Corners are one of the key local features of images and have been successfully applied to many computer vision applications such as object recognition, shape representation, and 3D reconstruction. Corner detection is one of the fundamental research topics in the field of image processing and has a wide range of applications in vehicle detection, UAV image matching, camera calibration, etc. In particular, fast corner detection is very useful for many real-time tasks. Existing corner detection methods can generally be divided into two categories: contour-based methods and gray-scale-based methods. Contour-based methods first extract edge contours from the input image and then detect corners by analyzing the shape changes on the contours, while gray-scale-based methods directly use the information of local gray-scale intensity changes to detect corners. Compared with gray-scale-based methods, contour-based methods have the characteristics of high efficiency and low detection error rate.

[0003] Rosenfeld and Johnston et al. (RJ) first proposed a contour corner detector using cosine as a discrete curvature metric. However, since the smoothing factor of the RJ algorithm depends on the curve length, it is very sensitive to geometric transformations. Mohanna and Mokhtarian et al. proposed using the curvature scale space technique (CSS) to detect corners on contours. The CSS technique has achieved great success in detecting curve corners, and a large number of variants of the CSS technique have been proposed subsequently. However, Mohammad Awrangjeb et al. pointed out that the existing detection schemes based on the CSS technique still face the following two main problems: 1) high-order derivatives lead to noise sensitivity; 2) it is difficult to select an appropriate smoothing scale factor. To solve the above problems, Mohammad Awrangjeb et al. proposed using the chord-to-point distance accumulation (CPDA) technique to locate corners on planar curves and gave a fast version of CPDA (F-CPDA), and verified the good performance of CPDA based on the evaluation criteria of AR and LE. However, CPDA still has some disadvantages, such as being unable to accurately detect some real corners, merging or missing some adjacent corners, etc. In response to the problems faced by CPDA, other scholars have also proposed some corresponding improvement schemes, such as the accumulated chord ratio sum (ACRA) and the chord-to-triangle arm ratio (CTAR), etc. At the same time, a large number of typical contour corner detection methods have emerged in recent years, such as the gradient correlation matrix (GCM), Laplacian of Gaussian (LoG), second-order contour difference (SODC), point-to-centroid distance (PCD), and second-order generalized Gaussian directional derivative (SOGGDD), etc.

[0004] Achieving higher detection accuracy and time efficiency is the goal pursued by various corner detectors, and developing an effective "discrete" curvature estimation method is the key to achieving this goal. The CPDA discrete curvature was proposed by Awrangjeb et al. Compared with corner detectors based on CSS technology, it has better robustness to local noise in the contour. However, due to the need to calculate the discrete curvature at each point on the contour, the computational complexity of CPDA is very high. Subsequently, Awrangjeb et al. improved the algorithm efficiency by only calculating the discrete curvature at candidate corners. However, for CPDA and F-CPDA, selecting a larger radius of support (RoS) may miss some weak corners. To overcome the shortcomings of CPDA, Teng et al. proposed the CTAR detection method using simple triangle theory. The evaluation based on the repetition rate criterion shows that CTAR performs better than CPDA and runs faster. However, Lin Xinyu et al. pointed out that CTAR is also time-consuming due to the inclusion of root-finding operations, and proposed a new corner detection scheme (SODC) without root-finding operations using the second-order contour difference technique. SODC has better robustness to affine transformation and higher computational efficiency. Summary of the Invention

[0005] Aiming at the technical problems of large computational complexity and low detection speed of existing corner detection methods, the present invention proposes a fast corner detection method based on the ratio of symmetric contour center distances, which has a faster detection speed and strong robustness.

[0006] To achieve the above object, the technical solution of the present invention is implemented as follows: A fast corner detection method based on the ratio of symmetric contour center distances, the steps are as follows:

[0007] Step 1: Convert the color image into a grayscale image;

[0008] Step 2: Use the Canny edge detector to extract the contour of the grayscale image, and select the curve in the contour as the target contour;

[0009] Step 3: Smooth the target contour using the Gaussian function to obtain a smooth curve;

[0010] Step 4: Arbitrarily select a point P on the smooth curve i , and calculate the discrete curvature of the smooth curve at point P i ;

[0011] Step 5: Mark the points on the smooth curve where the discrete curvature reaches a local maximum and the value is greater than the curvature threshold as corner points.

[0012] Preferably, in step 2, the target contour is a curve in the grayscale image whose contour length is greater than (H + W) / 25, where H is the height of the grayscale image and W is the width of the grayscale image.

[0013] Preferably, the thresholds of the Canny edge detector are low threshold low = 0.2 and high threshold high = 0.7; the expectation of the Gaussian function is 0 and the variance is 3.5, and the smoothing is achieved by convolving the Gaussian function with the curve.

[0014] Preferably, in step three, if the endpoints of two smooth curves are 1 pixel apart, the two smooth curves are connected and regarded as a smooth curve; the intersection points of the intersecting smooth curves are marked as T-shaped corner points.

[0015] Preferably, the implementation method of the symmetric contour center distance ratio is as follows: the discrete curve defined by taking P i-w as the starting point and P i+w as the ending point on the target contour is designated as the support domain of point P i , and the center point of the support domain is point C o ; a symmetric contour of the support domain is generated with point P i as the symmetric center, and the symmetric point of point P i-w on the symmetric contour is point P' i+w = 2P i - P i+w , the symmetric point of point P i+w on the symmetric contour is point P' i-w = 2P i - P i-w , point C s is the center of the symmetric contour, and points C o , C s and P i are collinear, and point C os is the center point of the combined contour formed by the discrete curve starting from P i-w and ending at P i and the discrete curve starting from P i and ending at P' i+e ; point C' os is the center point of the combined contour formed by the discrete curve starting from P i+w and ending at P i and the discrete curve starting from P i and ending at P' i-w ; the symmetric contour center distance ratio is the ratio of the distance from the contour center C o to the symmetric center C s to the distance from the center point C os to the center point C' os Since taking the ratio of the distance to as the point P iDiscrete curvature at

[0016] Preferably, the method for calculating the discrete curvature using the ratio of the symmetric contour center distances is as follows: The coordinates of point P i are (x i , y i ), the support domain is k = {i - w, …, i, …, i + w}, w is the support domain radius, and the corner response function is:

[0017]

[0018] where C o is the center point of the curve segment S i-w from point P i+w to point P w (P i ) on the smooth curve, C os is the center point of the curve segment formed by the point set {P k , k = i - w, …, i} ∪ {P′ k , k = i + 1, …, i + w}, the point P′ k = 2P i - P k is the symmetric point of point P w (P i ) on the symmetric contour with point P i as the symmetric center on the curve segment S k , point P k is any point from point P w (P i ) to point P i-w on the curve segment S i , and the coordinates of point P k are (x k , y k ).

[0019] Preferably, the support domain radius w = 3.

[0020] Preferably, the calculation method of the corner response function is:

[0021] The coordinates of the center point C w (P i ) of the curve segment S o are:

[0022] Point C os is the center point of the curve segment formed by the point set {P k , k = i - w, …, i} ∪ {P′ k , k = i + 1, …, i + w}, and the point P′ k on the symmetric contour = 2Pi -P k It can be known that the coordinates of the center point are:

[0023]

[0024] Through derivation, it can be obtained that:

[0025]

[0026] Since And Requiring fewer operations, take as the RCDSC discrete curvature at point P i Then:

[0027] Preferably, the curvature threshold under the average repetition rate criterion is set to 0.009, and the curvature threshold under the accuracy criterion is set to 0.007.

[0028] Compared with the prior art, the beneficial effects of the present invention are as follows: The present invention only needs to calculate the Euclidean distance twice and there is no root extraction operation to estimate the discrete curvature of each point on the contour, and it is faster than other corner detectors; by selecting a relatively large radius of the support domain (RoS) and using the relative distance instead of the absolute distance to construct the corner response function (CRF), the discrete curvature of the present invention has a high corner resolution and is also very robust to noise and local contour changes. The simulation experiment results based on the average repetition rate (AR), accuracy (ACU), and localization error (LE) verify the effectiveness and efficiency of RCDSC. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0030] Figure 1 It is a flow diagram of the present invention.

[0031] Figure 2 It is the principle of the present invention to calculate the discrete curvature using the ratio of the distances from the center of the symmetric contour.

[0032] Figure 3 It is the behavioral analysis of the RCDSC discrete curvature based on the Γ model.

[0033] Figure 4 It is a curve graph of the function F(t,θ) with respect to the variable t.

[0034] Figure 5 Schematic diagram of the RCDSC discrete curvature estimation of the present invention.

[0035] Figure 6 Partial images of the GCM dataset selected for the present invention.

[0036] Figure 7 Curve graph of the influence of parameter changes on the RCDSC discrete curvature. Among them, (a)-(c) are the average repetition rates, and (d)-(f) are the positioning errors.

[0037] Figure 8 Curve graph of the performance comparison of the average repetition rates of several methods. Among them, (a), (b), (c), (d), and (e) are the average repetition rate performances of the comparison algorithms under Gaussian noise, rotation transformation, uniform scale transformation, non-uniform scale transformation, and rotation-scale transformation respectively, and (f) is the average result of the above five transformations.

[0038] Figure 9 Curve graph of the performance comparison of the positioning errors of several methods. Among them, (a), (b), (c), (d), and (e) are the positioning error (here the positioning error is based on the Euclidean distance between the corner points detected in the original image and the corner points detected in the transformed image) performances of the comparison algorithms under Gaussian noise, rotation transformation, uniform scale transformation, non-uniform scale transformation, and rotation-scale transformation respectively, and (f) is the average result of the above five transformations.

[0039] Figure 10 Curve graph of the ACU evaluation of several methods on the GCM dataset. Among them, (a), (b), (c), (d), and (e) are the accuracy performances of the comparison algorithms under Gaussian noise, rotation transformation, uniform scale transformation, non-uniform scale transformation, and rotation-scale transformation respectively, and (f) is the average result of the above five transformations.

[0040] Figure 11 Curve graph of the positioning error evaluation of several methods on the GCM dataset. Among them, (a), (b), (c), (d), and (e) are the positioning error (here the positioning error is based on the Euclidean distance between the corner points detected in the real image and the corner points detected in the transformed image) performances of the comparison algorithms under Gaussian noise, rotation transformation, uniform scale transformation, non-uniform scale transformation, and rotation-scale transformation respectively, and (f) is the average result of the above five transformations.

[0041] Figure 12 Schematic diagram of the detection results of the present invention on the edge maps of 8 original images. Detailed implementation manner

[0042] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0043] As Figure 1 shown, a fast corner detection method based on the ratio of symmetric contour center distances (RCDSC) comprises the following steps:

[0044] Step 1: Convert the RGB image or color image into a grayscale image. The Canny operator for edge extraction mainly processes grayscale images, so conversion is required first.

[0045] Step 2: Use the Canny edge detector to extract the contours of the grayscale image, and select the curves with a contour length greater than (H + W) / 25 as the target contours, where H is the height of the grayscale image and W is the width of the grayscale image.

[0046] The thresholds of the Canny edge detector are selected as low = 0.2 and high = 0.7. Low and high are the two threshold parameters of the Canny operator. The high threshold (high) is used to distinguish the object to be extracted from the background, and the low threshold (low) is used to smooth the contours of the edges, satisfying 0 ≤ low < high ≤ 1. Setting the high threshold too large will result in discontinuous or insufficiently smooth edge contours. Smoothing the contour lines with the low threshold can connect discontinuous contour segments. The main purpose of selecting the thresholds as low = 0.2 and high = 0.7 is to extract as many robust contours as possible while reducing the introduction of small contours (or weak contours). In the subsequent contour smoothing step, the smoothing window must be larger than the contour length, so the extracted contour length cannot be too short. On the other hand, short contours are also less robust to affine transformation. Canny needs to set two threshold parameters: low and high, and for all images in the test image set, low = 0.2 and high = 0.7.

[0047] If the endpoints of two curves are 1 pixel apart, the two curves are connected and regarded as one curve to avoid missing corner detection. At the same time, mark the intersection point of the intersecting curves as a T-type corner. The T-type corner is a type of corner, and the T-type corner is also a corner, which is to avoid missing T-type corner detection.

[0048] Step 3: Smooth the target contours using a Gaussian function to obtain smooth curves to remove small details and quantization noise.

[0049] The expectation of the Gaussian function is 0 and the variance is 3.5. Smoothing is achieved by convolving the Gaussian function with the curve. The contours extracted from digital images often contain quantization noise. Gaussian smoothing is mainly used to remove quantization noise and small details.

[0050] Step 4: At any point P on the smooth curve i At point P, the smooth curve is calculated using the symmetric contour center distance ratio. i The discrete curvature of .

[0051] The method of calculating the discrete curvature using the center distance ratio of the symmetrical contour is: point P i The coordinates of (x i ,y i ), with point P i The w pixels forward and backward constitute a discrete contour segment {(x j ,y j ),j={iw,…,i,…,i+w} is the support domain, and the corner point response function is:

[0052]

[0053] Among them, point C o For a smooth curve from point P i-w To point P i+w The curve segment S formed by the points between w (P i ), point C os is the point set {P k ,k=iw,…,i}∪{P′ k , k=i+1,…,i+w}, point P′ k =2P i -P k is the curve segment S w (P i )Click P i Point P on the symmetric contour is the symmetry center k The symmetric point of k is the curve segment S w (P i ) from point P i-w To point P i Any point of k The coordinates of (x k ,y k ). Due to symmetry, the quotient ratio obtained after considering the other half of the point set is the same as the result of the listed formula. This can reduce the amount of calculation and improve calculation efficiency.

[0054] Select w = 3 pixels as the support domain radius, and the support domain is {(x j ,yj ), j = i - 3, …, i, …, i + 3}, and w = 3 is selected. If the radius of the support region is too small, the robustness against affine transformation and local noise is poor, while if it is too large, corner fusion is likely to occur. For example, if the distance between two corner points is relatively close, the corner point with a smaller intensity may not be detected. Here, w = 3 is determined through experiments, and when w = 3, the algorithm has the best robustness against affine transformation and noise.

[0055] The specific implementation method is as follows: Use Figure 2 to elaborate on the basic idea of this application. The purpose of this application is to estimate the "discrete curvature" at the target point P on the original contour: First, the line segment defined by the starting point P os and the end point P oe on the original contour is designated as the support region of point P, and the center of this line segment is marked as point C o ; Then, a symmetric contour of the original contour is generated with point P as the center of symmetry. Assume that point P ss and point P se are the symmetric points of point P os and P oe respectively, and point C s is the center of the line segment defined by the starting point P ss and the end point P se . It is not difficult to obtain that points C o , C s and P are collinear. Denote point C os as the center point of the combined contour formed by the line segment defined by the starting point P os and the end point P and the line segment defined by the starting point P and the end point P oe ; Define C′ os as the center point of the combined contour formed by the line segment defined by the starting point P ss and the end point P and the line segment defined by the starting point P and the end point P oe . The ratio of the center distance of the symmetric contour (RCDSC) of the present invention is the ratio of the distance from the contour center C o to the center of symmetry C s to the distance from the center point C os to the center point C′ os , that is is regarded as the "discrete curvature" at the target point P.

[0056] The target point P is located on the original contour, and the support region is the contour segment on the smooth curve from the starting point P os to the end point P oe , where C o is the center point of the contour segment; a symmetric curve of the original curve is generated with P as the symmetric point. In particular, point P ss and P os are symmetric, and point Pse and P oe is symmetric; denote C os as the contour segment on the original contour from point P os to P and the contour segment on the symmetric contour from point P to P oe The center of the combined contour formed by the two is denoted as C. Take the ratio of the distance to as the discrete curvature at point P. C o and C s are symmetric about point P, so there is C os and C′ os are symmetric about point P, so there is Therefore Thus

[0057] For the convenience of reasoning, analyze the curvature behavior of the RCDSC of this application based on the Γ model shown Figure 3 . Generally, the corner response function CRF should reach a local extremum at the corner, and at the same time, the corner response function CRF should be able to reflect the intensity of the corner. Figure 3 shows a broken line l with vertices at the origin (0, 0) and an included angle of π - 2θ, where θ ∈ [0, π / 2]. For the convenience of analysis, assume that the broken line l is symmetric about the y-axis, then the broken line l can be parameterized as:

[0058]

[0059] where u ∈ R is the arc length parameter, and R represents the set of real numbers. Let P(t) be a point on the broken line l, and l s is the symmetric contour of the broken line l about point P(t). First, calculate the corner response function CRF at point P(t), and then analyze its behavior. Here, set the support domain radius used to calculate the corner response function CRF as w, then the line segment defined along the broken line l starting from P os = P(t - w) and ending at P oe = P(t + w) is the support domain of point P(t). The centroid C o = (c ox , c oy ) of this support domain can be expressed as:

[0060]

[0061] Denote points P ss , P se as the symmetric points of the starting point P(t - w) and the ending point P(t + w) about point P(t) respectively, then there is

[0062]

[0063] Assume C os =(c osx , c osy ) is the center of the combined contour formed by the line segment defined on the broken line l with P os as the starting point and P(t) as the ending point, and the line segment defined on the symmetric contour l s with P(t) as the starting point and P oe as the ending point. The coordinates of any point (x, y) on this combined contour can be expressed as:

[0064]

[0065] It can be calculated that:

[0066]

[0067]

[0068] Then the distances from the centers C o , C os to the point P(t) are respectively:

[0069]

[0070] Denote the function There is

[0071]

[0072] where v = t / w. Taking the partial derivative of the function F(t, θ) with respect to t gives:

[0073]

[0074] There is:

[0075] (a) t ∈ [-w, 0];

[0076] (b) t ∈ [0, w];

[0077] That is, the function F(t, θ) is monotonically decreasing on the interval [-w, 0] and monotonically increasing on the interval [0, w]. Therefore

[0078]

[0079] Formula (13) shows that the RCDSC curvature reaches a maximum value at the origin or the corner points of the broken line l, Figure 4The partial derivative image of the function F(t,θ) with respect to t is given. It is not difficult to see that the function F(t,θ) is monotonically increasing with respect to θ in the interval (0,π / 2), which indicates that the RCDSC curvature is positively correlated with the corner angle.

[0080] Next, use Figure 5 to give an estimation scheme for the RCDSC discrete curvature on the discrete curve. Figure 5 A section of the original, discrete smooth curve and its symmetric discrete contour with respect to the point P i =(x i ,y i ) are shown. Define S w (P i ) as the curve segment on the original smooth curve consisting of the points from point P i-w to point P i+w , where w is the support domain radius. Assume that C o is the center point of the curve segment S w (P i ), then there is:

[0081]

[0082] Let C os be the center point of the curve segment formed by the point set {P k , k = i - w,..., i} ∪ {P' k , k = i + 1,..., i + w}, where the point P' k on the symmetric contour = 2P i - P k . It can be known that the coordinates of the center point are:

[0083]

[0084] Through derivation, it can be obtained that:

[0085]

[0086] Note that while requires fewer operations, the present invention takes as the RCDSC discrete curvature at point p i . Specifically, it can be expressed as:

[0087]

[0088] Step Five: Mark the points on the smooth curve where the RCDSC discrete curvature reaches a local maximum and the value is greater than 0.009 as corner points.

[0089] At present, there is no unified definition for corner points. For digital curves, the discrete curvature extreme points of the curve are usually defined as corner points. The main difference between different contour corner point detection algorithms lies in how to define the discrete curvature. The numerical value can be understood as the corner point strength. Here, the larger the numerical value, the higher (or sharper) the corner point strength. A value greater than 0.009 is used to remove those points with low corner point strength and improve the robustness of the algorithm to affine transformation and noise.

[0090] The present invention uses Figure 6 The 20 images shown in the figure to evaluate the proposed discrete curvature. This dataset was collected and sorted out by Professor Zhang Xiaohong of Chongqing University, and includes 13 artificial images (such as "fish") and 7 real images (such as "cameraman" and "lab"). Gaussian noise and four affine transformations shown in Table 1 are applied to the 20 images, and a total of 6940 test images can be obtained. Image transformations such as Gaussian noise, rotation, uniform scale, non-uniform scale, and rotation-scale are used to increase the number of test images, and the robustness of the proposed algorithm and the comparison algorithm to affine transformation and Gaussian noise is tested.

[0091] Table 1. Five image transformation methods

[0092]

[0093] The present invention uses three evaluation criteria, namely average repeatability, accuracy, and localization error, to evaluate the performance of RCDSC and other five contour corner point algorithms.

[0094] The average repeatability (AR) is a criterion proposed by Mohammad Awrangjeb et al. to evaluate the robustness of corner point detection methods. Assume N o represents the number of corner points detected in the original image, N t represents the number of corner points detected in the corresponding transformed image, and N r represents the number of corner points that are repeatedly detected between the original image and the transformed image. Then the average repeatability is defined as:

[0095]

[0096] The accuracy (ACU) is a criterion proposed by Mohanna and Mokhtarian et al. to evaluate the accuracy of corner point detection methods. Mohammad Awrangjeb et al. pointed out that the accuracy is an artificial system, so there are many difficulties in specific operations. For example, when the dataset is large, the annotation work is very time-consuming and it is difficult to accurately mark the true corner points completely. Assume N g represents the number of true corner points (ground truth) in the original image, N o represents the number of corner points detected in the test image, and Na Denote the number of matching corner points between the true corner points and the detected corner points, then the accuracy rate is defined as:

[0097]

[0098] The localization error (LE) represents the localization accuracy of the detector for corner points, and is defined by the following mean square error:

[0099]

[0100] For the average repeatability rate, (x oj , y oj ) is the position of the j-th matching corner point in the original image, (x tj , y tj ) is the position of the j-th matching corner point in the test image, and N r represents the number of corner points that are repeatedly detected between the original image and the transformed image. For the accuracy rate, (x oj , y oj ) is the position of the j-th matching corner point of the true corner point (ground truth), and (x tj , y tj ) is the position of the j-th matching corner point in the test image.

[0101] The average repeatability rate (AR) is the proportion of corner points that are repeatedly detected, and is used to evaluate the robustness to affine transformation. The accuracy rate is the proportion of corner points that are correctly detected, and is used to evaluate the correctness of corner point detection. The localization error is the Euclidean distance between the reference corner point and the test corner point, and is used to evaluate the localization accuracy of the corner point. A higher average repeatability rate means higher robustness of the detector, while a higher accuracy rate means higher corner point detection accuracy of the detector. A lower localization error means higher localization accuracy of the detector.

[0102] The present invention details the comparative performance of 6 corner detection methods, including SOGGDD (Second-Order Generalized Gaussian Directional Derivative), SODC (Second-Order Contour Difference), GCM (Gradient Correlation Matrices), CPDA (Chord-to-Point Distance Accumulation), F-CPDA, and RCDSC proposed by the present invention. The RCDSC of the present invention mainly includes three parameters: (1) the variance σ of Gaussian smoothing; (2) the support domain radius w; (3) the curvature threshold T. Figure 7It shows how the above three parameters affect the performance of the RCDSC. Gaussian smoothing and the support domain radius, as two smoothing methods, have the ability to remove noise. If the parameter values are set too large, important details in the target contour may be ignored. On the contrary, too small parameter values will weaken the noise reduction ability. It should be noted that different edge detection methods will have a great impact on the corner detection results. Therefore, for a fair comparison, the same Canny edge detector and contour tracking method are used for all comparison detectors. Contour tracking is mainly reflected in contour selection, that is, a curve with a contour length greater than (H + W) / 25 is selected as the target contour. On the other hand, the choice of the curvature threshold should also consider maintaining a balance between introducing false corners and missing true corners. Without loss of generality, the present invention only provides a parameter selection scheme based on AR and LE. According to Figure 7 , under the average repetition rate criterion, the curvature threshold T is set to 0.009, and under the accuracy criterion, the curvature threshold T is set to 0.007. The values of the Gaussian smoothing σ and the RoS radius w are set to 3.5 and 3 respectively. The optimal parameters of the RCDSC detector and five comparison detectors are shown in Table 2. To maintain fairness, the parameters of all comparison detection algorithms are optimized and adjusted.

[0103] Table 2. Related parameter settings

[0104]

[0105] Figure 8 and Figure 9 give the average repetition rate AR and the localization error LE performance of six comparison detection methods under Gaussian noise and geometric transformation attacks. Generally speaking, the RCDSC detection method of the present invention has the highest AR and the lowest LE. For Gaussian noise, as the noise intensity increases, the performance of all corner detection methods becomes worse. Specifically, the repetition rate scores of the comparison detection methods decrease, while the localization errors increase. However, from Figure 8(a) It can be seen that the score of the RCDSC of the present invention decreases more slowly than the other five corner detection methods, indicating that the RCDSC is more robust to Gaussian noise. For the four affine transformations, the RCDSC of the present invention is superior to other comparative detection algorithms in both AR and LE. This phenomenon indicates that the discrete curvature of the RCDSC proposed by the present invention has good robustness to geometric transformations. As a fast version of CPDA, F-CPDA performs the worst among the comparative corner detection methods. On the one hand, F-CPDA significantly reduces the corner search space, thus reducing its performance; on the other hand, considering that F-CPDA and CPDA use the same curvature estimation scheme, F-CPDA has similar problems to CPDA. The performance of GCM is slightly better than that of CPDA and F-CPDA, but worse than other corner detection algorithms. Awrangjeb et al. pointed out that since GCM uses the first derivative and a small support neighborhood (1×1), it will detect more false corners.

[0106] Figure 10 and Figure 11 shows the performance based on the accuracy criterion. Generally, the ACU of the RCDSC of the present invention is the highest, while the LE of F-CPDA is the lowest. This phenomenon indicates that the RCDSC of the present invention performs excellently in detecting real corners, while F-CPDA performs excellently in accurately locating corners. GCM ranks second in terms of ACU, which also indicates the excellent real corner localization ability of GCM. Figure 12 provides the detection results of the RCDSC detector on eight original images.

[0107] The running time evaluation environment of the detection method is configured as follows: Windows 10 desktop computer, Intel Core i7-4770, 3.40GHz processor, 8GB memory, Matlab-2016b. Since all detection methods use the same contour extraction algorithm, the running time does not include the edge extraction time. Given that the calculation of the square root is very time-consuming, the number of square root operations is used to simply analyze the operation efficiency of the detector, and the actual running time is given in Table 3. For a digital curve composed of n points, the CPDA method contains 54n square root operations, and F-CPDA contains n + 54n p square root operations, where n p represents the number of candidate points. The number of square root operations of the SODC method is 3n. As shown in formula (17), the RCDSC of the present invention only calculates the Euclidean distance twice and does not involve square root operations. Table 3 shows the running time of the comparative algorithms on the GCM dataset, and it can be seen that the RCDSC runs faster than the other five detectors. SODC is a fast corner detector proposed in 2017, but the use of the multi-scale curvature product technology limits its computational efficiency. Table 3 verifies the high efficiency of the RCDSC of the present invention in terms of computational performance.

[0108] Table 3. Comparison of time efficiency on GCM dataset

[0109]

[0110] The present invention uses the ratio of symmetric contour center distances technique (RCDSC) to propose a new corner response function, analyzes and studies its curvature behavior based on the Γ-model, and proposes a new efficient corner detection scheme based on this. The discrete curvature of RCDSC has high corner resolution and also has good robustness to Gaussian noise and geometric transformations. Experiments based on AR, ACU, and LE evaluation metrics show that the RCDSC detection method of the present invention is superior to five other comparative corner detection methods.

[0111] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A fast corner detection method based on the ratio of symmetric contour center distances, characterized in that The steps are as follows: Step 1: Convert the color image into a grayscale image; Step 2: Use the Canny edge detector to extract the contours of the grayscale image, and select the curves in the contours as the target contours; Step 3: Smooth the target contours using the Gaussian function to obtain smooth curves; Step 4. Arbitrarily select a point P on the smooth curve i , and calculate the discrete curvature of the smooth curve at point P i using the ratio of the distances from the center of the symmetric profile Step 5: Mark the points on the smooth curves where the discrete curvature reaches a local maximum and the value is greater than the curvature threshold as corner points; In Step 3, if the endpoints of two smooth curves are 1 pixel apart, connect the two smooth curves and regard them as one smooth curve; mark the intersection points of the intersecting smooth curves as T-type corner points; The method for realizing the ratio of the distances of the symmetric contour centers is as follows: Designate the discrete curve defined by taking P i-w as the starting point and P i+w as the ending point on the target contour as the support domain of point P i , and the center point of the support domain is point C o ; generate the symmetric contour of the support domain with point P i as the symmetric center, and the symmetric point of point P i-w on the symmetric contour is point P' i+w = 2P i - P i+w , and the symmetric point of point P i+w on the symmetric contour is point P' i-w = 2P i - P i-w , point C s is the center of the symmetric contour, and points C o , C s and P i are collinear. Point C os is the center point of the combined contour formed by the discrete curve with P i-w as the starting point and P i as the ending point and the discrete curve with P i as the starting point and P' i+w as the ending point; point C' os is the center point of the combined contour formed by the discrete curve with P i+w as the starting point and P i as the ending point and the discrete curve with P i as the starting point and P' i-w as the ending point; the ratio of the distances of the symmetric contour centers is the ratio of the distance from contour center C o to symmetric center C s and the distance from center point C os to center point C' os Since take the ratio of distance and as the discrete curvature at point P i .​ 2. The fast corner detection method based on the center distance ratio of symmetric contours according to claim 1, wherein, In Step 2, the target contour is a curve in the grayscale image with a contour length greater than (H + W) / 25, where H is the height of the grayscale image and W is the width of the grayscale image.

3. The rapid corner detection method based on the central distance ratio of symmetric contours according to claim 2, wherein, The threshold of the Canny edge detector is low threshold low = 0.2 and high threshold high = 0.7; the expectation of the Gaussian function is 0 and the variance is 3.5, and the smoothing is implemented by convolving the Gaussian function with the curve.

4. The rapid corner detection method based on the ratio of symmetric contour center distances according to any one of claims 1-3, characterized in that The method for calculating discrete curvature using the ratio of the distances from the center of the symmetric contour is as follows: For point P i with coordinates (x i , y i ), the support domain is k = {i - w, …, i, …, i + w}, where w is the support domain radius, and the corner response function is: Among them, C o is the center point of the curve segment S i-w formed by the points between point P i+w and point P w (P i ). C os is the center point of the curve segment formed by the point set {P k , k = i - w, …, i} ∪ {P′ k , k = i + 1, …, i + w}. The point P′ k = 2P i - P k is the symmetric point of point P w (P i ) on the symmetric contour with point P i as the symmetric center on the curve segment S k . The point P k is any point on the curve segment S w (P i ) from point P i-w to point P i . The coordinates of the point P k are (x k , y k ).

5. The fast corner detection method based on the central distance ratio of symmetric profiles according to claim 4, wherein The support domain radius w = 3.

6. The rapid corner detection method based on the central distance ratio of symmetric contours according to claim 4, characterized in that, The calculation method of the corner response function is: Curve segment S w (P i )'s center point C o The coordinates are: Point C os is the center point of the curve segment formed by the point set {P k , k = i - w, …, i} ∪ {P′ k , k = i + 1, …, i + w}. The point P′ on the symmetric contour k = 2P i - P k . It can be known that the coordinates of the center point are: Through derivation, it can be obtained that: Since and requires fewer operations, taking as the RCDSC discrete curvature at point P i then:

7. The fast corner detection method based on the central distance ratio of symmetric contours according to claim 6, wherein Under the average repeatability criterion, the curvature threshold is set to 0.009, and under the accuracy criterion, the curvature threshold is set to 0.007.

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