[0019] In the following, a method for rapid segmentation of image features based on curvature analysis of the present invention will be described in detail with reference to the accompanying drawings and a typical specific implementation. The algorithm specifically includes the following parts:
[0020] First, perform zero-order geometric continuation processing on the input image, the steps are as follows:
[0021] The algorithm uses the Canny operator to perform edge detection on the image to obtain discrete edge points. The 8-neighbor boundary tracking algorithm is used to filter out the edge points with spatial continuity in the image, and the continuous edges are connected and short edges removed. Finally, The Gaussian evolution method smoothes the continuous edges and further enhances the spatial continuity of the edge points.
[0022] The discrete edge points in the image are transformed into a set of edge points with spatial continuity after zero-order geometric continuity processing:
[0023] C={p i :(u i ,v i ),i=1,2,...n} (1)
[0024] Where p i And p i+1 Are neighboring points, (u i ,v i ) Is the edge point p i The coordinates in the image coordinate system, where n is the number of edge points, and:
[0025]
[0026] The algorithm uses the Gaussian evolution method to smooth the continuous edges: in the image coordinate system o'-uv, the detected spatial continuous edges are represented as C(s)={u(s),v(s)}, where, s is the arc length function. The Gaussian function is:
[0027]
[0028] σ is a scale parameter, and its value determines the degree of smoothing. The curve C(s)={u(s),v(s)} is expressed as C(s,σ)={u(s,σ),v(s,σ)} after Gaussian evolution, then:
[0029]
[0030] Gaussian evolution can well retain the global geometric characteristics of continuous edges, and can remove noise points in continuous edges, and at the same time smooth the edge points in the neighborhood of the intersection of characteristic curves into shorter arcs.
[0031] Through zero-order geometric continuity processing, discrete edge points are processed into edge points with spatial continuity. After that, the algorithm determines the intersection of the characteristic curve based on the discontinuity of the second-order geometry at the intersection of different curves, and the intersection of the characteristic curve becomes the extreme point of the second derivative, so as to realize the image feature segmentation.
[0032] In continuous space, for the curve C(s), the curvature κ(s) at the arc length s is:
[0033]
[0034] among them, with They are the first and second derivatives of u(s) and v(s) respectively.
[0035] In the discrete space pixel coordinate system o'-uv, the continuous edge C of space is at point p i Curvature κ i Approximately expressed as:
[0036]
[0037] Among them, the derivative is approximated in the form of intermediate difference:
[0038]
[0039] In order to improve the reliability of the screening of maximum curvature points, this paper establishes the functional relationship between angle and threshold, and derives the curvature threshold from the angle threshold, and designs the maximum curvature threshold. Set the maximum curvature threshold to be T κ , When a certain edge point is the point of maximum curvature and the curvature value is greater than T κ When it is judged as the intersection of characteristic curves. Edge point p i Curvature value κ i With p i The tangent curve included angle θ of the curve feature on both sides i Related, such as figure 2 Shown.
[0040] To establish κ i And θ i The function relationship of the algorithm to the curvature calculation process is a reasonable approximation, simplifying κ i And θ i The functional relationship of the approximation process is as figure 2 Shown, p i-2 -p i-1 -p i And p i -p i+1 -p i+2 Approximately a line segment, θ i It can be approximated by the angle between two line segments, and the coordinate value of each point is set as:
[0041]
[0042] From formulas (6), (7), (8), we can get:
[0043]
[0044] Since the Gaussian evolution causes a certain degree of distortion to the curvature, it is necessary to correct the functional relationship shown in equation (9), and correct κ through simulation calculations. i -θ i , The correction process is: generate θ i Continuously changing simulated image with continuous edges at p i The neighborhood of is approximately two intersecting line segments, and the angle between the line segments is θ i , After Gaussian evolution of continuous edges, the curvature value at the intersection of line segments is calculated as κ i , The correction result is as image 3 Shown.
[0045] For κ i -θ i The simulation curve is corrected, and the correction coefficient is k κ-θ , Then the revised κ i -θ i The mathematical model of the curve is:
[0046]
[0047] Table 1κ i -θ i Curve correction coefficient and fitting error table
[0048]
[0049]
[0050] The least square method is used for data curve fitting, and the correction coefficient and the root mean square error of curve fitting—RMSE are obtained. The correction results are shown in Table 1. Comprehensive σ vs κ i -θ i Curve smoothing effect, curvature distortion degree, and the influence of curve extreme, the default value of σ is designed by this algorithm. d = 9.
[0051] In order to make the algorithm in the present invention more general, it is proposed that when the prior information is insufficient, T θ The design method of the default value. Such as Figure 4 Shown, Ω κ (p i ) In the 5 spatial continuous edge points distributed in L θ ×H θ In the rectangular area, p i The included angle θ i Approximately:
[0052]
[0053] As the space is continuous, L θ ≤4, H θ ≤2, when H θ =0, at this time Ω κ (p i ) Is a straight line; when L θ = 4, H θ =2, θ i Take the maximum value θ imax = 135°. θ imax Is the pixel coordinate system in Ω with a radius of 2 κ (p i The maximum angle that can be resolved within ), therefore, let T θ =θ imax ,Calculate the maximum curvature threshold T from equation (10) κ :
[0054]
[0055] Among them, L θ Represents the pixel size of the neighborhood in the horizontal direction, H θ Indicates the pixel size of the neighborhood in the vertical direction.
[0056] Normally, when different characteristic curves/straight lines are tangent or intersect, the angle at the tangent point or intersection point is less than T θ , So through the curvature maximum threshold T κ The detected intersection of characteristic curves can basically realize the segmentation of edge points of different characteristic curves.
[0057] According to the geometric meaning of curvature, the curvature of a straight line is zero, and the edge points belonging to the straight line and the edge points belonging to the curve can be quickly separated by the method of detecting the zero point of curvature.
[0058] Let the set of edge points with continuous curvature be C mn , P m , P n Is C mn End point, C mn Expressed as:
[0059] C mn ={p i :(u i ,v i ),m≤i≤n) (13)
[0060] C mn The set of curvature values is κ mn :
[0061] κ mn ={κ i :m≤i≤n} (14)
[0062] κ mn The arithmetic mean of is
[0063]
[0064] In theory, When, C mn To be judged as a collection of straight edge points; When, C mn Determined as a collection of curve edge points.
[0065] Due to the quantization effect of digital images on space and the curvature distortion caused by Gaussian evolution, the curvature of the straight line edge points in the pixel coordinate system will be greater than zero. Therefore, it is necessary to design the curvature threshold T of the linear feature according to the scale parameter σ of Gaussian evolution line. The judgment criterion of the set of straight edge points and the set of curved edge points is revised to: When, C mn Determined as a collection of straight edge points; When, C mn Determined as a collection of curve edge points.
[0066] The algorithm in the present invention adopts the way of simulation calculation, and design T line. The angle between the generation and the horizontal direction of the image is θ line =1°~179°(Δθ line =1°) linear edge simulation image, respectively calculate the average curvature κ when σ=3~15 (Δσ=1) L , Generating κ L -σ curve, such as Figure 5 As shown, where Δθ line , Δσ is the change of included angle and evolution parameter respectively. analysis Figure 5 Available: σ increases, κ L Decrease, when σ=9, T line =κ L = 0.002.
[0067] Due to the adoption of the above-mentioned technical solution, the present invention has the following beneficial effects: the image feature fast segmentation algorithm based on curvature analysis obtains edges with spatial continuity through zero-order geometric continuity processing, reduces the number of edge points to be processed, and compares Points are represented in an orderly manner; a low-calculation maximum curvature filtering algorithm is designed to separate continuous edge points in the image; a low-calculation curvature zero point detection algorithm is designed to identify and separate straight edge points and ellipses Edge point: The curvature analysis image feature separation algorithm improves the speed of feature segmentation through continuous edge detection, curvature calculation and curvature zero detection.
[0068] It should be realized that the above description is only a specific embodiment of the present invention, and the present invention is not limited to the specific structure illustrated or described above. The claims will cover all the changes within the essential spirit and scope of the present invention.
