CN112785612B - Image edge detection method based on wavelet transformation - Google Patents
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Abstract
The invention discloses an image edge detection method based on wavelet transformation, which comprises the following steps: performing wavelet transformation on the image to obtain the modulus of the wavelet coefficient of each pixel point; acquiring quasi-edge pixel points; threshold filtering is carried out on all quasi-edge pixel points in the image, filtering quasi-edge pixel points are obtained, and the number of the filtering quasi-edge pixel points is n; searching edge pixel points, wherein the number of the edge pixel points is m; and a threshold adjusting step, namely returning to the step of performing threshold filtering on all quasi-edge pixel points in the image according to the size of the threshold k adjusted by m and n until the set conditions of m and n are met, and reserving the edge pixel points acquired at the last time to be output as the image edge detection result. According to the edge detection method, the determined threshold is used for filtering the image edge points according to the characteristic that the real edge points are continuous in space, so that misjudgment of non-edge pixels is reduced, loss of the edge pixels is reduced, and the accuracy is high.
Description
Technical Field
The invention belongs to the technical field of image processing, and particularly relates to an image edge detection method based on wavelet transformation.
Background
The image edge detection technology is an important image processing technology and is widely applied to the fields of image recognition and image segmentation.
The image edge detection algorithm based on wavelet transformation is one of edge detection methods, the existing image edge detection algorithm based on wavelet transformation is extremely easily affected by noise and false edges, a threshold value is added to the traditional algorithm for the situation, and only the maximum value larger than the threshold value is judged as an edge so as to filter the influence of the false edges and the noise.
The traditional algorithm uses threshold processing to filter out false edges, but brings new problems, when the selected threshold is too large, too much information including real edge information is filtered out, and when the selected threshold is too small, false edges are left, and the situation of each image is different, and the accurate selection of the threshold is a very difficult process.
Disclosure of Invention
The invention provides an improved image edge detection method based on wavelet transformation, which aims at solving the technical problem of low accuracy rate caused by unreasonable threshold value of an image edge detection algorithm based on wavelet transformation in the prior art.
In order to realize the purpose of the invention, the invention adopts the following technical scheme to realize:
an image edge detection method based on wavelet transformation comprises the following steps:
performing wavelet transformation on the image to obtain a modulus value of a wavelet coefficient of each pixel point;
dividing the image into a plurality of detection areas, and searching for the maximum modulus value in each detection area, wherein the pixel point corresponding to the maximum modulus value is a quasi-edge pixel point;
threshold filtering is carried out on all quasi-edge pixel points in the image, quasi-edge pixel points with module values not smaller than a threshold k are reserved, the quasi-edge pixel points are filtered, and the number of the filtered quasi-edge pixel points is n;
searching all filtering quasi-edge pixel points meeting the connectivity requirement as edge pixel points, wherein the number of the edge pixel points is m;
and a threshold adjusting step, namely returning to the step of performing threshold filtering on all quasi-edge pixel points in the image according to the size of the threshold k adjusted by m and n until the set conditions of m and n are met, and reserving the edge pixel points acquired at the last time to be output as the image edge detection result.
Further, before the wavelet transformation of the image, the method also comprises the steps of obtaining a basis function, and solving partial derivatives of the image in the x direction and the y direction respectively to obtain a basis function psi in the x direction and the y direction 1 (x, y) and Ψ 2 (x, y), wherein the x-direction represents a row direction of the image and the y-direction represents a column direction of the image;
and performing wavelet transformation on the image according to the acquired basis functions.
Further, in the above-mentioned case,
θ (x, y) is the gray value of the image at (x, y).
Further, in the step of performing wavelet transformation on the image, wavelet coefficients ω of the image in the row direction are obtained x (x, y) and wavelet coefficients ω in column direction y (x, y) according to ω x (x, y) and ω y (x, y) calculating the modulus ω (x, y) of the wavelet coefficients.
Further, the calculation method of the modulus ω (x, y) of the wavelet coefficient is as follows:
further, in the threshold value adjusting step, the communication ratio is calculated
The size of the threshold k is adjusted according to p.
And further, comparing p with a threshold value A, stopping adjusting the threshold value k when p is larger than or equal to A, and reserving the edge pixel points acquired at the last time to be output as an image edge detection result.
Furthermore, the initial value setting of the threshold k is larger than the empirical value, in the threshold adjusting step, when p is smaller than A, the threshold k is reduced according to the set step length, and the step of performing threshold filtering on all quasi-edge pixel points in the image is returned.
Further, in the threshold value adjusting step, when p is less than A, the current connectivity ratio p1 is compared with the previous connectivity ratio p2, if p1 is greater than p2, the threshold value k is reduced according to the set step length, the step of performing threshold value filtering on all quasi-edge pixel points in the image is returned, and otherwise, the edge pixel points obtained at the last time are reserved and output as the image edge detection result.
Further, the step of searching all the filtering quasi-edge pixel points meeting the connectivity requirement comprises:
finding out a plurality of connected regions from the filtering quasi-edge pixel points, wherein the filtering quasi-edge pixel points in each connected region meet continuous adjacency, the number of the filtering quasi-edge pixel points in the connected region is not less than B, the adjacency comprises row adjacency or column adjacency, and the filtering quasi-edge pixel points in the connected region are edge pixel points.
Compared with the prior art, the invention has the advantages and positive effects that: according to the image edge detection method based on wavelet transformation, the number of the filtering quasi-edge pixel points meeting the connectivity requirement and the number of the quasi-edge pixel points are searched for and the threshold is adaptively adjusted according to the characteristic that real edge points are continuous in space, so that the proper threshold is reasonably and effectively determined, the determined threshold is used for filtering the image edge points, misjudgment of non-edge pixels is reduced, loss of the edge pixels is reduced, and the accuracy is high.
Other features and advantages of the present invention will become more apparent from the following detailed description of the invention when taken in conjunction with the accompanying drawings.
Drawings
In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required to be used in the embodiments are briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on the drawings without creative efforts.
FIG. 1 is a flowchart of an embodiment of a wavelet transform-based image edge detection method according to the present invention;
FIG. 2 is a diagram illustrating an image edge pixel with a maximum modulus according to an embodiment;
FIG. 3 is a diagram illustrating several ways of communicating images according to one embodiment;
FIG. 4 is a graph showing the relationship between the threshold value and the connectivity ratio in the first embodiment;
fig. 5 is a preferred flowchart of the image edge detection method based on wavelet transform according to the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the accompanying drawings and embodiments.
It should be noted that in the description of the present invention, the terms of direction or positional relationship indicated by the terms "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc. are based on the directions or positional relationships shown in the drawings, which are merely for convenience of description, and do not indicate or imply that the device or element must have a specific orientation, be constructed and operated in a specific orientation, and thus, should not be construed as limiting the present invention. Furthermore, the terms "first," "second," and the like are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
Example one
Wavelet transform analysis is a new analysis method developed in recent decades, is discovered and developed based on fourier transform, breaks through and innovates on the basis of fourier transform, and is a powerful tool for processing images in a spatial domain and a frequency domain. The wavelet transformation analysis is to process and analyze images at various scales, so that information of the images at different scales can be obtained, and compared with the Fourier transformation, the wavelet transformation analysis can only analyze images at one scale and provide more information. The image edge detection algorithm based on wavelet transformation in the prior art has the technical problem of low accuracy due to the fact that a non-edge pixel is misjudged to be an edge pixel due to unreasonable threshold values, or the edge pixel is misjudged to be a non-edge pixel and the edge pixel is lost.
In order to solve the above problem, as shown in fig. 1, the present embodiment proposes a method for detecting an image edge based on wavelet transform, which includes the following steps:
and performing wavelet transformation on the image to obtain the modulus of the wavelet coefficient of each pixel point.
Dividing the image into a plurality of detection areas, searching for the maximum modulus value in each detection area, wherein the pixel point corresponding to the maximum modulus value is a quasi-edge pixel point, and the number of all quasi-edge pixel points in the image is n.
The wavelet coefficients reflect the rate of change of the image grey level, so the edges of the image can be found if the maximum value of the coefficients can be found, i.e. by calculating the modulus of the wavelet coefficients, the maximum modulus corresponds to the maximum value of the coefficients.
The method for searching the maximum modulus value is generally a local search, the image is divided into a plurality of detection areas, and the maximum modulus value in each detection area is found, for example, a range of 3 × 3 pixels may be adopted, but a local range of other sizes may also be adopted, as shown in fig. 2, where the maximum value of the modulus value is the oblique edge in fig. 2.
Because image components are complex, a large number of false edges exist in quasi-edge pixel points obtained through wavelet analysis, and in the case of the quasi-edge pixel points, a threshold k is added for filtering, and only the maximum value larger than the threshold is judged as an edge, so that the influence of the false edges and noise is filtered.
And performing threshold filtering on all quasi-edge pixel points in the image, reserving quasi-edge pixel points with the modulus value not less than a threshold k, and setting the number of the filtered quasi-edge pixel points to be n.
The method aims to solve the technical problems that when the selected threshold k is too large, too much information including real edge information is filtered, when the selected threshold k is too small, false edges are left, and the situation of each image is different, so that the threshold is difficult to accurately select. The embodiment further comprises a step of adjusting the threshold k to select a proper threshold k.
Searching all filtering quasi-edge pixel points which meet the connectivity requirement, wherein the filtering quasi-edge pixel points are edge pixel points, and the number of the edge pixel points is m;
because the real edge point has the characteristic of being continuous in space, the filtering quasi-edge pixel point meeting the connectivity requirement is determined as the edge pixel point in a reverse pushing mode. When the k value is reasonably selected, the number m of the edge pixel points should be close to the number n of the filtering quasi-edge pixel points, and theoretically, m is equal to n and is the best.
And a threshold adjusting step, namely returning to the step of performing threshold filtering on all quasi-edge pixel points in the image according to the size of the threshold k adjusted by m and n until the set conditions of m and n are met, and reserving the edge pixel points acquired at the last time to be output as the image edge detection result. Therefore, the size of the threshold k is adjusted according to the proximity relation between m and n, once the threshold k is changed, the corresponding m and n are changed, and only whether the proximity relation between the m and n meets the requirement or not needs to be seen.
According to the image edge detection method based on wavelet transformation, the number of the filtering quasi-edge pixel points meeting the connectivity requirement and the number of the quasi-edge pixel points are searched for and the threshold is adaptively adjusted according to the characteristic that real edge points are continuous in space, so that the proper threshold is reasonably and effectively determined, the determined threshold is used for filtering the image edge points, misjudgment of non-edge pixels is reduced, loss of the edge pixels is reduced, and the accuracy is high.
As a preferred embodiment, before the wavelet transformation of the image, the method further comprises obtaining basis functions, and obtaining partial derivatives of the image in the x direction and the y direction respectively to obtain basis functions Ψ in the x direction and the y direction 1 (x, y) and Ψ 2 (x, y), wherein the x-direction represents a row direction of the image and the y-direction represents a column direction of the image.
The edge of an image is essentially a transition point of image gray scale, and the transition in the frequency domain means a high frequency, so that the low frequency part of the image mainly contains information of the approximate shape of the image, and the high frequency part mainly contains detailed information such as image edge.
According to the obtained basis function Ψ 1 (x, y) and Ψ 2 (x, y) wavelet transforming the image.
In mathematics, the first derivative of a function can indicate the change rate of the function, so the maximum value of the first derivative indicates the position where the function changes most, and if the partial derivatives in x and y directions of an image are calculated, the partial derivatives are recorded as:
θ (x, y) is the gray value of the image at (x, y).
Taking the function as a basic function of wavelet transformation to perform wavelet transformation on the original input image, wherein the wavelet transformation is similar to series expansion, and a plurality of series of expansion coefficients omega are obtained after expansion x (x, y) and ω y (x,y)。
In the step of wavelet transformation of the image, wavelet coefficients omega of the image in the row direction are obtained x (x, y) and wavelet coefficients ω in column direction y (x, y) according to ω x (x, y) and ω y (x, y) calculating the modulus ω (x, y) of the wavelet coefficients.
Preferably, in this embodiment, the calculation method of the modulus ω (x, y) of the wavelet coefficient is:
in the threshold value adjusting step, the communication ratio is calculated
The size of the threshold k is adjusted according to p.
As shown in fig. 3, the edge of the image is usually connected pixels rather than isolated pixels, and thus, the edge pixels are usually continuous pixels, and the continuous pixels close to form the outline content in the image, there are 4 connection modes in a local range, for example, 3 × 3 range, as shown in fig. 3, i.e., horizontal, vertical, 45 degree oblique direction, 135 degree oblique direction, and the 4 connection modes are corresponding to the horizontal edge, the vertical edge, the 45 degree oblique edge, and the 135 degree oblique edge.
In general, the image edge pixels after the threshold filtering process are connected in one of the 4 manners, and it is easy to study the connection relationship of these pixels through the coordinate adjacency relationship, so the most ideal case is:
that is, all the filtered quasi-edge pixels after the thresholding are edge pixels, and there are no non-edge pixels, which is the core mathematical model of this embodiment.
According to the shortcomings of the conventional algorithm, when the threshold value is too large, the edge information is filtered to reduce the value of m, and when the threshold value is too small, the non-edge information is added to increase the value of n, both the above expression is lower than 100%, and the image is similar to a quadratic function image with a downward opening, as shown in fig. 4, and the edge quality is affected by selecting too large or too small threshold value.
The initial value of the threshold k is set to be larger than the empirical value, and the empirical value is a numerical value with a higher value-taking frequency according to the empirical value k. A larger value is selected when an initial value of a threshold is selected, partial edge information is filtered, but the calculation amount of the following data is small, the connectivity ratio p is monotonically increased, then pixel points meeting connectivity are marked, the proportion of the pixel points to the total number of the pixel points is calculated, the result of the connectivity ratio p is used as feedback information to be transmitted to the threshold for processing, if the result does not meet the requirement, the threshold is gradually reduced, so that the processed pixel points are gradually increased until the proportion meets a certain condition (for example, the proportion is greater than 98%), the threshold at the moment is the most reasonable threshold, and the adaptive threshold processing can be realized in the process. The flow chart of the whole process is shown in fig. 5, after the threshold k is adjusted each time, the step of threshold filtering is returned to be performed on all quasi-edge pixel points in the image, the threshold filtering is performed again, n and m are obtained again, and the connectivity ratio p is calculated again.
And comparing the p with a threshold value A, stopping adjusting the threshold value k when the p is more than or equal to the A, and reserving the edge pixel points acquired at the last time to be output as the image edge detection result. When p is larger than or equal to A, the threshold at the moment is the most reasonable threshold, so that the edge pixel points acquired at the last time are reserved and output as the image edge detection result.
The threshold value a is a threshold value set in advance, and is a value greater than 0 and less than or equal to 1, and the specific value may be set according to actual needs.
In the threshold adjusting step, when p is smaller than A, the threshold k is reduced according to the set step length, and the step of filtering the threshold of all quasi-edge pixel points in the image is returned.
Because a larger value is selected for the initial value of the threshold, part of edge information can be filtered, namely m obtained after threshold filtering is smaller, n is larger, and therefore the communication ratio p is smaller, then the threshold k is reduced according to the set step length, the corresponding m is increased, and n is reduced, so that the communication ratio p is monotonically increased, and then whether the communication ratio p meets the condition or not is judged again.
In order to prevent the situation that the communication ratio p is reduced after the threshold k is adjusted for multiple times, namely the communication ratio p is smaller when the threshold k is adjusted more, the condition that the communication ratio p is reduced due to over adjustment is caused after the threshold k is reduced again according to the step length. Therefore, in the threshold adjustment step, when p is less than a, the current connectivity ratio p1 is compared with the previous connectivity ratio p2, if p1 is greater than p2, the threshold k is reduced according to the set step size, the step of performing threshold filtering on all quasi-edge pixels in the image is returned, and otherwise, the edge pixels acquired at the last time are retained and output as the image edge detection result. That is, even if the final connectivity ratio p does not reach a, if the connectivity ratio p does not increase any more, no adjustment is necessary, indicating that p is already around the peak. The phenomenon that adjustment time is wasted due to over adjustment is avoided, and meanwhile, a high communication ratio p is guaranteed.
The step of searching all the filtering quasi-edge pixel points meeting the connectivity requirement comprises the following steps:
finding out a plurality of connected regions from the filtering quasi-edge pixel points, wherein the filtering quasi-edge pixel points in each connected region meet continuous adjacency, the number of the filtering quasi-edge pixel points in the connected region is not less than B, the adjacency comprises row adjacency or column adjacency, and the filtering quasi-edge pixel points in the connected region are edge pixel points. B is a positive integer value set as required, for example, in this embodiment, setting B to 10 means that it is required that the connection length of the pixel points is 10, that is, at least 10 pixel points are required to be continuous, and if the condition is not met, the pixel points are considered as non-edge pixels and are filtered, and this value may be used as an input control parameter to control the capability of the algorithm to filter the non-edge.
The above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be apparent to those skilled in the art that modifications may be made to the embodiments described in the foregoing embodiments, or equivalents may be substituted for some of the features thereof; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions.
Claims (10)
1. An image edge detection method based on wavelet transformation is characterized by comprising the following steps:
performing wavelet transformation on the image to obtain the modulus of the wavelet coefficient of each pixel point;
dividing the image into a plurality of detection areas, and searching for the maximum modulus value in each detection area, wherein the pixel point corresponding to the maximum modulus value is a quasi-edge pixel point;
threshold filtering is carried out on all quasi-edge pixel points in the image, quasi-edge pixel points with module values not smaller than a threshold k are reserved, the quasi-edge pixel points are filtered, and the number of the filtered quasi-edge pixel points is n;
searching all filtering quasi-edge pixel points meeting the connectivity requirement as edge pixel points, wherein the number of the edge pixel points is m;
and a threshold adjusting step, namely returning to the step of performing threshold filtering on all quasi-edge pixel points in the image according to the size of the threshold k adjusted by m and n until the set conditions of m and n are met, and reserving the edge pixel points acquired at the last time to be output as the image edge detection result.
2. The image edge detection method according to claim 1, further comprising obtaining basis functions before performing wavelet transform on the image, and obtaining partial derivatives of the image in x-direction and y-direction respectively to obtain basis functions Ψ in x-direction and y-direction 1 (x, y) and Ψ 2 (x, y), wherein the x-direction represents a row direction of the image and the y-direction represents a column direction of the image;
and performing wavelet transformation on the image according to the acquired basis functions.
3. The image edge detection method according to claim 2,
θ (x, y) is the gray value of the image at (x, y).
4. The image edge detection method according to claim 1, wherein in the step of performing wavelet transform on the image, wavelet coefficients ω of the image in a row direction are obtained x (x, y) and wavelet coefficients ω in column direction y (x, y) according to ω x (x, y) and ω y (x, y) calculating the modulus ω (x, y) of the wavelet coefficients.
5. The image edge detection method according to claim 4, wherein the modulus ω (x, y) of the wavelet coefficients is calculated by:
6. the image edge detection method according to claim 1, wherein in the threshold adjustment step, the connectivity ratio is calculated
The size of the threshold k is adjusted according to p.
7. The image edge detection method according to claim 6, wherein p is compared with a threshold value A, when p is larger than or equal to A, the threshold value k is stopped from being adjusted, and the edge pixel points obtained at the last time are reserved and output as the image edge detection result.
8. The image edge detection method according to claim 6, wherein an initial value of a threshold k is set to be larger than an empirical value, in the threshold adjustment step, when p is smaller than A, the threshold k is reduced according to a set step length, and the step of performing threshold filtering on all quasi-edge pixel points in the image is returned.
9. The image edge detection method according to claim 8, wherein in the threshold adjustment step, when p is less than a, the current connectivity ratio p1 is compared with the previous connectivity ratio p2, if p1 is greater than p2, the threshold k is reduced according to a set step size, the step of threshold filtering is returned to all quasi-edge pixel points in the image, otherwise, the last obtained edge pixel point is retained and output as the image edge detection result.
10. The image edge detection method according to any one of claims 1 to 9, wherein the step of finding all filtering quasi-edge pixel points satisfying connectivity requirements comprises:
finding out a plurality of connected regions from the filtering quasi-edge pixel points, wherein the filtering quasi-edge pixel points in each connected region meet continuous adjacency, the number of the filtering quasi-edge pixel points in the connected region is not less than B, the adjacency comprises row adjacency or column adjacency, and the filtering quasi-edge pixel points in the connected region are edge pixel points.
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