CN114972797B - Image invariant feature extraction method based on curve trace transformation - Google Patents
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Abstract
The invention relates to an image invariant feature extraction method based on curve trace transformation, and belongs to the field of image processing and computer vision. The method tracks images by using a new curve trace of curve trace transformation, maps functional results on the curve trace to a space generated by four parameters of angular velocity, amplitude, length and angle to obtain curve trace transformation results, and continuously performs functional integration on the results to obtain the quintuple curve trace space characteristics of the images. Different functions and different combinations of the same function are used on the curved trace to obtain different curved trace transformation characteristics, and the high-level semantic texture characteristics of the image can be represented in multiple dimensions. The method utilizes the texture features extracted by the curve trace transformation, keeps the RST invariance of the original trace transformation and the circular trace transformation features, can obtain deeper image texture information, and has better resolution capability for texture images containing any mixed curve, particularly periodic curve texture images.
Description
Technical Field
The invention relates to an image invariant feature extraction method based on curve trace transformation, and belongs to the field of image processing and computer vision.
Background
The image invariant feature can reflect the image essence, and when the image content is invariant, the external change of the image caused by illumination, angle, resolution, RST conversion and the like generally has stronger adaptability, and the feature quantity change amplitude is smaller or even invariant, so the invariant feature is widely applied to image analysis. Radon transformation based on geometric transformation and a generalization analysis method thereof are important branches of an invariant feature analysis method, wherein the Radon transformation transforms an image into an area projected according to an angle, performs integral projection on an image matrix at multiple angles, and performs statistical analysis on obtained data to extract features with image geometric invariance. Trace transform (Trace transform) is a generalization of Radon transform, proposed by Kadyrov and Petrou, and simultaneously proposed a triple invariant feature extraction method based on Trace transform, which can obtain the RST invariant feature of an image, has important application value in the field of invariant image analysis, and has been widely applied to various image analyses, such as texture classification, image retrieval, identity authentication, character recognition, human body action recognition, scene classification, medical image analysis, seismic exploration, and the like.
At present, a plurality of trace transformation related research results exist, theoretical research mainly comprises the steps of optimal combination of functional, design of new functional, analysis of invariance and sensitivity of function to RST transformation and the like, and the research focus is mainly put on the functional acting on the image; there are also many researchers applying trace transformation to engineering practice, and the emphasis is still to select a suitable functional for a particular problem. While the Trace is studied to fit the Image texture to a greater extent, it is not clear from the related literature, and there are only 2 research results about a method for extracting Circular Trace transformation and Its invariant Features in 2018, which has better description performance for Circular arc geometric textures, and is an Image supplementary characterization method for the Trace transformation, which is described in references [ Circular Trace transformation and Image texture analysis [ J ] electronics, 2018,46 (10): 2351-2358 ], cyclic Trace transformation and Its PCA-Based Fusion Features for Image reproduction, iet Image Process,2018,12 (10): 1797-1806 ], but still lacks the related research about Its invariant feature extraction method for images containing complex textures, especially periodic mixed curve textures.
Disclosure of Invention
In order to obtain an invariant feature which is more sensitive to a mixed curve texture image, the invention provides an image invariant feature extraction method based on curve trace transformation, so as to obtain an invariant texture feature with higher identification capability on an image containing mixed curve textures, particularly periodic curve textures.
In order to achieve the purpose, the invention adopts the following technical scheme.
An image invariant feature extraction method based on curve trace transformation comprises the following steps:
1) Quantizing the gray level of the original image to obtain an image F, mapping the quantized gray image F to a curved trace space Cv (phi, rho, a, omega, s), and enabling a point on the curved trace space to correspond to a unique point on the image F; phi is an included angle between a connecting line of two points of a central point Q and an origin of coordinates O of the curve and an x axis, rho is a distance between the central point Q and the origin of coordinates O of the curve, a is the amplitude of the curve, omega is the angular velocity of the curve, and s is a variable defined on a curve trace with a starting point at Q;
2) Removing the parameter s through the action of the curved line functional R to obtain a double characteristic, and obtaining four-dimensional characteristic data;
3) Removing the parameter omega through the action of an angular velocity functional W on the basis of the four-dimensional feature data obtained in the step 2) to obtain a double feature, and obtaining three-dimensional feature data;
4) Removing the parameter a through an amplitude functional A function on the basis of the three-dimensional characteristic data obtained in the step 3) to obtain triple characteristics, and obtaining a two-dimensional characteristic matrix;
5) Removing the parameter rho through the diameter functional P function on the basis of the two-dimensional feature matrix obtained in the step 4) to obtain quadruple features, and obtaining a one-dimensional feature vector;
6) Removing the parameter phi through the action of a circumferential functional phi on the basis of the one-dimensional feature vector obtained in the step 5) to obtain quintuple features, and obtaining a scalar, namely a real number; obtaining a final image characteristic through the functional combination effect of the steps 2) to 6);
7) And (5) repeating the steps from the step 2) to the step 6), and selecting proper different R, W, A, P and phi functional combinations to obtain different multi-dimensional curved trace transformation texture characteristics of the image.
Wherein, the space Cv (phi, rho, a, omega, s) of the curved trace in the step 1) adopts a regular sine curve, and the general expression of the sine curve is as follows
As shown in FIGS. 2 and 3, we can replace the initial phase ^ by changing the value of ρ, φ>
And variation of the offset k, as shown in fig. 2, the offset Δ k = ρ 'sin Φ' - ρ sin Φ, the variation of the offset k only affecting the up-and-down movement position variation of the sinusoid. As shown in FIG. 3, incipient phase +>
The change of (1) directly reflects the left-right movement change of the image of the sine curve on the coordinate system, and under the condition that rho is not changed, the change of phi can be used for expressing the initial phase/the position of the corresponding vessel>
Change wherein>
Initial phase->
The value of (b) simply represents the left and right position of the sinusoid in the coordinate system, and the initial phase(s) may be replaced by changing the value of phi without changing p>
A change in (c).
In summary, a general expression for defining a sinusoidal curve in a generalized manner is y = a · sin (ω x), where angular velocity ω and amplitude a of the curve, a distance ρ between a center point Q of the curve and a coordinate origin O, and an angle Φ between a connecting line of the two points Q and O and an x-axis are four parameters, which can determine a curve trace, and defining a parameter s on the curve trace, an image F is mapped to a five-dimensional space Cv (Φ, ρ, a, ω, s), and Cv is named as a curve trace space.
Each point in the curved trace space Cv corresponds to a unique point on the image F, and each image uniquely corresponds to one curved trace space projection data;
assuming that a point (phi, rho, a, omega, s) in the curved trace space Cv corresponds to a point (x, y) on the image F, the transformation relationship between them is as follows
Where ω is the angular velocity of the sinusoidal curve, a is the amplitude of the curve, ρ is the distance between the center point Q of the curve and the origin of coordinates O, φ is the angle between the line connecting the two points Q and O and the x-axis, and s is a variable defining the starting point on the curve at Q.
Further, the functional R in step 2), the functional W in step 3), the functional a in step 4), the functional P in step 5), and the functional Φ in step 6) are any mathematical operation function as a functional, that is, may be one or more of the amplitude and phase of the product, derivative, extremum, and harmonic.
Further, the functional R in step 2), the functional W in step 3), the functional a in step 4), the functional P in step 5), and the functional Φ in step 6) are other feature extraction methods as functional, that is, may be one or more of fourier transform, wavelet transform, local Binary Pattern (LBP), and gray level co-occurrence matrix (GLCM).
Further, the quintuple characteristics in the step 6) are calculated by the following functional formula:
Π(F)＝Φ(P(A(W(R(F(φ,ρ,a,ω,s))))))(2)
wherein F represents an image, F (phi, rho, a, omega, s) represents a projection of the image on a parametric system of the curvilinear trajectory transformation, and R, W, A, P, phi represent functionals defined on the parameters s, omega, a, rho, phi, respectively.
Further, the suitable functional in step 7) means that the selected functional has rotation, translation, scaling invariance or sensitivity, and can extract invariant features of the image.
The invention has the following beneficial effects:
1) Selecting proper functional or adjusting and transforming curve trace space projection data, extracting deeper image feature information by using curve trace transduction, wherein the extracted features have geometric invariance and can be applied to image identification, image classification and segmentation and the like.
2) An appropriate R functional is selected on a curve trace, any function curve can be decomposed into a group of different sine function curves according to a general approximation theorem, and any curve, especially a periodic curve, in an original image can form an extreme value in a curve trace space projection characteristic, so that the curve characteristic of the image can be extracted by a curve trace space projection method, and the image texture characteristic extracted by curve trace transformation has better discrimination capability for images containing different mixed curve textures, especially periodic curve textures.
Drawings
FIG. 1 is a flow chart of the image invariant feature extraction method based on the curved trace transformation of the present invention.
Fig. 2 is a graph showing the variation of the sinusoidal offset k.
FIG. 3 is a sine curve initial phase
A change map of (c).
FIG. 4 is a diagram illustrating the definition of curve trace transformation parameters.
FIG. 5 is a graph of classification results of curve trace transformation CvTT for 20 different classes of images randomly selected 100 times in the Coil-20-proc image library.
Fig. 6 is a graph of the classification result of curve trace transformation CvTT after 100 samples are randomly selected from 144 image libraries containing periodic mixed textures.
FIG. 7 is an example image in the Coil-20-proc image library.
FIG. 8 is an example image in a periodic blend curve texture image library.
Detailed Description
In order that the above objects, features and advantages of the present invention can be more clearly understood, a more particular description of the invention, taken in conjunction with the accompanying drawings and detailed description, is set forth below. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, however, the present invention may be practiced in other ways than those specifically described herein, and thus the present invention is not limited to the specific embodiments disclosed below.
The curve trace transformation and image invariant texture feature extraction process of the invention is shown in fig. 1, and the method comprises the following steps:
step 1): quantizing the gray level of an original image, setting the gray level as G, and the size of the original image as mxn, and converting the quantized gray level of the original image into a gray two-dimensional matrix, which is marked as F;
step 2): mapping the image F to a curved trace space Cv (phi, rho, a, omega, s), wherein a point on the curved trace space corresponds to a unique point on the image F;
step 3): removing the parameter s through the action of the curved line functional R to obtain a double characteristic, and obtaining four-dimensional characteristic data;
step 4): removing the parameter omega through the action of an angular velocity functional W on the basis of the four-dimensional feature data obtained in the step 3) to obtain a double feature, and obtaining three-dimensional feature data;
and step 5): removing the parameter a through an amplitude functional A function on the basis of the three-dimensional characteristic data obtained in the step 4) to obtain triple characteristics, and obtaining a two-dimensional characteristic matrix;
step 6): removing the parameter rho by the diameter functional P action on the basis of the two-dimensional feature matrix obtained in the step 5) to obtain quadruple features, and obtaining a one-dimensional feature vector;
step 7): removing the parameter phi through the action of a circumferential functional phi on the basis of the one-dimensional feature vector obtained in the step 6) to obtain quintuple features, and obtaining a scalar; obtaining a final image characteristic through the functional combination of the five steps;
step 8): and (5) repeating the step 2) to the step 7), selecting proper different R, W, A, P and phi functional combinations, and obtaining different multi-dimensional curve trace transformation texture characteristics of the image.
Wherein, the curved trace space Cv (phi, rho, a, omega, s) in the step 2), the parameter definition of the curve trace transformation is detailed as shown in fig. 2, 3 and 4, as shown in fig. 4, wherein the angular velocity omega, the amplitude a of the curve, the distance rho between the central point Q of the curve and the coordinate origin O, the included angle phi between the connecting line of the two points Q and O and the x-axis can determine a curve trace, and the parameter s is defined on the curved trace, then the image F is mapped to a five-dimensional space Cv (phi, rho, a, omega, s), and Cv is named as the curved trace space. The point on the curved trace space corresponds to a unique point on the image F, and each image uniquely corresponds to one curved trace space projection data. Assuming that a point (phi, rho, a, omega, s) in the curved trace space Cv corresponds to a point (x, y) on the image F, the transformation relationship between them is as follows
Where ω is the angular velocity of the sinusoidal curve, a is the amplitude of the curve, ρ is the distance between the center of the curve Q and the origin O, φ is the angle between the line connecting the two points Q and O and the x-axis, and s is a variable defining the starting point on the curve at Q. Sampling s on a curve trace, wherein the pixel coordinate is the position of a pixel in an image, sampling points are sampled according to the distribution rule of points on a sine curve, and fixed-point equidistant sampling is carried out on the position relation of the sampling points in the image according to the functional relation of the sine curve coordinate points. Setting the gray level as G and the size of the original image in the step 1)M × n, the gray level of the original image is quantized to become a gray two-dimensional matrix, which is denoted as F. For F (m, n), assume that the pixel coordinate of the sample point is(s) x ，s y ) The coordinates of the first sampling point are (m/2, 0), the abscissa of the sampling point is changed at equal intervals, and if the number of sampling points d =64 and step = m/d, s can be derived from the mapping relation x ＝n/2-round(a·sin(ω·m/d)，s y ＝a。
The functional R in the step 3), the functional W in the step 4), the functional A in the step 5), the functional P in the step 6) and the functional phi in the step 7) can be any mathematical operation function as a functional or other feature extraction methods as a functional. Any mathematical function can be an integral, a derivative, an extremum, an amplitude value and a phase of harmonic waves and the like, other feature extraction methods can be Fourier transform, wavelet transform, local Binary Pattern (LBP), gray level co-occurrence matrix (GLCM) and the like, and features reflecting different properties of the image can be obtained by adopting different functional combinations.
Wherein, the quintuple characteristics in the step 7) are calculated by the following functional formula:
∏(F)＝Φ(P(A(W(R(F(φ,ρ,a,ω,s)))))) (2)
wherein F represents an image, F (phi, rho, a, omega, s) represents a projection of the image on a parametric system of the curved trace transform, and R, W, A, P, phi represent functional functions defined on the parameters s, omega, a, rho, phi, respectively.
Wherein, the suitable different R, W, a, P, Φ functionals of step 8) generally means that the selected functionals have rotation, translation, scaling invariance or sensitivity suitable to extract invariant features. Table 1 lists the commonly used invariant functions IF and sensitive functions SF that produce invariant features, where ξ(s) represent the image function value along the curve trace.
TABLE 1 commonly used invariant and sensitive functionals that produce invariant features
Examples
FIG. 1 is a flowchart illustrating a method of extracting invariant texture features of an image using a curvelet Transform (CvTT) method. To evaluate the discrimination ability of the features obtained by this method against images, example simulation experiments were performed using the Coil-20-proc image library and an image library containing 144 periodic curve textures. Comprises the following steps.
Step 1: the images in the Coil-20-proc image library used in the examples and the images obtained by the crawler were both 128 × 128 gray scale images with a gray scale level of 256, and the gray scale image is denoted as F.
And 2, step: the gray scale image F is mapped to a curved trace space Cv (phi, rho, a, omega, s) where a point corresponds to a unique point on the image F.
And 3, step 3: and removing the parameter s through the action of the curved trace functional R to obtain a double characteristic, and obtaining four-dimensional characteristic data. After the functional R action removes the parameter s, the functional R action can be restored to a four-dimensional trace space, and points on the trace represent the numerical value of a curve trace functional R. The R functional used in this embodiment is ^ ξ(s) ds, where ξ(s) is the image gray scale value on the curved trace represented by parameter s, i.e., the sum of all pixel values on the curved trace is proportional to the degree to which the texture conforms to the curved shape, and an extremum is generated if the image contains texture conforming to the sinusoidal shape.
And 4, step 4: and 3) removing the parameter omega through an angular velocity functional W action on the basis of the four-dimensional characteristic data obtained in the step 3) to obtain a double characteristic, and obtaining three-dimensional characteristic data, wherein the parameter omega is removed through the functional W action, and then the three-dimensional characteristic data can be restored to a three-dimensional track space of the traditional track transformation. The present example used 3 functionals W in total, as shown in table 2, where g (W) represents the value of the functional R of the corresponding trace. This step enables 3 three-dimensional feature data to be obtained.
Table 2 functional W used in the present embodiment
And 5: and (4) removing the parameter a by using an amplitude functional A (the original trace functional R is cited in the embodiment) on the basis of the three-dimensional characteristic data obtained in the step (4) to obtain a triple characteristic, and obtaining a two-dimensional characteristic matrix. A total of 8 functional functions A were used in this example, as shown in Table 3, where f (a) is the function value on the trace, t k Points on the trace, f (t) k ) Is the functional value of the angular velocity functional W of the previous step,
mean is a median function, R + Indicating the integral over positive values of the integral variable. This step enables 1 × 3 × 8=24 two-dimensional feature matrices to be obtained.
TABLE 3 functional A used in the present example
Step 6: and (5) removing the parameter rho by the diameter functional P action on the basis of the two-dimensional feature matrix obtained in the step (5) to obtain quadruple features, and obtaining a one-dimensional feature vector. The present embodiment uses 3 functionals P, as shown in table 4, where g (P) represents the value of the functional a of the corresponding trace. This step can obtain 3 × 8 × 3=72 eigenvectors.
Table 4 functional P used in this example
And 7: and (4) removing the parameter phi through the action of the circumferential functional phi on the basis of the feature vector obtained in the step (6) to obtain quintuple features, and obtaining a scalar, namely a real number. The number of functionals Φ used in this example was 7, as shown in table 5. Obtaining the image invariant texture features with the total dimension of 1 × 3 × 8 × 3 × 7=504 dimension through different functional combination functions of five steps (step 3 to step 7), wherein N is the number of elements of the feature vector obtained in step 6, and x is the number of elements of the feature vector obtained in step 6 i Is the ith value of the circumferential functional Φ. In this step, 3 × 8 × 3 × 7=504 characteristic values can be obtained, i.e., a curved trace transformation pattern of 504 dimensions of the image is obtainedAnd (4) physical characteristics.
TABLE 5 functional Φ used in this example
And 8: and calculating the invariant characteristics of 504-dimensional curve trace transformation of all the images, and performing classification experiments by using a Support Vector Machine (SVM).
1) CvTT classification experiment on Coil-20-proc image library
The library of Coil-20-proc images includes 20 types of images, 1440 images in each type, each image is a PNG format image with size of 128 × 128, images in a group are images rotated every 5 ° for the same object, and classification and identification are performed on the 20 types of images in the library, and fig. 5 shows the result of the average classification accuracy of 100 times of randomly selecting samples from the 20 types of images when the number of samples is respectively 5, 9, 18, 27, 36 and 64. FIG. 7 is an example image in the Coil-20-proc image library.
2) Classification experiment on texture image containing periodic mixed curve
3 types (48 images in each type, 144 images in each type, each image in the JPG format with the size of 128 x 128, and images in the group are rotated images every 30 degrees for 4 different images) of images (such as sea level, cloud sea and desert) containing periodic mixed curve textures are selected, the 144 images in the 3 types are classified and identified, and fig. 6 shows the average classification accuracy result of randomly selecting 100 times of samples when the number of the samples is 12, 18, 24, 30, 36 and 42 respectively. FIG. 8 is an example image in a periodic blend curve texture image library.
The above description is only of the preferred embodiments of the present invention, and it should be noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the invention, and such modifications and adaptations are intended to be within the scope of the invention.
Claims (5)
1. An image invariant feature extraction method based on curve trace transformation is characterized by comprising the following steps:
1) Quantizing the gray level of an original image, mapping a quantized gray image F to a curved trace space Cv (phi, rho, a, omega, s), wherein the curved trace space Cv (phi, rho, a, omega, s) adopts a regular sine curve, a curve trace can be determined by four parameters of an angle velocity omega, an amplitude a of the curve, an included angle phi between a connecting line of a central point Q of the curve and a distance rho, Q and O of a coordinate origin O and an x axis, a parameter s is defined on the curved trace, and then mapping the image F to a five-dimensional space Cv (phi, rho, a, omega, s) which is named as a curved trace space, and a point on the curved trace space corresponds to a unique point on the image F; each point in the curved trace space Cv corresponds to a unique point on the image F, and each image uniquely corresponds to one curved trace space projection data;
assuming that a point (phi, rho, a, omega, s) in the curved trace space Cv corresponds to a point (x, y) on the image F, the transformation relationship between them is as follows
Wherein omega is the angular velocity of the sine curve, a is the amplitude of the curve, rho is the distance between the center Q of the curve and the original point O, phi is the included angle between the connecting line of the two points Q and O and the x axis, and s is a variable which is defined on the curve trace and the starting point of which is positioned at Q;
2) Removing the parameter s through the action of a curved line functional R to obtain a heavy characteristic and obtain four-dimensional characteristic data;
3) Removing parameter omega through an angular velocity functional W function on the basis of the four-dimensional feature data obtained in the step 2) to obtain a double feature, and obtaining three-dimensional feature data;
4) Removing the parameter a through an amplitude functional A function on the basis of the three-dimensional characteristic data obtained in the step 3) to obtain triple characteristics, and obtaining a two-dimensional characteristic matrix;
5) Removing the parameter rho through the diameter functional P function on the basis of the two-dimensional feature matrix obtained in the step 4) to obtain quadruple features, and obtaining a one-dimensional feature vector;
6) Removing the parameter phi through the action of a circumferential functional phi on the basis of the one-dimensional feature vector obtained in the step 5) to obtain quintuple features, and obtaining a scalar, namely a real number; obtaining a final image characteristic through the functional combination effect of the steps 2) to 6);
7) And (5) repeating the step 2) to the step 6), selecting different R, W, A, P and phi functional combinations, and obtaining different multi-dimensional curve trace transformation texture characteristics of the image.
2. The method for extracting image invariant features based on curvilinear trajectory transformation according to claim 1, wherein step 2) said functional R, step 3) said functional W, step 4) said functional a, step 5) said functional P, step 6) said functional Φ are all any mathematical operation function as a functional; may be one or more of integrating, differentiating, extreming, and amplitude and phase of harmonics.
3. The method for extracting image invariant features based on curvilinear trace transformation according to claim 1, wherein step 2) said functional R, step 3) said functional W, step 4) said functional A, step 5) said functional P, step 6) said functional phi are other feature extraction methods as functional; may be one or more of fourier transform, wavelet transform, local binary pattern, gray level co-occurrence matrix.
4. The method for extracting image invariant features based on curved trace transformation as claimed in claim 1, wherein said quintuple features of step 6) are calculated by the following functional formula:
П(F)＝Φ(P(A(W(R(F(φ,ρ,a,ω,s))))))(2)
where F represents the image, F (φ, ρ, a, ω, s) represents the projection of the image on the parametric system of the curvilinear trace transform, and R, W, A, P, φ represent the functional defined on the parameters s, ω, a, ρ, φ, respectively.
5. The method for extracting image invariant features based on curved trace transformation as claimed in claim 1, wherein the functional from step 2) to step 7) has rotation, translation, scaling invariance or sensitivity, and can extract invariant features of the image.
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