CN114119666A - Irregular frame target tracking system and method adopting polar coordinate transformation method - Google Patents

Irregular frame target tracking system and method adopting polar coordinate transformation method Download PDF

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CN114119666A
CN114119666A CN202111422525.0A CN202111422525A CN114119666A CN 114119666 A CN114119666 A CN 114119666A CN 202111422525 A CN202111422525 A CN 202111422525A CN 114119666 A CN114119666 A CN 114119666A
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伍雪冬
曹百亨
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Abstract

The invention discloses an irregular frame target tracking system and method adopting a polar coordinate transformation method, which are combined with a related filtering method to realize generation of an irregular target frame estimation result. Cutting the image according to the tracking target, and performing feature extraction and cosine window windowing; then, filtering by using a continuous correlation filter, and calculating by a Newton method to obtain an estimated target center point coordinate; generating four-corner point coordinates of a tracking target, and sampling a quadrilateral area formed by the generated four-corner point coordinates; and resampling the four corner point coordinates after the amplification and generating a continuous correlation filter and a scale and angle filter. The method based on continuous correlation filtering improves the defects of model degradation, boundary effect, response distortion and the like caused by the assumption that pixels of different feature extraction results are uniformly distributed in other correlation filtering methods, and improves the accuracy and robustness of the target tracking algorithm.

Description

Irregular frame target tracking system and method adopting polar coordinate transformation method
Technical Field
The invention relates to the design problem of a single target tracking algorithm under monocular vision, in particular to an irregular frame target tracking system and method adopting a polar coordinate transformation method.
Background
Visual Object Tracking (Visual Object Tracking) is a challenging problem in the field of computer vision. The purpose of visual target tracking is to identify a tracking target from a continuous video sequence and extract a target position, so as to obtain a motion track of the target. Since target tracking involves recognition and optimization problems, target identification requires the application of optimization methods and control techniques. The main problems involved in target tracking include: (1) establishing a model, wherein the model refers to an appearance model of a tracking target, and the part determines the tracking effect of the target to a great extent; (2) an image input, wherein the image comprises a group of element view inputs, the view provides a scene comprising an object and a constraint between input image characteristics, and the part mainly relates to the sampling of the image, the extraction of the characteristics and the definition of the frame range of the object; (3) and detecting the target, namely utilizing a filter model to search and input to track the position of the target in the image.
Through decades of research and development, computer-based target detection and tracking have been applied to video surveillance, autopilot, unmanned aerial vehicles, human-computer interaction, medical inspection, robotics, autonomous navigation, industrial inspection and assembly, and some occasions where accurate measurements are required. In addition, the target tracking technology is also applied to the fields of video-based motion analysis and synthesis, identification based on motion information, image retrieval, hydrological observation, port management, medical image analysis, remote measurement, part quality detection and the like.
In the actual tracking algorithm development process, many problems still exist, such as: 1) tracking drift problems. Due to the complex application scene of target tracking, noise with different ranges is always introduced into the target appearance model in the training process, and the tracking drift problem is caused by the accumulation of the noise; 2) aspect ratio problems. The traditional target tracking algorithm is based on the selection of a fixed aspect ratio and a scale pool aiming at the description of target scale change, so that the predicted target scale information influences the tracking precision and causes the loss of a tracked target. In view of the above, research into further development of object tracking technology is still of great value to scientific research in the fields of computer vision and pattern recognition.
In addition, the most similar comparison documents to the present invention are: jizhang, Ningwang, full convolution twin network target tracking algorithm with rotation and scale estimation [ J ] computer application 2021,41(9):7. The main defects of the prior art are as follows: (1) in the prior art, a twin convolutional neural network method is adopted to construct a target tracking algorithm framework, but due to the intervention of a deep learning method, the calculation amount of the algorithm is increased, a large amount of off-line training is needed to ensure the accuracy of the algorithm, and the calculation speed of on-line tracking is only 15 frames per second and is far lower than the real-time requirement of 30 frames per second; (2) the twin network adopted in the prior art is a typical deep learning based approach. Due to the characteristics of deep learning, the ductility of the method is low, and the method cannot be combined with some traditional methods which can obviously reduce the calculation amount and improve the prediction accuracy, so that the precision and the real-time performance of the algorithm are reduced, and a good improvement method is provided; (3) the scale and angle prediction method in the prior art is stopped at single-corner point prediction, and a quadrilateral frame with a fixed frame aspect ratio is adopted for rotation and scale prediction of a tracking target, so that frames generated by an algorithm are all rectangular or parallelogram, and in an actual tracking scene, irregular quadrilaterals are more, so that the accuracy and robustness of the algorithm are limited by the assumption of the fixed frame aspect ratio of the single-corner point prediction method, and the accuracy cannot be improved in a breakthrough manner.
Disclosure of Invention
The purpose of the invention is as follows: the invention provides an irregular frame target tracking system and method adopting a polar coordinate transformation method aiming at the aspect ratio problem, wherein an augmented four-corner joint prediction method is utilized to obtain a high-confidence irregular frame, a continuous filtering frame is combined, and an algorithm is improved aiming at the tracking drift problem by a method of training a layered filter, so that tracking target information returned by the algorithm has high confidence level, and the accuracy of a tracking result is improved.
The technical scheme is as follows: in order to achieve the purpose, the invention specifically adopts the following technical scheme:
the invention provides an irregular frame target tracking system adopting a polar coordinate transformation method, which comprises the following steps: an initial image sampling module for initializing parameters in the continuous correlation filtering algorithm and tracking the given position of the target, namely the target center point coordinate (x) in the first framec,yc) Cutting and sampling the image under the Cartesian coordinate system to obtain a sample image block x1(ii) a A cosine window windowing module for sampling image block x1Extracting features, and then performing series connection and cosine window windowing on the extracted features to obtain an image sample z'; the continuous correlation filtering module is used for obtaining a characteristic spectrum Z ' by carrying out fast Fourier transform on the characteristic Z ' of the image sample, then carrying out filtering processing on the characteristic spectrum Z ' by using a continuous correlation filter h to obtain a continuous filtering response spectrum r, and then calculating the continuous filtering response spectrum r by using a Newton method to obtain an estimated target central point coordinate
Figure BDA0003377008630000021
An irregular border estimation module to estimate coordinates of a target center point by using the estimated coordinates
Figure BDA0003377008630000022
Generating four-corner coordinates of a tracking target, and sampling and preprocessing a quadrilateral region formed by the generated four-corner coordinates to obtain the coordinate values of the augmented four-corner points
Figure BDA0003377008630000023
A continuous correlation filter generation module for generating the four-corner coordinate values after being amplified
Figure BDA0003377008630000024
Resampling for continuous correlation filter generation to obtain resampled image samples
Figure BDA0003377008630000025
And using the resampled image samples
Figure BDA0003377008630000031
Generating a filter f to obtain a generated filter
Figure BDA0003377008630000032
A scale and angle filter generation module to generate a scale and angle filter by using the resampled image samples
Figure BDA0003377008630000033
To filter
Figure BDA0003377008630000034
Generating to obtain the generated scale and angle filter
Figure BDA0003377008630000035
A finishing module for processing the augmented four corner point coordinate values
Figure BDA0003377008630000036
Generated filter
Figure BDA0003377008630000037
And a generated scale and angle filter
Figure BDA0003377008630000038
Reserving and amplifying the four-corner coordinate value
Figure BDA0003377008630000039
Applied to the image of the next frame to obtain a new image block x of the cropped sampleiAnd the video sequence is carried into a cosine window windowing module for operation, and the operation from the cosine window windowing module to an ending module is executed in a circulating way on each next frame until the video sequence is ended.
Further, in the irregular border estimation module, preprocessing is performedThe reason is as follows: carrying out feature extraction and windowing on the sampled quadrilateral area to obtain a single angular point feature map Z' for scale prediction; carrying out four-corner point rotation on the single corner point feature map Z' to obtain an augmented four-corner point feature space
Figure BDA00033770086300000310
For the feature space of the four corner points after the enlargement
Figure BDA00033770086300000311
Continuous correlation filtering is carried out, and the coordinate value of the four corner points after being amplified is obtained through the coordinate value S' of the amplification
Figure BDA00033770086300000312
Further, in the continuous correlation filter generation module, the coordinate values of the four corner points after the amplification are used
Figure BDA00033770086300000313
Resampling for successive correlation filter generation to obtain a correlation signal having w ═ wg+wh+wnWindowed resampled image samples for layer features
Figure BDA00033770086300000314
Wherein wgFor the number of Gray feature layers, whNumber of layers for HOG feature, wnThe number of CN characteristic layers is shown, and w is the number of synthetic characteristic layers;
the generation expression of the filter f obtained according to the continuous correlation filtering theory is
Figure BDA00033770086300000315
Wherein, WHIs a conjugate transpose of the weight matrix W of the filter f, AHIs a conjugate inversion matrix of A matrix, the expression of A matrix is
Figure BDA00033770086300000316
Gamma is opposite angleA line weight matrix of the expression
Figure BDA00033770086300000317
Gaussian type mark matrix
Figure BDA00033770086300000318
Is expressed as
Figure BDA00033770086300000319
Resampling image samples
Figure BDA00033770086300000320
Substituting the formula to generate a filter f to obtain a generated filter
Figure BDA00033770086300000321
Furthermore, in the scale and angle filter generation module, a single angle point filter is obtained according to the continuous correlation filtering theory
Figure BDA00033770086300000322
Is expressed as
Figure BDA0003377008630000041
Therein, <' >-1Is a matrix dot product operation, which is the inverse operation of the matrix dot product operation, k represents the k-th feature channel,
Figure BDA0003377008630000042
is a linear combination of the frames preceding the current frame,
Figure BDA0003377008630000043
is composed of
Figure BDA0003377008630000044
A result matrix after Fourier transformation, and
Figure BDA0003377008630000045
is composed of
Figure BDA0003377008630000046
The conjugate matrix of (a) is determined,
Figure BDA0003377008630000047
is the result of x after polar transformation, and
Figure BDA0003377008630000048
is composed of
Figure BDA0003377008630000049
The result matrix after feature extraction, | · | is that each element in the matrix is respectively solved for its modulus;
four corner points are enlarged to obtain
Figure BDA00033770086300000410
Wherein k represents the kth characteristic channel, and upsilon is enlarged through four corner points
Figure BDA00033770086300000411
Resampling image samples
Figure BDA00033770086300000412
Substituting the above formula for the filter
Figure BDA00033770086300000413
Generating to obtain the generated scale and angle filter
Figure BDA00033770086300000414
Furthermore, in the cosine window windowing module, the sample image block x is processed1Performing a feature extraction operation, the extracted features sequentially comprising: gray, HOG and CN; obtaining characteristics according to the characteristics GrayAtlas zgObtaining a characteristic map z according to the characteristic HOGhObtaining a characteristic map z according to the characteristic CNnWherein
Figure BDA00033770086300000415
wi(i∈[g,h,n]) Is a characteristic spectrum ziThe number of feature channels of (a); connecting the features Gray, the HOG and the CN in series according to the dimension of the number of the feature channels to obtain an image sample
Figure BDA00033770086300000416
Wherein w ═ wg+wh+wn，wgFor the number of Gray feature layers, whNumber of layers for HOG feature, wnThe number of CN characteristic layers is shown, and w is the number of synthetic characteristic layers; point-by-point two-dimensional cosine window cos for image sample zwindowThe window operation is expressed as z ═ z-windowThe as is a matrix dot product operation,
Figure BDA00033770086300000417
and z' is a feature spectrum, cos, windowed with a cosine windowwindowIs obtained by a function form of the cosine window, and the expression is
coswindow＝h(m)h(n)′
Wherein m and n are respectively the length and width of the frame of the tracked target, and h (m) and h (n) are both one-dimensional cosine window generating functions h (N), and the expression is
Figure BDA00033770086300000418
The period of the cosine window function is 2 pi/N, with N-m or N-N.
In addition, the invention provides an irregular frame target tracking method adopting a polar coordinate transformation method, which comprises the following steps: step 1, initializing parameters in a continuous correlation filtering algorithm, and tracking a given position of a target, namely a target central point coordinate (x) according to a first framec,yc) Cutting and sampling the images under the Cartesian coordinate system to obtain samplesThe image block x1(ii) a Step 2, sample image block x1Extracting features, and then performing series connection and cosine window windowing on the extracted features to obtain an image sample z'; step 3, the characteristic Z ' of the image sample is subjected to fast Fourier transform to obtain a characteristic spectrum Z ', the characteristic spectrum Z ' is subjected to filtering processing by using a continuous correlation filter h to obtain a continuous filtering response spectrum r, and the continuous filtering response spectrum r is calculated by a Newton method to obtain an estimated target central point coordinate
Figure BDA0003377008630000051
Step 4, by using the estimated coordinates of the target center point
Figure BDA0003377008630000052
Generating four-corner point coordinates of a tracking target, and sampling and preprocessing a quadrilateral region formed by the generated four-corner point coordinates to obtain the augmented four-corner point coordinates
Figure BDA0003377008630000053
Step 5, the four-corner coordinate value after being augmented is processed
Figure BDA0003377008630000054
Resampling for continuous correlation filter generation to obtain resampled image samples
Figure BDA0003377008630000055
And using the resampled image samples
Figure BDA0003377008630000056
Generating a filter f to obtain a generated filter
Figure BDA0003377008630000057
Step 6, using the resampled image sample
Figure BDA0003377008630000058
To filter
Figure BDA0003377008630000059
Generating to obtain the generated scale and angle filter
Figure BDA00033770086300000510
Step 7, the coordinate values of the four corner points after being augmented are processed
Figure BDA00033770086300000511
Generated filter
Figure BDA00033770086300000512
And a generated scale and angle filter
Figure BDA00033770086300000513
Reserving and amplifying the coordinate values of the four corner points
Figure BDA00033770086300000520
Applied to the image of the next frame to obtain a new image block x of the cropped sampleiAnd carrying out operation in the step 2, and circularly performing the operation from the step 2 to the step 7 for the next frames until the video sequence is finished.
Further, in step 4, the pretreatment is: carrying out feature extraction and windowing on the sampled quadrilateral area to obtain a single angular point feature map Z' for scale prediction; performing four-corner point rotation on the single corner point feature map Z' to obtain an augmented four-corner point feature space
Figure BDA00033770086300000514
For the feature space of the four corner points after the enlargement
Figure BDA00033770086300000515
Carrying out continuous correlation filtering, and obtaining the coordinate values of the four corner points after being amplified through the coordinate value S' after being amplified
Figure BDA00033770086300000516
Further, in the above-mentioned case,in step 5, the augmented four corner point coordinate values are used
Figure BDA00033770086300000517
Resampling for successive correlation filter generation to obtain a correlation signal having w ═ wg+wh+wnWindowed resampled image samples for layer features
Figure BDA00033770086300000518
Wherein wgFor the number of Gray feature layers, whNumber of layers for HOG feature, wnThe number of CN characteristic layers is shown, and w is the number of synthetic characteristic layers;
the generation expression of the filter f obtained according to the continuous correlation filtering theory is
Figure BDA00033770086300000519
Wherein, WHIs a conjugate transpose of the weight matrix W of the filter f, AHIs a conjugate inversion matrix of A matrix, the expression of A matrix is
Figure BDA0003377008630000061
Gamma is a diagonal weight matrix with the expression of
Figure BDA0003377008630000062
Gaussian type mark matrix
Figure BDA0003377008630000063
Is expressed as
Figure BDA0003377008630000064
Resampling image samples
Figure BDA0003377008630000065
Substituting the formula to generate a filter f to obtain a generated filter
Figure BDA0003377008630000066
Further, in step 6, a single corner filter is obtained according to the continuous correlation filtering theory
Figure BDA0003377008630000067
Is expressed as
Figure BDA0003377008630000068
Therein, <' >-1Is a matrix dot product operation, which is the inverse operation of the matrix dot product operation, k represents the k-th feature channel,
Figure BDA0003377008630000069
is a linear combination of the frames preceding the current frame,
Figure BDA00033770086300000610
is composed of
Figure BDA00033770086300000611
A result matrix after Fourier transformation, and
Figure BDA00033770086300000612
is composed of
Figure BDA00033770086300000613
The conjugate matrix of (a) is determined,
Figure BDA00033770086300000614
is the result of x after polar transformation, and
Figure BDA00033770086300000615
is composed of
Figure BDA00033770086300000616
The result matrix after feature extraction, | · | is that each element in the matrix is respectively solved for its modulus;
four corner points are enlarged to obtain
Figure BDA00033770086300000617
Wherein k represents the kth characteristic channel, and upsilon is enlarged through four corner points
Figure BDA00033770086300000618
Resampling image samples
Figure BDA00033770086300000619
Substituting the above formula for the filter
Figure BDA00033770086300000620
Generating to obtain the generated scale and angle filter
Figure BDA00033770086300000621
Further, in step 2, the sample image block x1Performing a feature extraction operation, the extracted features sequentially comprising: gray, HOG and CN; obtaining a characteristic map z according to the characteristic GraygObtaining a characteristic map z according to the characteristic HOGhObtaining a characteristic map z according to the characteristic CNnWherein
Figure BDA00033770086300000622
Figure BDA00033770086300000623
wi(i∈[g,h,n]) Is a characteristic spectrum ziThe number of feature channels of (a); connecting the features Gray, the HOG and the CN in series according to the dimension of the number of the feature channels to obtain an image sample
Figure BDA00033770086300000624
Wherein w ═ wg+wh+wn，wgFor the number of Gray feature layers, whNumber of layers for HOG feature, wnIs the number of CN characteristic layers, w is the synthesis characteristicThe number of layers; point-by-point two-dimensional cosine window cos for image sample zwindowThe window operation is expressed as z ═ z-windowThe as is a matrix dot product operation,
Figure BDA00033770086300000625
and z' is a feature spectrum, cos, windowed with a cosine windowwindowIs obtained from the function form of cosine window, and the expression is
coswindow＝h(m)h(n)′
Wherein m and n are respectively the length and width of the frame of the tracked target, and h (m) and h (n) are both one-dimensional cosine window generating functions h (N), and the expression is
Figure BDA0003377008630000071
The period of the cosine window function is 2 pi/N, with N-m or N-N.
Has the advantages that:
(1) the single-corner-point scale and rotation prediction model used by the invention adopts logarithmic polar coordinate transformation, and solves the joint prediction problem of target rotation and scale transformation. Because the continuous correlation filtering framework can apply the Meisen theorem in the signalology, the calculation process can be simplified on the basis of ensuring the calculation precision;
(2) according to the method, a high-confidence irregular frame four-corner-point prediction model with a non-fixed aspect ratio is added to a single-corner-point-scale and rotation-based prediction model, so that the problem of the fixed aspect ratio of a related filtering algorithm is solved, and the overall prediction precision of the algorithm is improved;
(3) the invention adopts a target tracking algorithm framework based on continuous correlation filtering. Due to the application of the cyclic matrix and the frequency domain calculation, the frame reduces the calculation amount and can ensure the real-time performance of tracking.
The algorithm has robustness, accuracy and real-time performance, can withstand the challenges of practical application scenarios, and has practical applicability. The invention provides a new solution for the aspect ratio relation of the frame, can form a unique irregular quadrilateral prediction frame, can meet the frame precision requirement in practical application, has low requirement on hardware by an algorithm, and has economic application value.
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FIG. 1 is a flowchart of an irregular frame target tracking method using polar coordinate transformation according to the present invention.
Detailed Description
The following description and the accompanying drawings are included to explain embodiments of the present invention in detail.
Example one
The embodiment discloses an irregular frame target tracking system adopting a polar coordinate transformation method, which is shown in fig. 1. Adopt irregular frame target tracking system of polar coordinate transform method, include: an initial image sampling module for initializing parameters in the continuous correlation filtering algorithm and tracking the given position of the target, namely the target center point coordinate (x) in the first framec,yc) Cutting and sampling the image under the Cartesian coordinate system to obtain a sample image block x1(ii) a A cosine window windowing module for sampling image block x1Extracting features, and then performing series connection and cosine window windowing on the extracted features to obtain an image sample z'; the continuous correlation filtering module is used for obtaining a characteristic spectrum Z ' by fast Fourier transform of the image sample characteristic Z ', then filtering the characteristic spectrum Z ' by using a continuous correlation filter h to obtain a continuous filtering response spectrum r, and then calculating the continuous filtering response spectrum r by a Newton method to obtain an estimated target central point coordinate
Figure BDA0003377008630000081
An irregular border estimation module for estimating the coordinates of the center point of the object by using the estimated coordinates
Figure BDA0003377008630000082
Generating four-corner point coordinates of a tracking target, and sampling and preprocessing a quadrilateral area formed by the generated four-corner point coordinates to obtain the coordinate values of the four-corner points after the four-corner points are enlarged
Figure BDA0003377008630000083
A continuous correlation filter generation module for generating the four corner point coordinate values after the amplification
Figure BDA0003377008630000084
Resampling for continuous correlation filter generation to obtain resampled image samples
Figure BDA0003377008630000085
And using the resampled image samples
Figure BDA0003377008630000086
Generating a filter f to obtain a generated filter
Figure BDA0003377008630000087
A scale and angle filter generation module to generate a scale and angle filter by using the resampled image samples
Figure BDA0003377008630000088
To filter
Figure BDA0003377008630000089
Generating to obtain the generated scale and angle filter
Figure BDA00033770086300000810
A finishing module for processing the augmented four corner point coordinate values
Figure BDA00033770086300000811
Generated filter
Figure BDA00033770086300000812
And a generated scale and angle filter
Figure BDA00033770086300000813
Reserving and amplifying the coordinate values of the four corner points
Figure BDA00033770086300000814
Applied to the image of the next frame to obtain a new image block x of the cropped sampleiAnd the video sequence is carried into a cosine window windowing module for operation, and the operation from the cosine window windowing module to an ending module is executed in a circulating way on each next frame until the video sequence is ended.
In the initial image sampling module, the parameters of each part involved in the relevant filtering algorithm are initialized. From a given position of the tracked object in the first frame (object center point coordinates (x)c，yc) Length and width m, n) of object frame), cut out the sampling to the image under the cartesian coordinate system, the scope is four angular points: upper left corner point s1＝(xc+m/2,yc+ n/2), upper right corner point s2＝(xc-m/2,yc+ n/2), lower right corner point s3＝(xc-m/2,yc-n/2), lower left corner point s4＝(xc+m/2,yc-n/2) defining a quadrangular area. The set of coordinate points may be represented as: s ═ S1 s2 s3 s4]T. Cropped sample image block x1Will be used to train the correlation filter after superimposing the cosine window.
In the cosine window windowing module, the sample image block x1Performing a feature extraction operation, the extracted features comprising in order: gray, HOG and CN; obtaining a characteristic map z according to the characteristic GraygObtaining a characteristic map z according to the characteristic HOGhObtaining a characteristic map z according to the characteristic CNnWherein
Figure BDA00033770086300000815
wi(i∈[g,h,n]) Is a characteristic spectrum ziThe number of feature channels of (a); connecting the features Gray, the HOG and the CN in series according to the dimension of the number of the feature channels to obtain an image sample
Figure BDA00033770086300000816
Wherein w ═ wg+wh+wn，wgFor the number of Gray feature layers, whFor the HOG feature layerNumber, wnThe number of CN characteristic layers is, and w is the number of synthetic characteristic layers; point-by-point two-dimensional cosine window cos for image sample zwindowThe window operation is expressed as z ═ z-windowThe as is a matrix dot product operation,
Figure BDA0003377008630000091
and z' is a feature spectrum, cos, windowed with a cosine windowwindowIs obtained from the function form of cosine window, and the expression is
coswindow＝h(m)h(n)′
Wherein m and n are respectively the length and width of the frame of the tracked target, and h (m) and h (n) are both one-dimensional cosine window generating functions h (N), and the expression is
Figure BDA0003377008630000092
The period of the cosine window function is 2 pi/N, with N-m or N-N. The function distribution characteristic of the one-dimensional cosine window is that h (N) is 0 when i is 0, h (N) is 1 when i is N/4, h (N) is 2 when i is N/2, h (N) is 1 when i is 3N/2, and h (N) is 0 when i is N, i shows a tendency that the cosine equation increases monotonically first and then decreases monotonically. And a two-dimensional cosine window cos obtained by the outer product of two one-dimensional cosine windowswindowThe method has the characteristic that the closer to the center, the larger the pixel value is, and the pixel values of a circle around the boundary are all 0.
In the continuous correlation filtering module, the image sample characteristics Z ' are subjected to fast Fourier transform to obtain a characteristic map spectrum Z ', and then the characteristic map Z ' is subjected to filtering processing by using a continuous correlation filter h to obtain a continuous filtering response map spectrum r, wherein the formula is
Figure BDA0003377008630000093
Wherein the content of the first and second substances,
Figure BDA0003377008630000094
representing an analog Fourier transform (iFFT), < is a matrix dot product operation, and
Figure BDA0003377008630000095
then, calculating the continuous filtering response spectrum r by a Newton method to obtain the estimated coordinates of the target central point
Figure BDA0003377008630000096
In the irregular frame estimation module, the coordinates of the center point of the target to be estimated are obtained
Figure BDA0003377008630000097
Then, generating four-corner point coordinates, wherein the generated four-corner point coordinates are as follows: point on the upper left corner
Figure BDA0003377008630000098
Upper right corner point
Figure BDA0003377008630000099
Lower right corner point
Figure BDA00033770086300000910
Lower left corner point
Figure BDA00033770086300000911
The set of coordinate points may be represented as: s ═ S'1 s′2 s′3 s′4]T. And then sampling a quadrilateral area formed by the generated four-corner point coordinates, and performing feature extraction and windowing operation to obtain a single corner point feature map Z' for scale prediction. Performing four-corner point rotation on Z' to obtain an augmented four-corner point feature space
Figure BDA0003377008630000101
Wherein
Figure BDA0003377008630000102
Is a spatial orthogonal superposition operator, and has
Figure BDA0003377008630000103
For a single corner point correlation filter gsAlso carrying out amplification to obtain an amplified scale and angle estimation filter
Figure BDA0003377008630000104
Formula pair of augmented four-corner point feature space by applying four-corner point joint prediction model
Figure BDA0003377008630000105
Carrying out continuous correlation filtering, and obtaining the coordinate values of the four corner points after being amplified by applying the formula of the amplified coordinate values S
Figure BDA0003377008630000106
The formula of the four-corner point joint prediction model and the formula of the augmented coordinate value S' are obtained in the following mode:
let the image I be in N × N size in Cartesian coordinate system with its upper coordinate
Figure BDA0003377008630000107
Has a pixel value of
Figure BDA0003377008630000108
The origin of the coordinate system is the upper left corner of the image, the positive direction of the x axis is the positive right direction, and the positive direction of the y axis is the positive down direction. Where i is 1,2, …, N. According to the definition, the coordinates of the pixel points at the upper left corner of the image I are (1,1), and the coordinates of the pixel points at the lower right corner of the image I are (N, N).
The polar coordinate representation of the image I can be regarded as the coordinate in the Cartesian coordinate system
Figure BDA0003377008630000109
To the polar coordinate system, coordinate
Figure BDA00033770086300001010
Non-linear, non-uniform transformation of (a). The polar coordinate is transformed into SfThen there is
Figure BDA00033770086300001011
In order to keep the integrity of the angle change of the polar coordinate, namely, the positive and negative values are uniformly distributed, and the image can be uniformly divided, namely, the image is diffused outwards from the datum point, and the values of all parts are basically uniform. The central point (x) of the image I under the Cartesian coordinate systemc，yc) As a reference point for polar coordinate transformation.
Under a polar coordinate system, an arbitrary coordinate point (rho)i，θi) Middle mode length rhoiIs expressed as
Figure BDA00033770086300001012
Phase thetaiIs expressed as
Figure BDA00033770086300001013
Wherein r is a reference standard direction vector, and the positive direction of the polar coordinate system is the same as the positive direction of the Cartesian coordinate system.
Image I (x) after polar coordinate changei，yi) Is an image I' (ρ)i，θi). In a Cartesian coordinate system, the phase angle θiHas a more concise expression form as shown in the following
Figure BDA0003377008630000111
In addition, an image I in a Cartesian coordinate system is divided into0Proceeding with die length
Figure BDA0003377008630000112
And phase
Figure BDA0003377008630000113
And generating a changed image I1When, the following correspondence relationship is given
Figure BDA0003377008630000114
Correspondingly, the antipodal coordinate mark is
Figure BDA0003377008630000115
As shown in the two formulas, the change of the image scale and the rotation in the Cartesian coordinate system can be converted into the translational motion along the axis in the polar coordinate system, and based on the characteristic, the target scale and the rotation transformation in the target tracking can be more simply calculated and estimated.
Through polar coordinate system transformation, a prediction model of single-angle-point scale and angle transformation of the trapezoid tracking target frame under polar coordinates can be constructed. The response calculation to the correlation filtering in polar coordinates has
Figure BDA0003377008630000116
Wherein the content of the first and second substances,
Figure BDA0003377008630000117
according to the s ═ p, theta pair IiSampling polar coordinates, wherein s' is the coordinate of s in a polar coordinate system, and the conversion formula is
Figure BDA0003377008630000118
Wherein, H and W are respectively the image I sampled according to the tracking target frameiLength and width of (d); rho' is the module length of s after the polar coordinate system transformation; and theta' is the phase of s after the polar coordinate system transformation.
The Fourier domain calculation used by the classic DCF target tracking framework can also be used for calculation under polar coordinate transformation, and the specific response calculation formula is
Figure BDA0003377008630000119
Wherein the content of the first and second substances,
Figure BDA00033770086300001110
as a function of polar transformation, gsA model weight matrix is estimated for the scale and angle. According to the formula
Figure BDA00033770086300001111
The scale and angle estimation under polar coordinates does not need to be converted and sampled for calculation
Figure BDA00033770086300001112
According to the formula
Figure BDA00033770086300001113
Only the weight matrix g of the scale and angle estimation model needs to be determinedsThe filtering operation can be done directly.
Converting the image into a polar coordinate system, solving the problem of scale and angle transformation of the tracking target under a Cartesian coordinate system, and converting the problem into the problem of translation and rotation of the tracking target under an estimated polar coordinate; or to be understood as: and solving the coordinate change problem of the original image and the image after translation and rotation in the polar coordinate system, wherein the problem can be solved through a phase correlation algorithm in the field of pattern recognition.
According to the theory of the phase correlation algorithm, image I1The result after feature extraction is phi (I)1) Image I1The result after feature extraction is phi (I)2) Image I2Is an image I1The impulse function matrix G between the translated and rotated images can be calculated as
Figure BDA0003377008630000121
Wherein k represents the kth characteristic channel,
Figure BDA0003377008630000122
representing the frequency domain form of the variable, for the shock function matrix G after inverse Fourier transform(k)The values of elements designated by coordinates corresponding to translation and rotation of the function matrix are not 0, and the values of the other elements are 0. Obtaining translation and rotation values corresponding to the coordinates of the maximum value element by superposing the impact function matrixes G of all D characteristic channels, and further enabling the impact function matrixes G to be used for processing
Figure BDA0003377008630000123
Converting into Cartesian coordinate system to complete the scale and angle values of the tracked target, which can be expressed as
Figure RE-GDA0003462169100000124
Wherein the content of the first and second substances,
Figure RE-GDA0003462169100000125
for the inverse Fourier transform, max (H) is a function of the maximum value, and max (H) returns are the maximum values in the matrix H. find (H; ζ) is a search function defined as: and returning the position information of the element zeta in the matrix H, namely the row value and column value information of zeta in H. Here, the search function functions have the role of: at filter response matrix
Figure RE-GDA0003462169100000126
In search of response maximum
Figure RE-GDA0003462169100000127
The position information s', H and ζ in the response map are temporary variables that are set for convenient function interpretation, and have no other role in the algorithm.
Corresponding calculation formula according to related filtering algorithm
Figure BDA0003377008630000128
And formula
Figure BDA0003377008630000129
Can obtain the product
Figure BDA00033770086300001210
Wherein f issThe argument of which is the image sample x, is a function of the response value. And for single corner point correlation filter
Figure BDA00033770086300001211
Has the following calculation formula
Figure BDA00033770086300001212
Wherein the content of the first and second substances,
Figure BDA00033770086300001213
is a linear combination of frames preceding the current frame. And | is to calculate the modulus of each element in the matrix.
For the ith frame
Figure BDA00033770086300001214
Derived formula as follows
Figure BDA0003377008630000131
Wherein λ iswIs a linear combination
Figure BDA0003377008630000132
The learning rate parameter of (2) is,
Figure BDA0003377008630000133
is transformed into x by polar coordinates
Figure BDA0003377008630000134
And performing a result matrix after feature extraction.
Bonding of
Figure BDA0003377008630000135
And of the ith frame
Figure BDA0003377008630000136
To obtain the following formula
Figure BDA0003377008630000137
Wherein, betajIs composed of
Figure BDA0003377008630000138
The previous actual coefficients, and j is 1,2, …, i.i. is equal to or greater than 1.
Then the formula
Figure BDA0003377008630000139
Is shown as
Figure BDA00033770086300001310
For the joint prediction model of four corner points, order
Figure BDA00033770086300001311
Wherein the content of the first and second substances,
Figure BDA00033770086300001312
is a spatial positive overlap adding operator, and has
Figure BDA00033770086300001313
If with x1Is a standard angle, xi+1Then is equal to xiThe rotation angle therebetween is 90 deg., and the direction is counterclockwise. The expression of the four corner point joint prediction model is
Figure BDA00033770086300001314
Due to x2,x3,x4Are all x1Is obtained by rotation transformation, then x1,x2,x3,x4All the dimensions of (A) are subject to a template S ═ W, H]Wherein W and H are each x1Length and width. The image size limitation adopts an image compression method, namely, the image is reduced without directly deleting image information.
In the expression of the four-corner point joint prediction model,
Figure BDA00033770086300001315
is gsAnd
Figure BDA00033770086300001316
corresponding to the form of augmentation. After the maximum value optimization is carried out on the final response obtained by the calculation of the four-corner joint prediction model, the obtained augmented coordinate value is
Figure RE-GDA00034621691000001317
Using the augmented four corner point coordinate values in the continuous correlation filter generation module
Figure BDA00033770086300001318
Resampling for filter generation to obtain w ═ wg+wh+wnWindowed resampled image samples for layer features
Figure BDA00033770086300001319
According to the theory of continuous filtering, the overall optimization function E (f) of continuous correlation filtering is
Figure BDA00033770086300001320
Wherein alpha isjPenalty term corresponding to j-th correlation filter
Figure BDA00033770086300001321
Penalty parameter of yjIs a Gaussian response map corresponding to the j-th correlation filter,
Figure BDA00033770086300001322
being a continuous filter, fdIs a filter for the D-th layer feature, D is the total number of layers of image features,
Figure BDA0003377008630000141
is a filter fdA corresponding weight matrix.
Discretizing each characteristic layer by continuous correlation filtering, and then the training formula with correlation filtering is as follows
Figure BDA0003377008630000142
Wherein, [ k ]]For the index variable after the discretization,
Figure BDA0003377008630000143
discrete compensation coefficients corresponding to the d-th layer features,
Figure BDA0003377008630000144
is the d-th layer characteristic.
The training formula of the correlation filtering is substituted into the overall optimization function of the continuous correlation filtering, and the pasival formula is applied to obtain the continuous correlation filtering
Figure BDA0003377008630000145
The simplified global optimization function
Figure BDA0003377008630000146
Is composed of
Figure BDA0003377008630000147
Wherein the content of the first and second substances,
Figure BDA0003377008630000148
is composed of
Figure BDA0003377008630000149
In the form of the enlargement of (a) or (b),
Figure BDA00033770086300001410
is composed of
Figure BDA00033770086300001411
In the form of an extension of | · |)2Is that
Figure BDA00033770086300001412
Standard euclidean norm below.
Figure BDA00033770086300001413
From 2K +1 rows and each
Figure BDA00033770086300001414
All have d characteristic channels and 2Kd+1 columns, each element value is respectively
Figure BDA00033770086300001415
To formula
Figure BDA00033770086300001416
The optimization problem is expressed with an optimal value of
Figure BDA00033770086300001417
Wherein A isHIs a conjugate transpose matrix of A matrix, and the expression of the matrix A is
Figure BDA00033770086300001418
Gamma is a diagonal weight matrix with the expression of
Figure BDA00033770086300001419
Gaussian type mark matrix
Figure BDA00033770086300001420
Is expressed as
Figure BDA00033770086300001421
The filter is generated by the expression
Figure BDA00033770086300001422
Resampling image samples
Figure BDA00033770086300001423
Substituting the formula to generate a filter f to obtain a generated filter
Figure BDA00033770086300001424
In the scale and angle filter generation module, the formula is matched
Figure BDA00033770086300001425
The four corner points are enlarged to obtain
Figure BDA0003377008630000151
Wherein upsilon is upsilon after four corners are enlarged
Figure BDA0003377008630000152
Resampling image samples
Figure BDA0003377008630000153
Substituting the above formula for the filter
Figure BDA0003377008630000154
Generating to obtain the generated scale and angle filter
Figure BDA0003377008630000155
In the ending module, the coordinate values of the four corner points after being augmented are processed
Figure BDA0003377008630000156
Generated filter
Figure BDA0003377008630000157
And a generated scale and angle filter
Figure BDA0003377008630000158
Reserving and amplifying the coordinate values of the four corner points
Figure BDA0003377008630000159
Applied to the image of the next frame to obtain a new image block x of the cropped sampleiAnd the video sequence is carried into a cosine window windowing module for operation, and the operation from the cosine window windowing module to an ending module is executed in a circulating way on each next frame until the video sequence is ended.
Example two
The embodiment provides an irregular frame target tracking method adopting a polar coordinate transformation method, as shown in fig. 1. The irregular frame target tracking method adopting the polar coordinate transformation method comprises the following steps: step 1, initializing parameters in a continuous correlation filtering algorithm, and tracking a given position of a target, namely a target central point coordinate (x) according to a first framec,yc) Cutting and sampling the image in Cartesian coordinate system to obtain sample image block x1(ii) a Step 2, sample image block x1Extracting features, and then performing series connection and cosine window windowing on the extracted features to obtain an image sample z'; step 3, obtaining a characteristic spectrum Z 'by fast Fourier transform of the image sample characteristic Z', and then using continuousThe related filter h carries out filtering processing on the characteristic spectrum Z' to obtain a continuous filtering response spectrum r, and then the continuous filtering response spectrum r is calculated through a Newton method to obtain the estimated coordinates of the target center point
Figure BDA00033770086300001510
Step 4, by using the estimated coordinates of the target center point
Figure BDA00033770086300001511
Generating four-corner coordinates of a tracking target, and sampling and preprocessing a quadrilateral region formed by the generated four-corner coordinates to obtain the coordinate values of the augmented four-corner points
Figure BDA00033770086300001512
Step 5, the coordinate values of the four corner points after being augmented are processed
Figure BDA00033770086300001513
Resampling for continuous correlation filter generation to obtain resampled image samples
Figure BDA00033770086300001514
And using the resampled image samples
Figure BDA00033770086300001515
Generating a filter f to obtain a generated filter
Figure BDA00033770086300001516
Step 6, using the resampled image sample
Figure BDA00033770086300001517
To filter
Figure BDA00033770086300001518
Generating to obtain the generated scale and angle filter
Figure BDA00033770086300001519
Step 7, the four-corner coordinate value after being augmented is processed
Figure BDA00033770086300001520
Generated filter
Figure BDA00033770086300001521
And a generated scale and angle filter
Figure BDA00033770086300001522
Reserving and amplifying the coordinate values of the four corner points
Figure BDA00033770086300001523
Applied to the image of the next frame to obtain a new image block x of the cropped sampleiAnd carrying out operation in the step 2, and circularly executing the operation from the step 2 to the step 7 for the next frames until the video sequence is ended.
In step 1, the parameters of the respective parts involved in the correlation filtering algorithm are initialized. From a given position of the tracked object in the first frame (object center point coordinates (x)c,yc) Length and width m, n) of object frame), cut out the sampling to the image under the cartesian coordinate system, the scope is four angular points: upper left corner point s1＝(xc+m/2,yc+ n/2), upper right corner point s2＝(xc-m/2，yc+ n/2), lower right corner point s3＝(xc-m/2,yc-n/2), lower left corner point s4＝(xc+m/2,yc-n/2) defining a quadrangular area. The set of coordinate points may be represented as: s ═ S1 s2 s3 s4]T. Cropped sample image block x1Will be used to train the correlation filter after superimposing the cosine window.
In step 2, the sample image block x is processed1Performing a feature extraction operation, the extracted features sequentially comprising: gray, HOG and CN; obtaining a characteristic map z according to the characteristic GraygObtaining a characteristic map z according to the characteristic HOGhObtaining a characteristic map z according to the characteristic CNnWherein
Figure BDA0003377008630000161
wi(i∈[g,h,n]) Is a characteristic spectrum ziThe number of feature channels of (a); connecting the features Gray, the HOG and the CN in series according to the dimension of the number of the feature channels to obtain an image sample
Figure BDA0003377008630000162
Wherein w ═ wg+wh+wn，wgFor the number of Gray feature layers, whNumber of layers for HOG feature, wnThe number of CN characteristic layers is, and w is the number of synthetic characteristic layers; point-by-point two-dimensional cosine window cos for image sample zwindowThe window operation is expressed as z ═ z-windowThe as is a matrix dot product operation,
Figure BDA0003377008630000163
and z' is a feature spectrum, cos, windowed with a cosine windowwindowIs obtained from the function form of cosine window, and the expression is
coswindow＝h(m)h(n)′
Wherein m and n are respectively the length and width of the frame of the tracked target, and h (m) and h (n) are both one-dimensional cosine window generating functions h (N), and the expression is
Figure BDA0003377008630000164
The period of the cosine window function is 2 pi/N, with N-m or N-N. The function distribution characteristic of the one-dimensional cosine window is that h (N) is 0 when i is 0, h (N) is 1 when i is N/4, h (N) is 2 when i is N/2, h (N) is 1 when i is 3N/2, and h (N) is 0 when i is N, i shows a tendency that the cosine equation increases monotonically first and then decreases monotonically. And a two-dimensional cosine window cos obtained by the outer product of two one-dimensional cosine windowswindowThe method has the characteristic that the closer to the center, the larger the pixel value is, and the pixel values of a circle around the boundary are all 0.
In step 3, the image sample characteristics Z ' are subjected to fast Fourier transform to obtain a characteristic spectrum Z ', and then the characteristic spectrum Z ' is subjected to filtering processing by using a continuous correlation filter h to obtain a continuous filtering response spectrum r, wherein the formula is
Figure BDA0003377008630000171
Wherein the content of the first and second substances,
Figure BDA0003377008630000172
representing an analog Fourier transform (iFFT), < is a matrix dot product operation, and
Figure BDA0003377008630000173
then, calculating the continuous filtering response spectrum r by a Newton method to obtain the estimated coordinates of the target central point
Figure BDA0003377008630000174
In step 4, the estimated coordinates of the center point of the target are obtained
Figure BDA0003377008630000175
Then, generating four-corner point coordinates, wherein the generated four-corner point coordinates are as follows: point on the upper left corner
Figure BDA0003377008630000176
Upper right corner point
Figure BDA0003377008630000177
Lower right corner point
Figure BDA0003377008630000178
Lower left corner point
Figure BDA0003377008630000179
The set of coordinate points may be represented as: s ═ S'1 s′2 s′3 s′4]T. Then the generated four-corner point coordinate structure is alignedAnd sampling the formed quadrilateral area, and performing feature extraction and windowing operation to obtain a single corner feature map Z' for scale prediction. Rotating the four corner points of Z' to obtain the feature space of the four corner points after being enlarged
Figure BDA00033770086300001710
Wherein
Figure BDA00033770086300001711
Are orthogonal superposition operators of space, and have
Figure BDA00033770086300001712
For a single corner point correlation filter gsAlso carrying out amplification to obtain an amplified scale and angle estimation filter
Figure BDA00033770086300001713
Formula pair of augmented four-corner point feature space by applying four-corner point joint prediction model
Figure BDA00033770086300001714
Carrying out continuous correlation filtering, and obtaining the coordinate values of the four corner points after being amplified by applying the formula of the amplified coordinate values S
Figure BDA00033770086300001715
The formula of the four-corner point joint prediction model and the formula of the augmented coordinate value S' are obtained in the following mode:
let the image I be in N × N size in Cartesian coordinate system with its upper coordinate
Figure BDA00033770086300001716
Has a pixel value of
Figure BDA00033770086300001717
The origin of the coordinate system is the upper left corner of the image, the positive direction of the x axis is the positive right direction, and the positive direction of the y axis is the positive down direction. Where i is 1,2, …, N. According to the definition, the coordinates of the pixel points at the upper left corner of the image IAnd the coordinate of the pixel point at the lower right corner of the image is (1,1) and is (N, N).
The polar coordinate representation of the image I can be regarded as the coordinate in the Cartesian coordinate system
Figure BDA00033770086300001718
To the polar coordinate system, coordinate
Figure BDA00033770086300001719
Non-linear, non-uniform transformation of (a). The polar coordinate is transformed into SfThen there is
Figure BDA00033770086300001720
In order to keep the integrity of the angle change of the polar coordinate, namely, the positive and negative values are uniformly distributed, and the image can be uniformly divided, namely, the image is diffused outwards from the datum point, and the values of all parts are basically uniform. The central point (x) of the image I under the Cartesian coordinate systemc,yc) As a reference point for polar coordinate transformation.
Under a polar coordinate system, an arbitrary coordinate point (rho)i,θi) Middle mode length rhoiIs expressed as
Figure BDA0003377008630000181
Phase thetaiIs expressed as
Figure BDA0003377008630000182
Wherein r is a reference standard direction vector, and the positive direction of the polar coordinate system is the same as the positive direction of the Cartesian coordinate system.
Image I (x) after polar coordinate changei,yi) Is an image I' (ρ)i,θi). In a Cartesian coordinate system, the phase angle θiHas a more concise expression form as shown in the following
Figure BDA0003377008630000183
In addition, an image I in a Cartesian coordinate system is divided into0Proceeding with die length
Figure BDA0003377008630000184
And phase
Figure BDA0003377008630000185
And generating a changed image I1When, the following correspondence relationship is given
Figure BDA0003377008630000186
Correspondingly, the antipodal coordinate mark is
Figure BDA0003377008630000187
As shown in the two formulas, the change of the image scale and the rotation in the Cartesian coordinate system can be converted into the translational motion along the axis in the polar coordinate system, and based on the characteristic, the target scale and the rotation transformation in the target tracking can be more simply calculated and estimated.
Through polar coordinate system transformation, a prediction model of single-angle-point scale and angle transformation of the trapezoid tracking target frame under polar coordinates can be constructed. The response calculation to the correlation filtering in polar coordinates has
Figure BDA0003377008630000188
Wherein the content of the first and second substances,
Figure BDA0003377008630000189
according to the s ═ p, theta pair IiSampling polar coordinates, where s' is the coordinate of s in polar coordinate system, and convertingIs given by the formula
Figure BDA00033770086300001810
Wherein, H and W are respectively the image I sampled according to the tracking target frameiLength and width of (d); rho' is the module length of s after the polar coordinate system transformation; and theta' is the phase of s after the polar coordinate system transformation.
The Fourier domain calculation used by the classic DCF target tracking framework can also be used for calculation under polar coordinate transformation, and the specific response calculation formula is
Figure BDA0003377008630000191
Wherein the content of the first and second substances,
Figure BDA0003377008630000192
as a function of polar transformation, gsA model weight matrix is estimated for the scale and angle. According to the formula
Figure BDA0003377008630000193
The scale and angle estimation under polar coordinates does not need to be converted and sampled for calculation
Figure BDA0003377008630000194
According to the formula
Figure BDA0003377008630000195
Only the weight matrix g of the scale and angle estimation model needs to be determinedsThe filtering operation can be done directly.
Converting the image into a polar coordinate system, solving the problem of scale and angle transformation of the tracking target under a Cartesian coordinate system, and converting the problem into the problem of translation and rotation of the tracking target under an estimated polar coordinate; or to be understood as: and solving the coordinate change problem of the original image and the image after translation and rotation in the polar coordinate system, wherein the problem can be solved through a phase correlation algorithm in the field of pattern recognition.
According to the theory of the phase correlation algorithm, image I1The result after feature extraction is phi (I)1) Image I1The result after feature extraction is phi (I)2) Image I2Is an image I1The impulse function matrix G between the translated and rotated images can be calculated as
Figure BDA0003377008630000196
Wherein k represents the kth characteristic channel,
Figure BDA00033770086300001912
representing the frequency domain form of the variable, for the shock function matrix G after inverse Fourier transform(k)The values of elements designated by coordinates corresponding to translation and rotation of the function matrix are not 0, and the values of the other elements are 0. Obtaining translation and rotation values corresponding to the coordinates of the maximum value element by superposing the impact function matrixes G of all D characteristic channels, and further enabling the impact function matrixes G to be used for processing
Figure BDA0003377008630000197
Converting into Cartesian coordinate system to complete the scale and angle values of the tracked target, which can be expressed as
Figure RE-GDA0003462169100000199
Wherein the content of the first and second substances,
Figure RE-GDA00034621691000001910
for the inverse Fourier transform, max (H) is a function of the maximum value, and max (H) returns are the maximum values in the matrix H. find (H; ζ) is a search function defined as: and returning the position information of the element zeta in the matrix H, namely the row value and column value information of zeta in H. Here, the search function functions have the role of: at filter response matrix
Figure RE-GDA00034621691000001911
In search of response maximum
Figure RE-GDA00034621691000001912
The position information s', H and ζ in the response map are temporary variables that are set for convenient function interpretation, and have no other role in the algorithm.
Corresponding calculation formula according to related filtering algorithm
Figure BDA0003377008630000201
And formula
Figure BDA0003377008630000202
Can obtain the product
Figure BDA0003377008630000203
Wherein f issThe argument of which is the image sample x, is a function of the response value. And for single corner point correlation filter
Figure BDA0003377008630000204
Has the following calculation formula
Figure BDA0003377008630000205
Wherein the content of the first and second substances,
Figure BDA0003377008630000206
is a linear combination of frames preceding the current frame. And | is to calculate the modulus of each element in the matrix.
For the ith frame
Figure BDA0003377008630000207
Derived formula as follows
Figure BDA0003377008630000208
Wherein λ iswIs a linear combination
Figure BDA0003377008630000209
The learning rate parameter of (2) is,
Figure BDA00033770086300002010
is transformed into x by polar coordinates
Figure BDA00033770086300002011
And performing a result matrix after feature extraction.
Bonding of
Figure BDA00033770086300002012
And of the ith frame
Figure BDA00033770086300002013
To obtain the following formula
Figure BDA00033770086300002014
Wherein, betajIs composed of
Figure BDA00033770086300002015
The previous actual coefficients, and j is 1,2, …, i.i. is equal to or greater than 1.
Then the formula
Figure BDA00033770086300002016
Is shown as
Figure BDA00033770086300002017
For the joint prediction model of four corner points, order
Figure BDA00033770086300002018
Wherein the content of the first and second substances,
Figure BDA00033770086300002019
is a spatial positive overlap adding operator, and has
Figure BDA00033770086300002020
If with x1Is a standard angle, xi+1Then is equal to xiThe rotation angle therebetween is 90 deg., and the direction is counterclockwise. The expression of the four corner point joint prediction model is
Figure BDA00033770086300002021
Due to x2，x3，x4Are all x1Is obtained by rotation transformation, then x1，x2，x3，x4All the dimensions of (A) are subject to a template S ═ W, H]Wherein W and H are each x1Length and width. The image size limitation adopts an image compression method, namely, the image is reduced without directly deleting image information.
In the expression of the four-corner point joint prediction model,
Figure BDA00033770086300002022
is gsAnd
Figure BDA00033770086300002023
corresponding to the form of augmentation. After the maximum value optimization is carried out on the final response obtained by the calculation of the four-corner joint prediction model, the obtained augmented coordinate value is
Figure RE-GDA0003462169100000211
In step 5, the augmented four corner point coordinate values are used
Figure BDA0003377008630000212
Resampling for filter generation is performed to obtain a signal with w ═ wg+wh+wnWindowed resampled image samples for layer features
Figure BDA0003377008630000213
According to the theory of continuous filtering, the overall optimization function E (f) of continuous correlation filtering is
Figure BDA0003377008630000214
Wherein alpha isjPenalty term corresponding to j-th correlation filter
Figure BDA0003377008630000215
Penalty parameter of yjIs a Gaussian response map corresponding to the j-th correlation filter,
Figure BDA0003377008630000216
being a continuous filter, fdIs a filter for the D-th layer feature, D is the total number of layers of image features,
Figure BDA0003377008630000217
is a filter fdA corresponding weight matrix.
Discretizing each characteristic layer by continuous correlation filtering, and then the training formula with correlation filtering is as follows
Figure BDA0003377008630000218
Wherein, [ k ]]For the index variable after the discretization,
Figure BDA0003377008630000219
discrete compensation coefficients corresponding to the d-th layer features,
Figure BDA00033770086300002110
is the d-th layer characteristic.
The training formula of the correlation filtering is substituted into the overall optimization function of the continuous correlation filtering, and the pasival formula is applied to obtain the continuous correlation filtering
Figure BDA00033770086300002111
The simplified global optimization function
Figure BDA00033770086300002112
Is composed of
Figure BDA00033770086300002113
Wherein the content of the first and second substances,
Figure BDA00033770086300002114
is composed of
Figure BDA00033770086300002115
In the form of the enlargement of (a) or (b),
Figure BDA00033770086300002116
is composed of
Figure BDA00033770086300002117
In the form of an extension of | · |)2Is that
Figure BDA00033770086300002118
Standard euclidean norm below.
Figure BDA00033770086300002119
From 2K +1 rows and each
Figure BDA00033770086300002120
All have d characteristic channels and 2Kd+1 columns, each element value is respectively
Figure BDA00033770086300002121
To formula
Figure BDA00033770086300002122
The optimization problem is expressed with an optimal value of
Figure BDA0003377008630000221
Wherein A isHIs a conjugate transpose matrix of A matrix, and the expression of the matrix A is
Figure BDA0003377008630000222
Gamma is a diagonal weight matrix with the expression of
Figure BDA0003377008630000223
Gaussian type mark matrix
Figure BDA0003377008630000224
Is expressed as
Figure BDA0003377008630000225
The filter is generated by the expression
Figure BDA0003377008630000226
Resampling image samples
Figure BDA0003377008630000227
Substituting the formula to generate a filter f to obtain a generated filter
Figure BDA0003377008630000228
In step 6, the formula is matched
Figure BDA0003377008630000229
The four corner points are enlarged to obtain
Figure BDA00033770086300002210
Wherein upsilon is upsilon after four corners are enlarged
Figure BDA00033770086300002211
Resampling image samples
Figure BDA00033770086300002212
Substituting the above formula for the filter
Figure BDA00033770086300002213
Generating to obtain the generated scale and angle filter
Figure BDA00033770086300002214
In step 7, the augmented four corner point coordinate values are calculated
Figure BDA00033770086300002215
Generated filter
Figure BDA00033770086300002216
And generated scale and angle filter
Figure BDA00033770086300002217
Reserving and amplifying the coordinate values of the four corner points
Figure BDA00033770086300002218
Applied to the image of the next frame to obtain a new image block x of the cropped sampleiAnd carrying out operation in the step 2, and circularly executing the operation from the step 2 to the step 7 for the next frames until the video sequence is ended.
The method and the way for implementing the technical scheme are many, and the above is only the preferred embodiment of the invention. It should be noted that, for those skilled in the art, without departing from the principle of the present invention, several improvements and modifications can be made, and these improvements and modifications should also be construed as the protection scope of the present invention. All the components not specified in the present embodiment can be realized by the prior art.

Claims (10)

1. An irregular-frame target tracking system using a polar coordinate transformation method, comprising:
an initial image sampling module for initializing parameters in the continuous correlation filtering algorithm and tracking the given position of the target, namely the target center point coordinate (x) in the first framec，yc) Cutting and sampling the image in Cartesian coordinate system to obtain sample image block x1；
A cosine window windowing module for windowing the sample image block x1Extracting features, and then performing series connection and cosine window windowing on the extracted features to obtain an image sample z';
the continuous correlation filtering module is used for performing fast Fourier transform on the image sample characteristics Z ' to obtain a characteristic spectrum Z ', then performing filtering processing on the characteristic spectrum Z ' by using a continuous correlation filter h to obtain a continuous filtering response spectrum r, and then calculating the continuous filtering response spectrum r by a Newton method to obtain an estimated target central point coordinate
Figure FDA0003377008620000011
An irregular border estimation module to estimate the coordinates of the target center point by using the estimated coordinates
Figure FDA0003377008620000012
Generating four-corner point coordinates of the tracking target, and sampling and preprocessing a quadrilateral region formed by the generated four-corner point coordinates to obtain the augmented four-corner point coordinate values
Figure FDA0003377008620000013
A continuous correlation filter generation module for generating the augmented four corner point coordinate values
Figure FDA0003377008620000014
Resampling for continuous correlation filter generation to obtain resampled image samples
Figure FDA0003377008620000015
And using the resampled image samples
Figure FDA0003377008620000016
Generating a filter f to obtain a generated filter
Figure FDA0003377008620000017
A scale and angle filter generation module to generate a scale and angle filter by using the resampled image samples
Figure FDA0003377008620000018
To filter
Figure FDA0003377008620000019
Generating to obtain the generated scale and angle filter
Figure FDA00033770086200000110
A finishing module for processing the augmented four corner point coordinate values
Figure FDA00033770086200000111
The generated filter
Figure FDA00033770086200000112
And the generated scale and angle filter
Figure FDA00033770086200000113
Reserving and amplifying the coordinate values of the four corner points
Figure FDA00033770086200000114
Applied to the image of the next frame to obtain a new image block x of the cropped sampleiAnd the video sequence is carried into a cosine window windowing module for operation, and the operation from the cosine window windowing module to an ending module is executed in a circulating way on each next frame until the video sequence is ended.
2. The irregular-frame target tracking system using the polar coordinate transformation method according to claim 1, characterized in that: in the irregular border estimation module, the preprocessing is: carrying out feature extraction and windowing on the sampled quadrilateral area to obtain a single angular point feature map Z' for scale prediction; carrying out four-corner point rotation on the single corner point feature map Z' to obtain an augmented four-corner point feature space
Figure FDA00033770086200000115
For the feature space of the four corner points after the enlargement
Figure FDA00033770086200000222
Carrying out continuous correlation filtering, and obtaining the coordinate values of the four corner points after the amplification through the coordinate values S' after the amplification
Figure FDA0003377008620000021
3. The irregular-frame target tracking system using the polar coordinate transformation method according to claim 2, characterized in that: in the continuous correlation filter generation module, the correlation filter is generated,
using the augmented four corner point coordinate values
Figure FDA0003377008620000022
Resampling for successive correlation filter generation to obtain a correlation signal having w ═ wg+wh+wnWindowed resampled image samples for layer features
Figure FDA0003377008620000023
Wherein wgFor the number of Gray feature layers, whNumber of layers for HOG feature, wnThe number of CN characteristic layers is shown, and w is the number of synthetic characteristic layers;
the generation expression of the filter f obtained according to the continuous correlation filtering theory is
Figure FDA0003377008620000024
Wherein, WHIs a conjugate transpose of the weight matrix W of the filter f, AHIs a conjugate transpose matrix of A matrix, and the expression of the matrix A is
Figure FDA0003377008620000025
Gamma is a diagonal weight matrix with the expression of
Figure FDA0003377008620000026
Gaussian type mark matrix
Figure FDA0003377008620000027
Is expressed as
Figure FDA0003377008620000028
Resampling image samples
Figure FDA0003377008620000029
Substituting the formula to generate a filter f to obtain a generated filter
Figure FDA00033770086200000210
4. The irregular-frame target tracking system using the polar coordinate transformation method according to claim 3, characterized in that: in the scale and angle filter generation module,
according to the continuous phaseSingle corner filter obtained by filter-related theory
Figure FDA00033770086200000211
Is expressed as
Figure FDA00033770086200000212
Therein, <' >-1Is a matrix dot product operation, which is the inverse operation of the matrix dot product operation, k represents the k-th feature channel,
Figure FDA00033770086200000213
is a linear combination of the frames preceding the current frame,
Figure FDA00033770086200000214
is composed of
Figure FDA00033770086200000215
A result matrix after Fourier transform, and
Figure FDA00033770086200000216
is composed of
Figure FDA00033770086200000217
The conjugate matrix of (a) is determined,
Figure FDA00033770086200000218
is the result of x after polar transformation, and
Figure FDA00033770086200000219
is composed of
Figure FDA00033770086200000220
The result matrix after feature extraction, | · | is that each element in the matrix is respectively solved for its modulus;
four corner points are enlarged to obtain
Figure FDA00033770086200000221
Wherein k represents the kth characteristic channel, and gamma is augmented by four corner points
Figure FDA0003377008620000031
Resampling image samples
Figure FDA0003377008620000032
Substituting the above formula for the filter
Figure FDA0003377008620000033
Generating to obtain the generated scale and angle filter
Figure FDA0003377008620000034
5. The irregular-frame target tracking system using the polar coordinate transformation method according to claim 4, characterized in that: in the cosine window windowing module, the cosine window is set to zero,
for sample image block x1Performing a feature extraction operation, the extracted features sequentially comprising: gray, HOG and CN;
obtaining a characteristic map z according to the characteristic GraygObtaining a characteristic map z according to the characteristic HOGhObtaining a characteristic map z according to the characteristic CNnWherein z isg，zh，
Figure FDA0003377008620000035
wi(i∈[g，h，n]) Is a characteristic spectrum ziThe number of feature channels of (a);
connecting the features Gray, the HOG and the CN in series according to the dimension of the number of the feature channels to obtain an image sample
Figure FDA0003377008620000036
Wherein w ═ wg+wh+wn，wgFor the number of Gray feature layers, whNumber of layers for HOG feature, wnThe number of CN characteristic layers is shown, and w is the number of synthetic characteristic layers;
point-by-point two-dimensional cosine window cos for image sample zwindowThe window operation is expressed as z ═ z-windowThe as is a matrix dot product operation,
Figure FDA0003377008620000037
and z' is a feature spectrum, cos, windowed with a cosine windowwindowIs obtained from the function form of cosine window, and the expression is
coswindow＝h(m)h(n)′
Wherein m and n are respectively the length and width of the frame of the tracked target, and h (m) and h (n) are both one-dimensional cosine window generating functions h (N), and the expression is
Figure FDA0003377008620000038
The period of the cosine window function is 2 pi/N, with N-m or N-N.
6. An irregular frame target tracking method adopting a polar coordinate transformation method comprises the following steps:
step 1, initializing parameters in a continuous correlation filtering algorithm, and tracking a given position of a target, namely a target central point coordinate (x) according to a first framec，yc) Cutting and sampling the image in Cartesian coordinate system to obtain sample image block x1；
Step 2, for the sample image block x1Extracting features, and then performing series connection and cosine window windowing on the extracted features to obtain an image sample z';
step 3, obtaining a characteristic spectrum Z 'by fast Fourier transform of the image sample characteristic Z', and then using continuous correlation filteringThe wave filter h carries out filtering processing on the characteristic spectrum Z' to obtain a continuous filtering response spectrum r, and then the continuous filtering response spectrum r is calculated through a Newton method to obtain an estimated target central point coordinate
Figure FDA0003377008620000041
Step 4, by using the estimated target center point coordinates
Figure FDA0003377008620000042
Generating four-corner point coordinates of the tracking target, and sampling and preprocessing a quadrilateral region formed by the generated four-corner point coordinates to obtain the augmented four-corner point coordinate values
Figure FDA0003377008620000043
Step 5, the coordinate values of the four corner points after the amplification are processed
Figure FDA00033770086200000418
Resampling for continuous correlation filter generation to obtain resampled image samples
Figure FDA0003377008620000044
And using the resampled image samples
Figure FDA0003377008620000045
Generating a filter f to obtain a generated filter
Figure FDA0003377008620000046
Step 6, using the resampled image sample
Figure FDA0003377008620000047
To filter
Figure FDA0003377008620000048
Generating to obtain the generated scale and angle filter
Figure FDA0003377008620000049
Step 7, the coordinate values of the four corner points after the amplification are processed
Figure FDA00033770086200000410
The generated filter
Figure FDA00033770086200000411
And the generated scale and angle filter
Figure FDA00033770086200000412
Reserving and amplifying the coordinate values of the four corner points
Figure FDA00033770086200000413
Applied to the image of the next frame to obtain a new image block x of the cropped sampleiAnd carrying out operation in the step 2, and circularly executing the operation from the step 2 to the step 7 for the next frames until the video sequence is ended.
7. The irregular-frame target tracking method using the polar coordinate transformation method according to claim 6, characterized in that: in step 4, the pretreatment is as follows: carrying out feature extraction and windowing on the sampled quadrilateral area to obtain a single angular point feature map Z' for scale prediction; performing four-corner point rotation on the single corner point feature map Z' to obtain an augmented four-corner point feature space Z; for the feature space of the four corner points after the enlargement
Figure FDA00033770086200000419
Carrying out continuous correlation filtering, and obtaining the coordinate values of the four corner points after the amplification through the coordinate values S' after the amplification
Figure FDA00033770086200000414
8. The irregular-frame target tracking method using the polar coordinate transformation method according to claim 7, characterized in that: in the step 5, the process is carried out,
using the augmented four corner point coordinate values
Figure FDA00033770086200000415
Resampling for successive correlation filter generation to obtain a correlation signal having w ═ wg+wh+wnWindowed resampled image samples for layer features
Figure FDA00033770086200000416
Wherein wgFor the number of Gray feature layers, whNumber of layers for HOG feature, wnThe number of CN characteristic layers is shown, and w is the number of synthetic characteristic layers;
the generation expression of the filter f obtained according to the continuous correlation filtering theory is
Figure FDA00033770086200000417
Wherein, WHIs a conjugate transpose of the weight matrix W of the filter f, AHIs a conjugate transpose matrix of A matrix, and the expression of the matrix A is
Figure FDA0003377008620000051
Gamma is a diagonal weight matrix with the expression of
Figure FDA0003377008620000052
Gaussian type mark matrix
Figure FDA0003377008620000053
Is expressed as
Figure FDA0003377008620000054
Resampling image samples
Figure FDA0003377008620000055
Substituting the formula to generate a filter f to obtain a generated filter
Figure FDA0003377008620000056
9. The irregular-frame target tracking method using the polar coordinate transformation method according to claim 8, characterized in that: in a step 6, the process is carried out,
obtaining a single corner filter according to the continuous correlation filtering theory
Figure FDA0003377008620000057
Is expressed as
Figure FDA0003377008620000058
Therein, <' >-1Is a matrix dot product operation, which is the inverse operation of the matrix dot product operation, k represents the k-th feature channel,
Figure FDA0003377008620000059
is a linear combination of the frames preceding the current frame,
Figure FDA00033770086200000510
is composed of
Figure FDA00033770086200000511
A result matrix after Fourier transform, and
Figure FDA00033770086200000512
is composed of
Figure FDA00033770086200000513
The conjugate matrix of (a) is determined,
Figure FDA00033770086200000514
is the result of x after polar transformation, and
Figure FDA00033770086200000515
is composed of
Figure FDA00033770086200000516
The result matrix after feature extraction, | · | is that each element in the matrix is respectively solved for its modulus;
four corner points are enlarged to obtain
Figure FDA00033770086200000517
Wherein k represents the kth characteristic channel, and gamma is augmented by four corner points
Figure FDA00033770086200000518
Resampling image samples
Figure FDA00033770086200000519
Substituting the above formula for the filter
Figure FDA00033770086200000520
Generating to obtain the generated scale and angle filter
Figure FDA00033770086200000521
10. The irregular-frame target tracking method using the polar coordinate transformation method according to claim 9, characterized in that: in the step 2, the process is carried out,
for sample image block x1Performing a feature extraction operation, the extracted features sequentially comprising: gray, HOG and CN;
obtaining a characteristic map z according to the characteristic GraygObtaining a characteristic map z according to the characteristic HOGhObtaining a characteristic map z according to the characteristic CNnWherein z isg，zh，
Figure FDA00033770086200000522
wi(i∈[g，h，n]) Is a characteristic spectrum ziThe number of feature channels of (a);
connecting the features Gray, the HOG and the CN in series according to the dimension of the number of the feature channels to obtain an image sample
Figure FDA0003377008620000061
Wherein w ═ wg+wh+wn，wgFor the number of Gray feature layers, whNumber of layers for HOG feature, wnThe number of CN characteristic layers is shown, and w is the number of synthetic characteristic layers;
point-by-point two-dimensional cosine window cos for image sample zwindowThe window operation is expressed as z ═ z-windowThe as is a matrix dot product operation,
Figure FDA0003377008620000062
and z' is a feature spectrum, cos, windowed with a cosine windowwindowIs obtained from the function form of cosine window, and the expression is
coswindow＝h(m)h(n)′
Wherein m and n are respectively the length and width of the frame of the tracked target, and h (m) and h (n) are both one-dimensional cosine window generating functions h (N), and the expression is
Figure FDA0003377008620000063
The period of the cosine window function is 2 pi/N, with N-m or N-N.
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