CN109671108B - Single multi-view face image attitude estimation method capable of rotating randomly in plane - Google Patents

Single multi-view face image attitude estimation method capable of rotating randomly in plane Download PDF

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CN109671108B
CN109671108B CN201811550656.5A CN201811550656A CN109671108B CN 109671108 B CN109671108 B CN 109671108B CN 201811550656 A CN201811550656 A CN 201811550656A CN 109671108 B CN109671108 B CN 109671108B
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human face
face image
angle
gamma
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CN109671108A (en
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傅由甲
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Tuoerte Intelligent Technology Wuhan Co ltd
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Chongqing University of Technology
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    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06TIMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00Image analysis
    • G06T7/30Determination of transform parameters for the alignment of images, i.e. image registration
    • G06T7/33Determination of transform parameters for the alignment of images, i.e. image registration using feature-based methods
    • G06T7/344Determination of transform parameters for the alignment of images, i.e. image registration using feature-based methods involving models
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06VIMAGE OR VIDEO RECOGNITION OR UNDERSTANDING
    • G06V40/00Recognition of biometric, human-related or animal-related patterns in image or video data
    • G06V40/10Human or animal bodies, e.g. vehicle occupants or pedestrians; Body parts, e.g. hands
    • G06V40/16Human faces, e.g. facial parts, sketches or expressions
    • G06V40/161Detection; Localisation; Normalisation
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06VIMAGE OR VIDEO RECOGNITION OR UNDERSTANDING
    • G06V40/00Recognition of biometric, human-related or animal-related patterns in image or video data
    • G06V40/10Human or animal bodies, e.g. vehicle occupants or pedestrians; Body parts, e.g. hands
    • G06V40/16Human faces, e.g. facial parts, sketches or expressions
    • G06V40/172Classification, e.g. identification
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06TIMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00Indexing scheme for image analysis or image enhancement
    • G06T2207/30Subject of image; Context of image processing
    • G06T2207/30196Human being; Person
    • G06T2207/30201Face

Abstract

The invention discloses a single multi-view face image posture estimation method capable of rotating randomly in a plane, which comprises the following steps of 1, establishing a pre-estimated value set of a gamma angle according to a face image to be detected, wherein the gamma angle represents a deflection angle around a Z axis, 2, traversing the pre-estimated value set of the gamma angle, calculating α and β angles corresponding to the pre-estimated values of the gamma angle by adopting a calculation method of solving α and β angles meeting an objective function under the condition of the specified gamma angle, α represents the deflection angle around the X axis, β represents the deflection angle around the Y axis, and 3, forming an alternative set by values of the objective function corresponding to the pre-estimated values of the gamma angle, selecting a minimum objective function value from the alternative set, and taking the gamma angle pre-estimated value, α and β angles corresponding to the minimum objective function value as a face posture of the face image to be detected.

Description

Single multi-view face image attitude estimation method capable of rotating randomly in plane
Technical Field
The invention relates to the technical field of face recognition, in particular to a face gesture recognition model and a face gesture recognition method.
Background
In the face identification, face images at various angles need to be collected in advance, and then the face image to be detected is aligned with the face image collected in advance, however, in practical application, the face image to be detected does not always face the camera, and deflection occurs in a three-dimensional space in most cases, so that the face pose (the deflection angle of the face around each coordinate axis in the three-dimensional space) in the face image to be detected needs to be identified, and the face alignment can be performed.
In addition, the head rotation direction and the eye fixation position can be obtained through posture estimation, the basis of human-computer interaction and visual monitoring in a multi-view environment is provided, the human face posture is corrected through the posture estimation, and the accuracy of multi-view human face recognition and analysis can be improved.
The face image is recorded with face information in a two-dimensional space (XY plane), and therefore, it is relatively easy to estimate the face pose γ (the angle of deflection around the Z axis perpendicular to the XY plane) on the XY plane, and generally the angle between the line between the two eyes and the X axis (horizontal direction).
In addition, for a frontal face, the rotation angle γ in the XY plane can be calculated by the inclination angle of the line connecting the centers of both eyes, but for a face that is severely affected by perspective and is deflected laterally, even if there is no rotation in the plane, the line connecting the centers of both eyes also has an inclination angle, as shown in fig. 1, and therefore, the rotation angle γ cannot be simply adopted as a method of calculating the inclination angle of the line connecting the centers of both eyes.
The general human face three-dimensional sparse model is a parameterized 3D model, is originally used for the application of human face coding based on the model, and has a small number of matching points and triangular surfaces, so that the modeling of the general human face three-dimensional sparse model only needs little computing time, and is widely applied to video animation and transmission, and fig. 2 is a standard wire frame structure of the general human face three-dimensional sparse model. Multi-view face pose fast estimation method on single image suitable for arbitrary rotation in plane
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a single multi-view face image posture estimation method capable of rotating freely in a plane, solves the technical problem that the target face posture is detected by relying on prior conditions in the prior art, can realize target face posture estimation only by a single image to be detected, and does not need to be trained or learned in advance.
In order to solve the technical problems, the invention provides the following technical scheme: a single multi-view face image posture estimation method capable of rotating randomly in a plane comprises the following steps:
step 1: establishing a pre-evaluation value set of a gamma angle according to a face image to be detected, wherein the gamma angle represents a deflection angle around a Z axis;
step 2, traversing the estimated value set of the gamma angles, and calculating α and β angles corresponding to the estimated values of the gamma angles by adopting a calculation method of solving α and β angles meeting an objective function under the condition of the specified gamma angles, wherein α represents a deflection angle around an X axis, and β represents a deflection angle around a Y axis;
and 3, combining the values of the objective function corresponding to the gamma angle estimated values into an alternative set, selecting a minimum objective function value from the alternative set, and taking the gamma angle estimated values, α angles and β angles corresponding to the minimum objective function value as the human face posture estimation parameters of the human face image to be detected.
Preferably, in step 1, a search algorithm is used to establish a set of estimated values of γ angles, and the method includes the following steps:
step 101: detecting an included angle theta between a central line of two eyes and a horizontal line on a face image to be detected;
step 102: determining the estimated range of the gamma angle:
Figure BDA0001910550310000021
Figure BDA0001910550310000022
is the search range;
step 103: search is performed in search steps: γ ═ θ ± t; wherein, t is the current searching times,
Figure BDA0001910550310000023
carrying out positive and negative searching by using a searching step length t in each searching; storing the obtained estimated value of the gamma angle into an estimated value set of the gamma angle every time the search is carried out;
step 104: and after the search is finished, establishing an estimated value set of the gamma angle.
Preferably, in step 2, α angles and β angles corresponding to the estimated values of the gamma angles are calculated in parallel according to the estimated values of the gamma angles.
Preferably, the method for calculating α and β angles under the specified gamma angle in step 2 comprises the following steps:
step 201: establishing general human face three-dimensional sparse model
Figure BDA0001910550310000024
The general human face three-dimensional sparse model
Figure BDA0001910550310000025
The human face three-dimensional sparse model is a general human face three-dimensional sparse model which does not deflect on an X, Y, Z axis;
step 202: establishing general human face three-dimensional sparse model
Figure BDA0001910550310000026
Three-dimensional coordinate matrix V of upper designated point3D
Figure BDA0001910550310000031
The designated point comprises a reference point;
wherein the content of the first and second substances,
Figure BDA0001910550310000032
three-dimensional sparse model representing general human face
Figure BDA0001910550310000033
The (i) th designated point of (c),
Figure BDA0001910550310000034
step 203: establishing general human face three-dimensional sparse model of human face image to be detected
Figure BDA0001910550310000035
Two-dimensional coordinate matrix V of matching points corresponding to the upper designated point2D: the matching points do not include reference points;
Figure BDA0001910550310000036
wherein the content of the first and second substances,
Figure BDA0001910550310000037
it represents the i-th matching point and,
Figure BDA0001910550310000038
n is the number of face matching points on the face image to be detected;
step 204, taking the vector X as an independent variable (s, α), and initializing values of s, α and β, wherein s represents a scaling coefficient, α represents a deflection angle around an X axis, and β represents a deflection angle around a Y axis;
step 205: universal human face three-dimensional sparse model rotating around Z axis at specified gamma angle
Figure BDA0001910550310000039
206-rotating the Utility model around the X-axis at an angle of αFace three-dimensional sparse model
Figure BDA00019105503100000310
And rotating the general human face three-dimensional sparse model around the Y axis at an angle of β
Figure BDA00019105503100000311
Universal human face three-dimensional sparse model after rotation by scaling factor s
Figure BDA00019105503100000312
Zooming is carried out;
step 207: the zoomed general human face three-dimensional sparse model
Figure BDA00019105503100000313
Orthographic projection is carried out on an XY plane, and a two-dimensional projection model is obtained
Figure BDA00019105503100000314
Step 208: translation two-dimensional projection model
Figure BDA00019105503100000315
Modeling two-dimensional projection
Figure BDA00019105503100000316
The reference point on the face image is superposed with the reference point on the face image to be detected; the reference point is contained in the matching point;
step 209: from two-dimensional projection models
Figure BDA00019105503100000317
Establishing a target function by the sum of squares of the distances between the upper designated point and the corresponding point on the face image to be detected;
step 2010, updating the vector X (s, α) by using a search algorithm, and repeating the steps 206 to 208 each time the vector X is updated until the optimal solution of the objective function is searched;
step 2011: and storing the optimal solution of the objective function into the alternative set.
Preferably, the designated points include a subnasal point, a corner point of eyes, a nose tip point, and a mouth corner point, and the reference point is a subnasal point among the matching points.
Preferably, the objective function minF (X) is constructed using an internal penalty function method as follows:
minF(X)=min[f(X)+r/s];
Figure BDA0001910550310000041
wherein r is a barrier factor, r > 0; s is a scaling factor;
(X) representing a two-dimensional projection model
Figure BDA0001910550310000042
The sum of squares of the distances between the upper designated point and the corresponding point on the face image to be detected,
Figure BDA0001910550310000043
wherein n represents a two-dimensional projection model
Figure BDA0001910550310000044
The number of the upper designated points;
R3Dthree-dimensional sparse model representing general human face
Figure BDA0001910550310000045
The rotation matrix of (a);
P3Dthree-dimensional sparse model representing general human face
Figure BDA0001910550310000046
The forward projection matrix of (a);
S3Dthree-dimensional sparse model representing general human face
Figure BDA0001910550310000047
The scaling matrix of (a);
T2Drepresenting two-dimensional projection models
Figure BDA0001910550310000048
The translation matrix of (a) is,
Figure BDA0001910550310000049
Figure BDA00019105503100000410
indicating a reference point on the face image to be detected,
Figure BDA00019105503100000411
representing two-dimensional projection models
Figure BDA00019105503100000412
The above reference point.
Preferably, in step 2010, the optimal solution of the objective function minf (x) is calculated by using a modified Newton method, and the method comprises the following steps:
step 111: let the current iteration number be k, k being an integer greater than or equal to zero, and the current gradient vector
Figure BDA00019105503100000413
XkRepresenting a current vector;
step 112: the initialization k is 0 and the initialization k is,
Figure BDA00019105503100000414
and jumps to step 116;
step 113: constructing a Newton direction: calculating the current function F (X)k) Current direction derivative P ofkAccording to the following formula:
Pk=-Gk -1gkwherein G iskIs F (X)k) The Hesse matrix of (a) is,
Figure BDA00019105503100000415
Figure BDA00019105503100000416
step 114: one-dimensional search is carried out, and the current iteration step length t is calculated by using a golden section methodkTo update the current vector XkThe updated vector isXk+1,Xk+1=Xk+tkPkAnd calculating F (X)k+1);
Step 115: let k equal k +1, rk+1=crkC is the obstacle factor reduction coefficient, c is 0.1, and step 116 is entered;
step 116: judge g | |kIf the | is less than or equal to the established limit, the given limit is set; if yes, go to step 117; if not, go back to step 113;
step 117: judgment of rkWhether the/s is less than or equal to true or not; if yes, stopping iteration and using current vector XkOutputting as an optimal solution; if not, go back to step 113.
Compared with the prior art, the invention has the following advantages:
1. the method directly carries out attitude estimation on the target face on a single image without knowing the camera parameters of the image, taking other attitude pictures of the target face as references and needing no prior training or learning, and is simple to realize.
2. The method separates the estimated values of the gamma angle and the α and β angles, solves the problems of complex independent variable, large calculated amount and sensitivity to initial iteration values of a target function caused by simultaneous solving of rotation angles in three directions in the prior art, calculates the α and β angles corresponding to each gamma angle estimated value in a parallel mode after estimating the gamma angle, and greatly improves the operation speed.
3. According to the invention, based on the included angle theta between the central line of the two eyes and the horizontal line, the optimal human face plane external deflection angles α and β in a certain range around the included angle theta are searched to obtain the in-plane rotation angle gamma of the multi-view human face, so that the in-plane rotation angle calculation errors caused by large parallax and human face deflection are avoided.
4. The invention utilizes the universal human face three-dimensional sparse model after rotation, scaling, projection and translation
Figure BDA0001910550310000051
α which is overlapped with the face image to be detected, thereby the two-dimensional image can not be directly detected,β corner, converting to solve general human face three-dimensional sparse model
Figure BDA0001910550310000052
The human face postures around the X axis and the Y axis on the two-dimensional image are detected (under the condition of specifying the gamma angle).
5. The model coincidence process and the solving process of the objective function have synchronicity: the vector X needs to be continuously updated in the process of solving the optimal solution of the objective functionkEvery time vector X is updatedkThen the updated s, α and β pairs of universal human face three-dimensional sparse models are used
Figure BDA0001910550310000053
And rotating and zooming are carried out, and then projection and coincidence are carried out, so that the solving process of the optimal solution can be visually represented, and the coincidence degree of the model and the face image to be detected can be visually represented.
6. To ensure that s, α, β is calculated under the condition that s > 0, an internal penalty function is used to construct the augmented objective function of f (X).
7. The target function of the invention is calculated based on the distance from point to point in a two-dimensional plane, and the calculation in a three-dimensional space is not needed, so that the dimension is reduced, and the calculation speed can be improved.
8. The designated points are infranasal points, binocular corner points, nasal cusp points and mouth corner points, the characteristics of the points are prominent and easy to position, and only 8 designated points are adopted, so that the calculation speed can be greatly improved.
9. In the method for estimating the deflection angle of the human face around the X, Y axis, the translation amount of the model is determined by a method of overlapping the subnasal points, so that independent variables in an objective function are reduced to s and α, the model is constrained to rotate only by taking the subnasal point as the center by increasing the alignment point of the nasal tip, the complexity of an algorithm and the dependency on an initial point are reduced, and the α estimation can be completed only by small iteration times.
Drawings
FIG. 1 is a schematic illustration of the line connecting the centers of the eyes;
FIG. 2 is a standard wireframe structure diagram of a general human face three-dimensional sparse model;
FIG. 3 is a flow chart for calculating α, β angles at a specified γ angle;
fig. 4 is a test effect diagram of the method for estimating the pose of a single multi-view face image arbitrarily rotated in a plane in the present embodiment.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and preferred embodiments.
A single multi-view face image posture estimation method capable of rotating randomly in a plane comprises the following steps:
step 1: establishing a pre-evaluation value set of a gamma angle according to a face image to be detected, wherein the gamma angle represents a deflection angle around a Z axis;
step 2, traversing the estimated value set of the gamma angles, and calculating α and β angles corresponding to the estimated values of the gamma angles by adopting a calculation method of solving α and β angles meeting an objective function under the condition of the specified gamma angles, wherein α represents a deflection angle around an X axis, and β represents a deflection angle around a Y axis;
and 3, combining the values of the objective function corresponding to the gamma angle estimated values into an alternative set, selecting a minimum objective function value from the alternative set, and taking the gamma angle estimated values, α and β angles corresponding to the minimum objective function value as estimation parameters of the human face pose of the human face image to be detected.
In the present embodiment, in step 2, α angles and β angles corresponding to the estimated values of each γ angle are calculated in parallel according to the estimated values of each γ angle.
In this embodiment, the search algorithm is used to establish the estimated value set of the γ angle in step 1, and the following steps are performed:
step 101: detecting an included angle theta between a central line of two eyes and a horizontal line on a face image to be detected;
step 102: determining the estimated range of the gamma angle:
Figure BDA0001910550310000071
Figure BDA0001910550310000072
is the search range;
step 103: search is performed in search steps: γ ═ θ ± t; wherein, t is the current searching times,
Figure BDA0001910550310000073
carrying out positive and negative searching by using a searching step length t in each searching; storing the obtained estimated value of the gamma angle into an estimated value set of the gamma angle every time the search is carried out;
step 104: and after the search is finished, establishing an estimated value set of the gamma angle.
In this embodiment, as shown in fig. 3, the method for calculating α and β angles under the condition of specifying the γ angle in step 2 includes the following steps:
step 201: establishing general human face three-dimensional sparse model
Figure BDA0001910550310000074
The general human face three-dimensional sparse model
Figure BDA0001910550310000075
The human face three-dimensional sparse model is a general human face three-dimensional sparse model which does not deflect on an X, Y, Z axis; the general face three-dimensional sparse model can adopt a code-3 and sparse face grid model and the like;
step 202: establishing general human face three-dimensional sparse model
Figure BDA0001910550310000076
Three-dimensional coordinate matrix V of upper designated point3D
Figure BDA0001910550310000077
The designated point comprises a reference point;
wherein the content of the first and second substances,
Figure BDA0001910550310000078
three-dimensional sparse model representing general human face
Figure BDA0001910550310000079
To (1) aThe number of the i designated points is,
Figure BDA00019105503100000710
step 203: establishing general human face three-dimensional sparse model of human face image to be detected
Figure BDA00019105503100000711
Two-dimensional coordinate matrix V of matching points corresponding to the upper designated point2D: the matching points do not include reference points;
Figure BDA00019105503100000712
wherein the content of the first and second substances,
Figure BDA00019105503100000713
it represents the i-th matching point and,
Figure BDA00019105503100000714
n is the number of face matching points on the face image to be detected;
step 204, taking the vector X as an independent variable (s, α), and initializing values of s, α and β, wherein s represents a scaling coefficient, α represents a deflection angle around an X axis, and β represents a deflection angle around a Y axis;
step 205: universal human face three-dimensional sparse model rotating around Z axis at specified gamma angle
Figure BDA00019105503100000715
206, rotating the general human face three-dimensional sparse model around the X axis at an angle of α
Figure BDA00019105503100000716
And rotating the general human face three-dimensional sparse model around the Y axis at an angle of β
Figure BDA00019105503100000717
Universal human face three-dimensional sparse model after rotation by scaling factor s
Figure BDA00019105503100000718
Zooming is carried out;
step 207: the zoomed general human face three-dimensional sparse model
Figure BDA00019105503100000719
Orthographic projection is carried out on an XY plane, and a two-dimensional projection model is obtained
Figure BDA0001910550310000081
Step 208: translation two-dimensional projection model
Figure BDA0001910550310000082
Modeling two-dimensional projection
Figure BDA0001910550310000083
The reference point on the face image is superposed with the reference point on the face image to be detected; the reference point is contained in the matching point;
step 209: from two-dimensional projection models
Figure BDA0001910550310000084
Establishing a target function by the sum of squares of the distances between the upper designated point and the corresponding point on the face image to be detected;
step 2010, updating the vector X (s, α) by using a search algorithm, and repeating the steps 206 to 208 each time the vector X is updated until the optimal solution of the objective function is searched;
step 2011: and storing the optimal solution of the objective function into the alternative set.
In this specific embodiment, the designated points include a subnasal point, a corner point of eyes, a nose tip point, and a mouth corner point, and the reference point is a subnasal point in the matching points.
In this embodiment, the objective function minF (X) is constructed using an interior penalty function method as follows:
minF(X)=min[f(X)+r/s];
Figure BDA0001910550310000085
wherein r is a barrier factor, r > 0; s is a scaling factor;
(X) representing a two-dimensional projection model
Figure BDA0001910550310000086
The sum of squares of the distances between the upper designated point and the corresponding point on the face image to be detected,
Figure BDA0001910550310000087
wherein n represents a two-dimensional projection model
Figure BDA0001910550310000088
The number of the upper designated points;
R3Dthree-dimensional sparse model representing general human face
Figure BDA0001910550310000089
The rotation matrix of (a);
P3Dthree-dimensional sparse model representing general human face
Figure BDA00019105503100000810
The forward projection matrix of (a);
S3Dthree-dimensional sparse model representing general human face
Figure BDA00019105503100000811
The scaling matrix of (a);
T2Drepresenting two-dimensional projection models
Figure BDA00019105503100000812
The translation matrix of (a) is,
Figure BDA00019105503100000813
Figure BDA00019105503100000814
indicating a reference point on the face image to be detected,
Figure BDA00019105503100000815
representing two-dimensional projection models
Figure BDA00019105503100000816
The above reference point.
Of course, min f (X) can also be directly used as the objective function, but convergence is slow, and a negative solution of s occurs.
In this embodiment, s is an initial value s in step 2040For pupil distance and two-dimensional projection model on human face image to be detected
Figure BDA0001910550310000091
Ratio of interpupillary distance above, initial value α of α, β0、β0Are all 0 degrees; initial value r of r0=100。
In this embodiment, in step 2010, a modified Newton method is used to calculate an optimal solution of an objective function minf (x), and the method includes the following steps:
step 111: let the current iteration number be k, k being an integer greater than or equal to zero, and the current gradient vector
Figure BDA0001910550310000092
XkRepresenting a current vector;
step 112: the initialization k is 0 and the initialization k is,
Figure BDA0001910550310000093
and jumps to step 116;
step 113: constructing a Newton direction: calculating the current function F (X)k) Current direction derivative P ofkAccording to the following formula:
Pk=-Gk -1gkwherein G iskIs F (X)k) The Hesse matrix of (a) is,
Figure BDA0001910550310000094
Figure BDA0001910550310000095
step (ii) of114: one-dimensional search is carried out, and the current iteration step length t is calculated by using a golden section methodkTo update the current vector XkThe updated vector is Xk+1,Xk+1=Xk+tkPkAnd calculating F (X)k+1);
Step 115: let k equal k +1, rk+1=crkC is the obstacle factor reduction coefficient, c is 0.1, and step 116 is entered;
step 116: judge g | |kIf the | is less than or equal to the established limit, the given limit is set; if yes, go to step 117; if not, go back to step 113;
step 117: judgment of rkWhether the/s is less than or equal to true or not; if yes, stopping iteration and using current vector XkOutputting as an optimal solution; if not, go back to step 113.
In the present embodiment, f (x) is expanded and simplified as:
Figure BDA0001910550310000096
wherein, c0To c12Are all constants and are calculated as follows:
Figure BDA0001910550310000097
Figure BDA0001910550310000098
Figure BDA0001910550310000101
Figure BDA0001910550310000102
Figure BDA0001910550310000103
Figure BDA0001910550310000104
wherein n represents a two-dimensional projection model
Figure BDA0001910550310000105
The number of upper matching points.
Experiments on virtual 3D faces and real face images show that the average estimation error of the invention for α angles is 6.5 degrees, the average estimation error of β angles is 4.6 degrees, the calculation time of the deflection estimation of the face around the X, Y axis of a specified in-plane rotation angle is less than 1ms, a parallel calculation mode of an independent thread is created for the deflection estimation calculation of each axis around the X, Y axis, the average calculation time of the whole algorithm is less than 5ms, and partial test effects are shown in figure 4.

Claims (9)

1. A single multi-view face image posture estimation method capable of rotating randomly in a plane is characterized in that: the method comprises the following steps:
step 1: establishing a pre-evaluation value set of a gamma angle according to a face image to be detected, wherein the gamma angle represents a deflection angle around a Z axis;
step 2, traversing the estimated value set of the gamma angles, and calculating α and β angles corresponding to the estimated values of the gamma angles by adopting a calculation method of solving α and β angles meeting an objective function under the condition of the specified gamma angles, wherein α represents a deflection angle around an X axis, and β represents a deflection angle around a Y axis;
step 3, combining the values of the objective functions corresponding to the gamma angle pre-estimated values into an alternative set, selecting a minimum objective function value from the alternative set, and taking the gamma angle pre-estimated values, α and β angles corresponding to the minimum objective function value as the human face posture estimation parameters of the human face image to be detected;
in the step 1, a search algorithm is adopted to establish an estimated value set of a gamma angle, and the method comprises the following steps:
step 101: detecting an included angle theta between a central line of two eyes and a horizontal line on a face image to be detected;
step 102: determining the estimated range of the gamma angle:
Figure FDA0002482594810000011
Figure FDA0002482594810000012
is the search range;
step 103: search is performed in search steps: γ ═ θ ± t; wherein, t is the current searching times,
Figure FDA0002482594810000013
carrying out positive and negative searching by using a searching step length t in each searching; storing the obtained estimated value of the gamma angle into an estimated value set of the gamma angle every time the search is carried out;
step 104: and after the search is finished, establishing an estimated value set of the gamma angle.
2. The method for estimating pose of single multi-view face image with arbitrary rotation in plane according to claim 1, wherein the method for calculating α and β angles under the designated γ angle in step 2 comprises the following steps:
step 201: establishing general human face three-dimensional sparse model
Figure FDA0002482594810000014
The general human face three-dimensional sparse model
Figure FDA0002482594810000015
The human face three-dimensional sparse model is a general human face three-dimensional sparse model which does not deflect on an X, Y, Z axis;
step 202: establishing general human face three-dimensional sparse model
Figure FDA0002482594810000016
Three-dimensional coordinate matrix V of upper designated point3D
Figure FDA0002482594810000017
The designated point comprises a reference point;
wherein the content of the first and second substances,
Figure FDA0002482594810000018
three-dimensional sparse model representing general human face
Figure FDA0002482594810000019
The (i) th designated point of (c),
Figure FDA00024825948100000110
step 203: establishing three-dimensional sparse model of face to be detected and general face on face image
Figure FDA00024825948100000111
Two-dimensional coordinate matrix V of matching points corresponding to the upper designated point2D: the matching points do not include reference points;
Figure FDA00024825948100000112
wherein the content of the first and second substances,
Figure FDA0002482594810000021
it represents the i-th matching point and,
Figure FDA0002482594810000022
n is the number of face matching points on the face image to be detected;
step 204, taking the vector X as an independent variable (s, α), and initializing values of s, α and β, wherein s represents a scaling coefficient, α represents a deflection angle around an X axis, and β represents a deflection angle around a Y axis;
step 205: universal human face three-dimensional sparse model rotating around Z axis at specified gamma angle
Figure FDA0002482594810000023
206, rotating the general human face three-dimensional sparse model around the X axis at an angle of α
Figure FDA0002482594810000024
And rotating the general human face three-dimensional sparse model around the Y axis at an angle of β
Figure FDA0002482594810000025
Universal human face three-dimensional sparse model after rotation by scaling factor s
Figure FDA0002482594810000026
Zooming is carried out;
step 207: the zoomed general human face three-dimensional sparse model
Figure FDA0002482594810000027
Orthographic projection is carried out on an XY plane, and a two-dimensional projection model is obtained
Figure FDA0002482594810000028
Step 208: translation two-dimensional projection model
Figure FDA0002482594810000029
Modeling two-dimensional projection
Figure FDA00024825948100000210
The reference point on the face image is superposed with the reference point on the face image to be detected; the reference point is contained in the matching point;
step 209: from two-dimensional projection models
Figure FDA00024825948100000211
Establishing a target function by the sum of squares of the distances between the upper designated point and the corresponding point on the face image to be detected;
step 2010, updating the vector X (s, α) by using a search algorithm, and repeating the steps 206 to 208 each time the vector X is updated until the optimal solution of the objective function is searched;
step 2011: and storing the optimal solution of the objective function into the alternative set.
3. The method for estimating the pose of a single multi-view face image rotated arbitrarily in a plane according to claim 2, wherein: the designated points comprise subnasal points, binocular eye corner points, nasal cusp points and mouth corner points, and the reference points are the subnasal points.
4. The method for estimating the pose of a single multi-view face image rotated arbitrarily in a plane according to claim 2, wherein: the objective function min f (X) is as follows:
Figure FDA00024825948100000212
Figure FDA0002482594810000031
wherein n represents a two-dimensional projection model
Figure FDA0002482594810000032
The number of upper matching points;
R3Dthree-dimensional sparse model representing general human face
Figure FDA0002482594810000033
The rotation matrix of (a);
P3Dthree-dimensional sparse model representing general human face
Figure FDA0002482594810000034
The forward projection matrix of (a);
S3Dthree-dimensional sparse model representing general human face
Figure FDA0002482594810000035
The scaling matrix of (a);
T2Drepresenting two-dimensional projection models
Figure FDA0002482594810000036
The translation matrix of (a) is,
Figure FDA0002482594810000037
Figure FDA0002482594810000038
indicating a reference point on the face image to be detected,
Figure FDA0002482594810000039
the reference points on the representation.
5. The method for estimating the pose of a single multi-view face image rotated arbitrarily in a plane according to claim 2, wherein: the objective function min F (X) is constructed using the internal penalty function method as follows:
min F(X)=min[f(X)+r/s];
Figure FDA00024825948100000310
wherein r is a barrier factor, r > 0; s is a scaling factor;
(X) representing a two-dimensional projection model
Figure FDA00024825948100000311
The sum of squares of the distances between the upper designated point and the corresponding point on the face image to be detected,
Figure FDA00024825948100000312
wherein n represents a two-dimensional projection model
Figure FDA00024825948100000313
The number of the upper designated points;
R3Drepresenting a generic faceThree-dimensional sparse model
Figure FDA00024825948100000314
The rotation matrix of (a);
P3Dthree-dimensional sparse model representing general human face
Figure FDA00024825948100000315
The forward projection matrix of (a);
S3Dthree-dimensional sparse model representing general human face
Figure FDA00024825948100000316
The scaling matrix of (a);
T2Drepresenting two-dimensional projection models
Figure FDA00024825948100000317
The translation matrix of (a) is,
Figure FDA00024825948100000318
Figure FDA00024825948100000319
indicating a reference point on the face image to be detected,
Figure FDA00024825948100000320
representing two-dimensional projection models
Figure FDA00024825948100000321
The above reference point.
6. The method for estimating the pose of a single multi-view facial image rotated arbitrarily in a plane according to claim 5, wherein: initial value s of s in step 2040For pupil distance and two-dimensional projection model on human face image to be detected
Figure FDA00024825948100000322
Ratio of interpupillary distance above α, βInitial value α0、β0Are all 0 degrees; initial value r of r0=100。
7. The method for estimating the pose of a single multi-view facial image rotated arbitrarily in a plane according to claim 5, wherein: in step 2010, an optimal solution of an objective function minF (X) is calculated by adopting a modified Newton method, and the method comprises the following steps:
step 111: let the current iteration number be k, k being an integer greater than or equal to zero, and the current gradient vector
Figure FDA0002482594810000041
XkRepresenting a current vector;
step 112: the initialization k is 0 and the initialization k is,
Figure FDA0002482594810000042
and jumps to step 116;
step 113: constructing a Newton direction: calculating the current function F (X)k) Current direction derivative P ofkAccording to the following formula:
Pk=-Gk -1gkwherein G iskIs F (X)k) The Hesse matrix of (a) is,
Figure FDA0002482594810000043
Figure FDA0002482594810000044
step 114: one-dimensional search is carried out, and the current iteration step length t is calculated by using a golden section methodkTo update the current vector XkThe updated vector is Xk+1,Xk+1=Xk+tkPkAnd calculating F (X)k+1);
Step 115: let k equal k +1, rk+1=crkC is the obstacle factor reduction coefficient, c is 0.1, and step 116 is entered;
step 116: judge g | |kWhether | is less than or equal toGiven a termination limit; if yes, go to step 117; if not, go back to step 113;
step 117: judgment of rkWhether the/s is less than or equal to true or not; if yes, stopping iteration and using current vector XkOutputting as an optimal solution; if not, go back to step 113.
8. The method for estimating the pose of a single multi-view facial image rotated arbitrarily in a plane according to claim 5, wherein: (x) expanded and simplified as:
Figure FDA0002482594810000045
wherein, c0To c12Are all constants and are calculated as follows:
Figure FDA0002482594810000046
Figure FDA0002482594810000047
Figure FDA0002482594810000048
Figure FDA0002482594810000051
Figure FDA0002482594810000052
Figure FDA0002482594810000053
wherein n represents a two-dimensional projection model
Figure FDA0002482594810000054
The number of upper matching points.
9. The method for estimating the pose of a single multi-view facial image rotated arbitrarily in a plane according to claim 1, wherein in step 2, α angles and β angles corresponding to each gamma angle estimated value are calculated in parallel according to each gamma angle estimated value.
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