TWI374392B - Face recognition method based on the estimated curvature - Google Patents

Description

Γ374392

101 years 7 replacement page ~ I IX, invention description: [Technical field of the invention] The present invention relates to a curvature calculation method, in particular, a line integral method for calculating curvature, so that the curvature is applied Applications in the field of 2D face recognition or other computer graphics. - [Prior Art] The traditional development of face recognition using two-dimensional (2D) images is that even for the same person, the facial image still has great variation and sex, and there are many reasons for the variation. For example, light, posture, expression changes, etc., consider the use of two-dimensional information to improve the accuracy of face recognition. Using the = face information, face recognition can be protected from changes in light, and even changes in posture can be easily corrected. In the field of computer graphics, many applications need to use information about curvature, such as contour alignment, contour cutting, image processing, feature extraction, and object recognition. Therefore, information on robust curvature can increase these. Application performance and accuracy. Φ In the application of 2D face recognition, there are two basic requirements for the features obtained from the surface of the face: 1. The captured features should be able to represent the local characteristics on the surface of the face (丨ocal characteristics). 'That is, the geometrical properties of different areas of the surface of the face will change', so the features used should be able to reflect such changes. 2. In the case of noise interference, such as the noise of the sensor, the error caused by the signal being converted into digitization, etc., the calculation result of this feature must be 5 Γ 374392. The correction is stable and reliable on July 5, 101. of. In order to meet the requirements of the above two points, it is better to adopt the curvature feature, because the curvature feature is not affected by the change of the observation angle, that is, the characteristic of invariant, and the curvature feature is defined at one point. The infinitesimal surrounding area, which means that it can represent the local characteristics on the surface, so the 3D face recognition system using the curvature feature will greatly improve the recognition performance. However, the current curvature calculation method is susceptible to noise and quantization error during numerical calculations. The calculation result is very unstable. Please refer to the original sine of adding Gaussian noise as shown in Figure 6A. Wave k' 'derivative of tangent (M. Worring and AWM Smeulders. Digital curvature estimation) > Calabi et al. 'calculation method (e_ Clabi, P. j. 〇lver, C. Shakiban, A Tannenbaum, and S. Haker. Differential and numerically invariant signature curves applied to object recognition. International Journal of Computer Vision, 26(2): 107-135, 1998) and Taubin calculation (G. Taubin.

Estimatin the tensor of curvature of a surface form a polyhedral approximaiton. In Proc International Conference on Computer Vision, pages 902-907, 1995) Two kinds of different ways of estimating curvature are shown in Figures 6 to 6d, respectively. There is a significant difference between the continuous curvature (indicated by the dashed line) and the estimated curvature (indicated by the solid line). If the curvature of the closed curve of Figure 7A is estimated, the tangent is 6 Γ 374392 L — Ψ Γ 曰, 曰, let me only derivative (derivative oftangent), Caiabieta 丨, 计 曾法 W calculation method of the estimated curvature Displayed in the seventh B~7〇's respectively, the same is true in the actual curvature (there is a significant gap between the virtual mountains) and the estimated curvature (solid line representation). [Invention] Therefore, the object of the present invention is Provide a fast method to solve the problem of noise and quantization error on the error of the alien error' and calculate the curvature for computer image recognition. In order to achieve the foregoing objectives, the present invention comprises: a three-dimensional face image generated by using a three-dimensional face information, a 3D material image; a singular identification for performing image pre-processing, and a temperature _ π ^ Τ Take a look at the two-dimensional face image who is / normalized; 豕 advance to select the area to be processed, injury ^ λ ... in the three-dimensional face image to select the image area to be processed < take out an implementation Curvature calculation, the transmission of ^·, +, 3D face image to be processed to the shadow of the curvature to + curvature and vertical curvature, wherein the curvature of the leaf further includes the following steps: 仃 define the line integral area, tied to a song A book out of the book Xin Xi Xi Temple is a Beijing ^ and judges the prime minister's one, set a radius value and define the circle where the pixel point is the center of the circle; 1 solid M to judge the circle and the intersection of the curve & A second coordinate of the second & the circle intersects the curve at the intersection of the younger brother and a second intersection 駄I," This is the person who went to the poem Chu W. And the second intersection and the point have a second coordinate and a third point respectively Line integral area, first phase six mail - ~ re-seat 7 1374392 July 5, 101 revised replacement page ^ to calculate the first coordinate and the second coordinate difference to calculate a first vector, the first coordinate Calculating a second vector from the difference between the third coordinate; the angle between the first vector and the coordinate axis is set to - the first angle, and the second vector and the coordinate axis of the coordinate axis are set to - a second lost angle; inputting a radius value, a first lost angle, and a second angle to a plurality of trigonometric functions 5 to obtain a plurality of trigonometric operation results, and inputting the result of the one angular function into a total variance a matrix; performing eigenvalue decomposition on the common variance matrix to obtain an eigenvalue of the common variogram matrix; inputting the eigenvalue into a judgment formula to determine a curvature value of the pixel point, according to the total pixel point The curvature value identifies the facial features of the face.

Wherein the pixel point on the curve is a, and the circle defined by the 3 points is a radius r, so that the circle intersects the curve at the first intersection point 6 and the second intersection point b to form a line integral. The area 〇, the first vector system is G, and the second vector system is ac; the first vector d and an X axis have a first angle, and the angle between the second vector ac and an X axis is defined as In the step of calculating the covariance matrix of the line integral region by a trigonometric function, let X be rc〇s<9, y be rsin0, X2 be r2c〇s20, y2 be r2sin20, and the covariance matrix Σβ(〇) It is represented by angle & integral to q and expressed as; Σ0(〇= w) 1 Γ ι2Λχ) JaM ia(y2)\ La(C) Ja(x)L(y) i2Ay) h (χ2) = -~ [ θ{ -θ0+ sin θλ cos θλ - sin θ0 cos θ0 ] 2 where 8 丄j/4392 » · I〇(y2) =—[ei-0o-(sin θλ cos 6>, - sin θ0 cos θ0)] Person (work = ^^ίη2 Θ - sin2 Θ.] /0(^) = r2[sin^ -sin^J h W = ~r2 [cos θλ - cos θ0 ] A (C) = "(β - θ0 〇, in the step of performing eigenvalue decomposition on the common variator matrix, The matrix D = c^g(A],;g and the orthogonal matrix 干 干 LVJJ, the orthogonal matrix 'has two eigenvectors Vl, v2; the foregoing step of calculating the curvature value of the pixel point using the eigenvalue In the middle, it is determined whether the inner product of the first-dimensional quantity and the second vector and any of the feature vectors have the same sign t 'if the symbols are different, the curvature value of the pixel point: K~S-7, if the symbols are the same The curvature value of the prime point is 2r. In the process of line integral, the trigonometric function is used to reduce the complexity of the operation, and the curvature is estimated compared with other integral methods.

In the present invention, only the constant complexity can be calculated to calculate the curvature of the household, and the 3D face image can be recognized by the curvature. [Embodiment] "Monthly reference to the figure - No, for the curve - 〇 ' want to estimate the curvature of a point a (S.) on the curve, first the tangent vector of the point "(s.) (tangent vector And the normal vector (n〇rma丨vect〇r) respectively correspond to the real space—the X-axis and the y-axis, as an area coordinate system of the point a(s.). Then, the Taylor expansion (Tay|〇r expansj〇n) can be derived at ^0. The regional curve equation y of this point is: 9 July 5, 2011, the correction replaces a hundred less = coffee) = grandchild) + attack (9) + f f (9) + ρ - since g (0) = 0, g, (〇) =茗 and 茗(0) is the curvature of the point a(s.), where the above equation is expressed as eight y=g(x)«-x2 (2) where κ is the curvature of the stagnation point of 〇:0). Taking a(s.) as the center of the circle r as the radius, a circle Ω can be obtained. r 51 Ω, where a(s) intersects at two points to form a region C where the line is integrated. (3) I(f) = icf(x,y)dl ,·^^&)}' The line integral of the above formula/(7) can be expressed as c = {〇, state / = is shown as: 1(f) « 1(f) = Jn+ f(X>y)dl - jf f{r,y)dy^ f(-r,y)dy (4) where the upper half of the circle, ie W = {(x,_y) ) W = 〆, (4). Principal Component Analysis (PCA) is applied to the region C. If the current Χ == η / | Γ α... L L less, then the covariance matrix of the region c is not: I ( C) = Jc(xm)(Xm)^/ (5) where 1((:)=[edge,, 7 v

Jc ζΛ Χβ represents the length and center of gravity of C, respectively. Because the region Ω: is symmetrical, skew you & too, & 存 for any odd function f its line integral f(/) is zero. I{x) « 7(jc) = 〇. (6) I(xy) «I(xy) =: 〇 Using the above formula (4), we can get (7) Γ374392 r2dl ^-r3-Kr* 2 Similarly, 2, π 3 Λ: 3 Λ I(y ) «—r3--r , , ' 7 2 12 (8) /〇)»2r2- K 4 L = /(1) (9)(10) (11) The covariance matrix Σ((:) can be expressed as Σ(〇-r3-xr4 〇2 1 0 0 - 0 -r3--r6 L 2 12 J_~ _ 斯~Kr2 〇(2r2 ' r _ (12) / According to the above formula (12), the relationship between the curvature % line integral regions C can be expressed as: ^'Γ3-/cr4 =r> ^ ^1·1 .Σ, 2r r4 where Συ Is the region C line 从8 from u (13). The deep integration of the covariance matrix is obtained by the characteristic decompose) (4) - the eigenvalues of the two x-axes, The purpose of special micro-value decomposition is to do the day-to-day conversion. 4 猱 system and real coordinate system The following is for the real coordinate system, please refer to the _ B -. Curvature estimation further < 哼第The main steps are as follows: 'When estimating the radius of any point a on the curve, a circle ^^ is obtained, and the sheep takes a as the center of the circle, "Yes, A and the curve intersect at two points b and c to form ~ 11 1374392 The region C of the July 101 line integral, the first vector and the χ axis have a missing angle of 0, and the _ vector ac and the X axis have an angle of 0丨. 2. Using trigonometric function integration, convert X to rcos0, y to broad as 0 X2 to r2cos20, y2 to PsinM, from angle 61. Integration to q, you can get the covariance matrix of the regional C line integral. ^匸), using trigonometric function integration can reduce the complexity of the operation, and make the curvature operation more efficient. Λ (^2) = γ + sin Θ, cos - sin θ0 cos θ0 ]

Hiy ) = ~[^-〇0~ (sinθλ cos- sinθ0 cosθ0)] r3 /a(^) = —[si^^-sin2^] 2 L(x) = r2 [sin Θλ - sin θ0 ] 1 a (^) = ~r2 [cos θλ - cos θ0 ]

La(Q = r(0}-0o) Σ0(〇= Ύ) ^(xy) 1 ι2Λχ) k(4) L{y2)\ La(C) iliy) (14) 3. Due to the matrix of covariances\(〇 A symmetric matrix, so there exists - orthogonal matrix V, and satisfies the following formula '(〇 = ^ (15) - the characteristic matrix D = 唂 唂 (from " v = [ViV2]. The covariance matrix is C ) is a real number and (4), so the two eigenvectors, the heart, and the lines are orthogonal to each other. 4 The unit tangent at point a is denoted as ...), which must be parallel to the eigenvector heart or v2, and the eigenvectors are parallel to...) Then, the curvature can be calculated as the eigenvalue of the system (refer to equation (13). Here, by means of the two directions: the symbol of the product, the heart, and "', where /=1, 2, the characteristics can be determined. The value of the right feature is parallel to t(4), and the two inner products have the same sign. 12 The judgment code can be expressed as Λ: »-ί-_ Λ. 2r〆else

Referring to the third figure in Fig. 3, when the curvature estimation is performed by the sinusoidal waveform shown in the first paragraph of the present invention, ":: real =: the estimated curvature (indicated by the solid line) is quite close to the actual curvature (in the case of the dotted line)曲率The curvature of the closed curve shown in Figure 7A is estimated. The results are as shown in the fourth figure. The same results are obtained. 八° The practical application of the invention: FRGC version 2.0 (Face Recognition Grand

Challenge 3D face image for face recognition experiments. In the frgc data set, the resolution of the 3D face image is 64〇χ48〇, and all the face images are divided into two parts: the training part (training partm〇n) and the validation partition (validation partition). There are 943 and 4〇〇 7 3D images. There are six sets of experiments in FRGC version 2_0, of which Experiment 3 is designed for 3D face recognition, the purpose of which is to evaluate the effectiveness of 3D face recognition technology. In Experiment 3, there are two parts of experiment 3s and experiment 3t; experiment 3s is only used for shape channe in 3D image and 3t is used only for texture channel in 3D image because curvature estimation is compared with shape channe丨Correlation 'so only use shape channe丨 data as 13 1374392 ♦ « July 5, 2011 revised replacement page identification basis, FRGC experiment 3 s as a test environment. The results of the experiment are presented in the form of a Receiver Operating Characteristic (ROC) curve. The horizontal axis of the R〇c curve is the False Acceptance Rate and the vertical axis is the Verification Rate. The result of the experiment is stored in a matrix of 4007x4007, called the similarity matrix. In the similarity matrix, the values of the jth row and the column represent the validation partition. The i-th image and the j-th image, the similarity β between the two is further explained as follows: The FRGC data is from the University of Notre Da me. These data are biological features that are polymorphic. A subject session represents a collective name for collecting a person's biometrics and collecting these images. Each object set contains 4 controlled still images, 2 uncontrolled φ static images and 1 3D image (including shape and texture information). Please refer to Appendix A to Annex I for the display. All the images contained in a set of objects, the four controlled images represented by Figure A of Figure A, are not taken in the environmental background of the photo studio. The lighting environment of the front facial image is two sets of lights (two Species or three kinds of photographic lights) and two facial expressions (smile or normal expression); and the two uncontrolled images shown in Figure 8 are taken in different brightness environments ( Like in the corridor, atrium, outdoor), it also contains two expressions (smile or normal). The image is controlled by the Viv丨d 900/910 sensor in the control of brightness 374392. Replace ΐ~~ Shooting in the environment 'In FRGC, 3D images are composed of range and texture channels ° Static images are shot with a 4 million pixel Canon PowerShot G2 camera' image resolution of 1704χ2272 or 1200x1600, format Is JPEG The size of an image to be stored is between 2 Mbytes and 3.1 Mbytes. The 3D image is obtained by the Minolta Vivid 900/910 series sensor. The photosensitive elements of the Minolta Vivid 900/910 series sensor can take a color image of 640x480, and the subject person stands or sits about 1_5 meters away from the sensor. The FRGC uses images that do not use the 900/910 series to reduce the resolution of the fast mode, making the resolution of 3D face images 64 〇χ 480. The data of the FRGC experiment is divided into a training group and a confirmation group. The training group was taken in the 2002-2003 school year and can be further divided into two training sets (trajnjng sets). The first large static training set was used to train a static face recognition algorithm. It contained 222 subjects and had 12 776 images, of which 6,388 were controlled still images and 6 388 It is an uncontrolled static image, and each subject has 9 to 16 object sets (subjeet sessiGns>. Among the second large static training set, there are 943 object sets (subject sessi〇ns), Contains 3 broom images, controlled images, and uncontrolled still images. The 3D training set is used to train 3d algorithms. When comparing 3D and static algorithms, static faces The algorithm can be trained from the 3D training set. The 3D face scan is 15 Γ 374392 in the 2〇〇2_2〇〇3 year, and the correction is collected on July 5, 101. The image of the Validation partition is in 2003- It was collected during the 2004 school year. 'It contains 466 subjects with 4,007 subject sessions. The demographics of the confirmed group are classified by gender, age, ethnicity. Each subject further contains 'to 22 subject sessi o door s ° 3D face recognition process A, access to 3D face information: With the current 3D scanner technology, a 3D image usually contains two parts, texture and shape. Texture represents two-dimensional color or gray The image represents the shape of the surface of the object. In order to explore the best recognition performance of pure 3D technology, it is deliberate not to use 2D face images, but only use 3D face information (shape B Pre-processing: Normalize the 3D face information directly using FRGC baseline, for example, normalizing the face shape (p〇se), size _ (size), position (丨ocation). A face area: the frgc baseline algorithm directly uses a three-dimensional image of the entire face surface after normalization, but in the present invention, it is a certain area of the face surface, for example, the rectangle is circled on the second attachment. The selected area is characterized by the curvature information of the area as the feature vector. D. Curvature calculation: FRGC baseline is directly used to calculate the 3D data of the face. In the selected area, each point (p'lxe|) is taken from the area, and the horizontal and vertical curvature of the point is calculated 1734392.. • I am revised on July 5, 2011. Rate is used as the basis for identification. As shown in Annex III, the horizontal curvature feature of the 3D image of the face surface is displayed. Red indicates a value with a large curvature, and blue indicates a value with a small curvature. We can observe that the curvature of the nose is large and the value is positive. The value of the corner of the eye is negative, so the curvature can reflect the regional characteristics of the face. . E. Reduce the dimension of the feature vector: PCA (Principal Component analysis) or LDA (Linear Discriminant Analysis) can be used to reduce the dimension of the feature vector without affecting the recognition performance. The advantage is that the classification can be reduced ( The computational complexity of classification. As mentioned above, there are 943 = 'quasi' V images in the FRGC training group. By using these data, a low-dimensional vector space can be trained. After the original feature vector is projected into the low-dimensional vector space, The effect of reducing the dimension can be achieved. Two more F, Classification: The similarity between Mahalanobis cosine as the feature vector. The larger the value, the similarity between the two, please refer to the fifth figure, using curvature as the invariant feature. Greatly improve the performance of the 3D face recognition system, compared to the Ca|ab丨丨^ algorithm (shown by curve b), the Taubin estimate method, the estimate#忐(curve c), etc. Method, the estimation method of the present invention (curve a: (fA. . . ^ ^丁11 has a good recognition ability (aiscnminating capability) = [schematic description]

First Figure 2 is a schematic diagram showing the curvature of the point on the estimated curve of the present invention on the estimated curve of the present invention. Another illustration of the curvature of the point. 17 Second figure: This is a schematic diagram of the estimation of the positive estimate of the six-A diagram of the present invention. Curvature Curvature Curvature Estimation 2: Fruit::: The invention is closed to the closed curve. The fifth figure is a comparison chart of the present invention and its efficiency. It is used for 3D face recognition. /, A~6D: a sine wave curve and a schematic diagram for estimating the curvature of the curve in a conventional manner.

A seven-D diagram is a schematic diagram of a one-time closed curve and a conventional method for estimating the curvature of the curve. Annex A to Annex I D: is an image contained in a subject sessi〇n. Annex 2: A schematic diagram of selecting a face area. Annex II. Schematic diagram of the curvature characteristics when using the present invention to identify a human face. [Main component symbol description] Benefits *,

Claims (1)

1374392 I · Patent application scope: -1 - ' 1 · - Use the line integral ancient + quality mountain * method, including: & curvature to identify the face image using 2D face information, take the _ ^ ..., servant - 3D scanner to capture the 3D face image generated by the object to be identified; perform image pre-processing, take the normalization _; * Aberdeen 2D face image is selected for processing The area, passed in #一处理处理影像 area...隹Selected in the face image - Perform curvature calculation, calculate the point of each pixel point in the front & face face, V like a curve open, / water + curvature and vertical curvature, wherein the implementation of the dry leaf really further comprises the following steps: taking a book on a curve and taking the first coordinate of the pixel point, setting a radius value and the same as the tomb a circle with the estimated point as a circle; determining a two-point coordinate of the circle intersecting the curve, the circle and the curve being the father at a first intersection point and the first phase of the flute forming a line integral region, wherein The first intersection point is on the silver __ The first intersection of the younger brother has the second coordinate and the second coordinate. Before the Chengdi. The difference between the first coordinate and the second coordinate of the wall is calculated as a first vector, to lose, +, enough ^ A month The coordinate and the third seat calculate a second vector; this difference is the first vector ifo ^ , the angle between a private axis is set to - the first angle, the angle of the first _ | is calculated; - the first inward The angle between the coordinate axis and the coordinate axis is set to a IK ife. 19 1374392 July 5, 2011 repair j Enter the aforementioned radius value, the first-declination angle, and the second angle into a plurality of two-dimensional function calculation formula to obtain a plurality of trigonometric operation results, the trigonometric operation results are input to a common variogram matrix; eigenvalue decomposition is performed on the covariance matrix to obtain eigenvalues of the covariance matrix; the eigenvalue is input to Judging formula to determine the curvature value of the pixel point, and identifying the facial face of the face based on the curvature value of all the pixel points 2) A method for recognizing a face image using a curvature calculated by line integral as described in the item i of the patent application, wherein: the pixel point on the curve is a, defined by the pixel point 3 as a center The circle has a radius r such that the circle intersects the curve at the first intersection point b and the second intersection point c to form the line integration region, the first vector is g, and the second direction is; the first vector There is a first angle 弋 between 3 and an X axis, and the angle between the _ vector ac and an X axis is defined as the second angle. Calculate the covariance matrix of the line integral region by trigonometric function, let X be rcos0, y be rsin0, X2 be r2cos20, y2 be r2sin20, : covariance matrix Σβ (〇 is from angle 0. integral to 3 and Expressed as; " Σσ(〇= L(x2) LM Λ(^) Uy2) 丄ι2Λχ) LaiC)Ua{x)L{y) ia^)ia{y)iliy) where , .r3 total CO = y [Θ, - Θ. + sin 0 cos Θ - sin 0. Cos ] ,r3 L(y ) = — [^i - - (smcos- sinθ0 cosθ0)] 20-day correction for "5^ (^) = — [sin2 θλ - sin2 θύ] h (χ) = r2 [sin χ χ - sin θ0 ] ^〇(y) = ~r2[cos^, - cos^J 4(.)=咐-6>0). 3 · If the ninth curvature of the patent application is used to identify the face image, M j is calculated using the line integral to calculate the line eigenvalue decomposition step 1 to find the intersection matrix of the common variability matrix V 卩 ·. Matrix D = do this (ΛΛ) and the positive parent matrix v = [ViV2], the orthogonal moment /, there are two features facing V;, v2; using this eigenvalue to calculate the system judgment when -τ 异出6玄In the step of estimating the curvature value of the nose point, the right side returns Μ η and the inner product of the second vector and any eigenvector is the same as the paying number. The curvature value of the pixel point is the target paying number, if the symbols are different The curvature value of the pixel point is uli, 2r r4 π eight. 2r r4 Η一,图: If the next page 21 1-374392, * ~~ July 5, 2003 revised replacement page VII. Designated representative map: (1) The representative representative of the case is: (2). (2) A brief description of the symbol of the representative figure·· None 8. If there is a chemical formula in this case, please disclose the chemical formula that best shows the characteristics of the invention: