System and method for face recognition with two-dimensional sensing modality

A system for facial recognition in which facial images in a database are defined by facial coordinates in a plane common to other images in order to facilitate comparison or likeness of the facial images:

• at least one input operatively connected to the at least one processor and configured to input the corners of the eyes and mouth coordinates F1, F2, F3, F4, F5, F6, F7, F8, F9, F10, F11, F12 from a facial image into the at least one processor using a vector
• F=(F1, . . . ,F12)t
• where t represents the transpose, F1 represents the horizontal coordinate of the left eye outer corner, F2 represents the vertical coordinate of the left eye outer corner, F3 represents the horizontal coordinate of the left eye inner corner, F4 represents the vertical coordinate of the left eye inner corner, F5 represents the horizontal coordinate of the right eye outer corner, F6 represents the vertical coordinate of the right eye outer corner, F7 represents the horizontal coordinate of the right eye inner corner, F8 represents the vertical coordinate of the right eye inner corner, F9 represents the horizontal coordinate of the left mouth corner, F10 represents the vertical coordinate of the left mouth corner, F11 represents the horizontal coordinate of the right mouth corner, and F12 represents the vertical coordinate of the right mouth corner;
• the at least one processor configured to convert the first coordinates F1, F2, F3, F4, F5, F6, F7, F8, F9, F10, F11, F12 into second coordinates for the corners of the eye and mouth in a virtual vertical plane comprising P1=(−xe1,ye1,0), P2=(−xe2,ye2,0), P3=(xe1,ye1,0), P4=(xe2,ye2,0), P5=(−xm,ym,0), and P6=(xm,ym,0), where P1 is the estimated left eye outer corner coordinates, P2 is, the estimated left eye inner corner coordinates, P3 is the estimated right eye outer corner coordinates, P4 is the estimated right eye inner corner coordinates, P5 is the estimated left mouth corner coordinates and P6 is the estimated right mouth corner coordinates;
• and wherein x and y represent horizontal and vertical distances from a facial reference point, xe1 and −xe1 represent the horizontal coordinates of the outer corners of the eyes, xe2 and −xe2 represent the horizontal coordinates of the inner corners of the eyes, ye1 and ye2 represent the vertical coordinates of the outer and inner corners of the eyes, xm and −xm represent the horizontal coordinates of the corners of the mouth, ym represent the vertical coordinates of the corners of the mouth in the virtual vertical plane;
• the at least one processor being configured to solve for the parameter vector Vp using the equation Vp=(xe1, ye1, xe2, ye2, xm, ym, θ, φ, ψ, α)t wherein the parameter vector Vp comprises 10 parameters xe1, ye1, xe2, ye2, xm, ym, θ, φ, ψ, α and wherein θ represents the yaw, φ represents the pitch, ψ represents the roll and α represents the scale in the following equation:
• Vp=(xe1,ye1,xe2,ye2,xm,ym,θ,φ,ψ,α)t
• where xe1, ye1, xe2, ye2, xm, ym, represent the virtual plane coordinates of the corners of the eyes and mouth in the vertical virtual plane, and wherein the error to be minimized is the error between the inputted corners of the eyes and mouth coordinates F1, F2, F3, F4, F5, F6, F7, F8, F9, F10, F11, F12 and the least square estimation model function f(Vp) coordinates of the estimated inputted corners of the eyes and mouth coordinate values comprising horizontal coordinates f1(Vp), f3(Vp), f5(Vp), f7(V) f9(Vp), f11(Vp),and vertical coordinates f2(Vp), f4(Vp), f6(Vp), f8(Vp), f10(Vp), f12 (Vp) and where the least square model function f(Vp) is computed using
• f1(Vp)=α[1,0,0]TP1
• f2(Vp)=α[0,1,0]TP1
• f3(Vp)=α[1,0,0]TP2
• f4(Vp)=α[0,1,0]TP2
• f5(Vp)=α[1,0,0]TP3
• f6(Vp)=α[0,1,0]TP3
• f7(Vp)=α[1,0,0]TP4
• f8(Vp)=α[0,1,0]TP4
• f9(Vp)=α[1,0,0]TP5
• f10(Vp)=α[0,1,0]TP5
• f11(Vp)=α[1,0,0]TP6
• f12(Vp)=a [0,1,0]TP6
• where T correlates to the head orientation θ, φ, ψ and the matrix T=Tθ·Tφ·Tψ
• where
• T
• θ
• =
• [
• cos
• 
• 
• θ
• sin
• 
• 
• θ
• 0
• -
• sin
• 
• 
• θ
• cos
• 
• 
• θ
• 0
• 0
• 0
• 1
• ]
• T
• φ
• =
• [
• cos
• 
• 
• φ
• 0
• sin
• 
• 
• φ
• 0
• 1
• 0
• -
• sin
• 
• 
• φ
• 0
• cos
• 
• 
• φ
• ]
• T
• ψ
• =
• [
• 1
• 0
• 0
• 0
• cos
• 
• 
• ψ
• sin
• 
• 
• ψ
• 0
• -
• sin
• 
• 
• ψ
• cos
• 
• 
• ψ
• ]
• .
• whereby the common plane coordinates P1 through P6 are used to find a match in a database of a plurality of images of people represented by facial coordinates in a plane common to other images in order to identify or recognize an individual.

A system for facial recognition in which facial image representations stored in a database are defined by facial coordinates in a plane common to other images in the database;

• at least one processor configured to compare the likeness of the facial images by comparing the common plane facial coordinates, the common plane being determined by the locations of the eyes and mouth corners;
• at least one input operatively connected to the at least one processor and configured to input the corners of the eyes and mouth coordinates from a facial image into the at least one processor;
• the at least one processor configured to convert the inputted coordinates for the corners of the eyes and mouth into estimated coordinates in a common plane by minimizing the error between the inputted corners of the eyes and mouth coordinates and the estimated coordinates corners of the eyes and mouth obtained from an estimation of the common plane coordinates of the corners of eyes and mouth;
• the at least one processor configured to perform facial recognition to determine identification of a subject by comparing the common plane facial coordinates of an inputted facial image.