Hierarchical Fusion of Multi Spectral Face Images for Improved ... - IIIT

face is detected using triangle based face detection algorithm [10]. Let the size ofdetected face image I ( x,y)be N x N. Face image is transformed into its log polar form.The log polar transformation converts original face image I ( x,y)into I ( r,θ ) in whichthe angular coordinates are represented on the vertical axis and the logarithmiccoordinates of radius are represented on the horizontal axis. More precisely, with respectto a center point x , y ),(c cr = log ( x − xc)2+ ( y − yc)2, 0 ≤ r ≤ r−⎛ y − yθ tan 1 c⎞=⎜⎟ , 0 ≤ θ ≤ 2π⎝ x − xc⎠max(1)Here a crucial decision is the choice of center point x , y ). In a face image, there are(c cvery few points such as the center of mouth, eye locations, and nose tip which remainconsistent and are easy to locate. The proposed face detection algorithm uses thecoordinates of both eyes to detect a face image. The best choice is the center x , y ) of(c cline joining the two eye coordinates and the proposed algorithm uses this point as thecenter point. The mapping process converts the scale change and rotation of face imageinto constant horizontal and cyclic vertical shifts in the log polar plane. This processeliminates the need for using multiple templates to cover scale and rotation variations offace image.In the next step, polar face image is expressed into 2D Fourier domain,1⎡ 2πr 2πj ⎤I ( ρ,φ)= ∑∑I( r,θ j ) exp⎢−i ρ + φµλ⎥ (2)r j⎣ µ λ ⎦4