Face Recognition Using Log-Polar Images and Gabor Filters María José Escobar, Javier Ruiz-del-Solar, José Rodríguez P.
Abstract The MLPG architecture, a new biologically based architecture for face recognition is here proposed. In this architecture log-polar images and Gabor Filtering are employed for modeling the way in which face images are processed between the retina and the primary visual cortex. Some simulations of the recognition abilities of the MLPG using the Yale Face Database are presented, together with a comparison with the EBMG and LPG architectures.
Introduction •Face Recognition is a very lively and expanding research field, where many different approaches have been proposed to solve this task. •Gabor analysis is biologically based, and their oriented filters (Gabor filters) model the kind of visual processing carried out by the simple and complex cells of the primary visual cortex of higher mammals.
Introduction •Log-Polar Transformation - LPT models the Retinothopic Mapping of the visual information between the retina and the area V1 of the visual cortex. •Dynamic link architecture is a general face recognition technique that represents the faces by projecting them onto an elastic grid where a Gabor filter bank response is measured at each grid node. The recognition of the faces is performed by measuring the similarity of the filter response at each node (Gabor-Jets) between different face images.
Introduction •One of the most successful dynamic link architectures is the Elastic Bunch Graph Matching - EBGM. •In a previous work, we presented a face recognition system based on the EBGM architecture, and in which input images are first processed using the LPT. This architecture was called LPG ( Log-Polar Gabor architecture ). •Here we proposed a modified version of LPG, called MLP ( Multi Log-Polar Gabor architecture ), in which we use several log-polar images instead just one.
Architecture Proposed
Log-Polar Transformation ( ) If I(x,y) is a rectangular image in I x , y Cartesian coordinates, then the LPT with origin (x 0 ,y 0 ) will be given by: ( ) { ( ) ( ) } ρ φ = I * , L I x , y ; x 0 , y 0 where ( ) , ρ = M log r ( ) ( ) , = − + − 2 2 r x x y y 0 0 ( ) ρ , φ − I * y y φ = − 1 0 tan a − x x 0
Log-Polar Transformation In the presented architecture, we will use four different Log-Polar images ( Fp = 4), obtained using as center of the transformation the position of each pupil (a. for the right pupil and b. for the left one), the center of the mouth (c.) and the middle point between the eyes (d.).
Gabor Filtering r ( ) = The Filters used are given by ( ): x x , y r ( ) − σ − r 2 2 2 r r k ( ) 1 x ψ = − j x exp exp i k x exp σ σ j j 2 2 2 2 ϕ + r v 2 π k k cos − µ = = jx v = π ϕ µ = µ k k 2 2 ϕ j k k sen v µ jy v 8 With ν and µ the parameters of the frequency and orientation respectively. The width of the Gaussian depends of the σ = π frequency and is given by 2 k j The family of Gabor Filters used (5 frequencies and 8 orientation) is:
Gabor Filtering The Gabor Filtering is applied to our Fp Log-polar different images, centering the filters in the middle of the lowest row of each one. When the hole family of filters is applied to each image, we obtain a Gabor- = Jet formed by a vector of 40 complex numbers ( ). J j , j 0 ,..., 39 + σ + σ 2 r x 2 y ( ) ( ) ( ) ( ) ∑ ∑ = = ψ − − J x J x , y I i , j x i , y j j j j = − σ = − σ i x 2 j y 2 ψ where is the j -th member of the family of Gabor Filters. j
Similarity Matching This block measures the similarity between two groups of Gabor-Jets. T T To compare the group of Fp Gabor-Jets ( J ) of the image I ,with the group n M of Fp Gabor-Jets ( ) of the image M we use the following expression: J I n ( ) ( ) F 1 ∑ p = T M T M S I , I S J , J G a n n F = n 1 p ( ) S This expression is the mean value of the similarities measures , which is a given by: Gf ∑ T M a a ( ) j j = = T M j 1 S J , J a ( ) ( ) Gf Gf ∑ ∑ 2 2 T M a a j j = = j 1 j 1 i = a where , is the magnitude of the j -th complex component of the j 1 ,..., G j f i Gabor Jet . J
Simulations We perform a comparison between our proposed MLPG architecture, with the LPG and EBGM architectures. Table 1. Mean recognition rates using different numbers of training images per class (N), and taking the average of 20 different training sets (small numbers correspond to the standard deviations). N EBGM LPG MLPG 91.96% 74.11% 70.41% 2 (3.58%) (5.63%) (4.85%) 3 93.42% 79.38% 82.00% (2.01%) (4.04%) (4.09%) 4 95.05% 83.33% 83.90% (1.87%) (3.29%) (3.68%) 5 94.88% 85.55% 87.89% (1.97%) (2.98%) (3.02%) 6 94.87% 89.13% 88.27% (2.12%) (2.25%) (2.83%) 7 96.25% 89.75% 90.25% (1.82%) (3.55%) (3.09%) 8 95.55% 91.22% 91.77% (2.11%) (3.45%) (3.48%)
Simulations Table 2. Total number of multiplications needed to obtain the Gabor-Jets for recognition. EBMG LPG MLPG 1009664 946176 63104
Conclusions •In our biologically based approach, the way in which face images are processed between the retina and the primary visual cortex of our visual system, is modeled using the Log-Polar Transformation and Gabor Filtering. •The simulations were done using the Yale Face Database and compared with the EBMG and LPG architectures. •The recognition rates obtained with MLPG are slightly smaller than EBMG and very similar to LPG. •MLPG has an smaller computational cost than EBMG or LPG. MLPG is 16 times faster than EBMG and 15 times faster than LPG.
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