Feature Extractors in .NET

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for face recognition [11], the extraction of facial subgraphs for head pose estimation [12], the analysis of Gabor kernels using univariate statistical techniques for discriminative region nding [13], the weighting of elastic graph nodes using quadratic optimization for authentication [14], the use of principal component analysis (PCA) to determine the importance of Gabor features [15], boosting Gabor features [9], and Gabor frequency/orientation selection using genetic algorithms [16]. A relevant work on Gabor lters for face recognition that is closely related to the research presented here is by Wiskott et al. [17]. Their work [17 21] proposes a framework for face recognition that is based on modeling human face images as labeled graph. Termed elastic bunch graph matching (EBGM), the technique has become a cornerstone in face recognition research. Each node of the graph is represented by a group of Gabor lters/wavelets (called jets ) which are used to model the intensity variations around their locations. The edges of the graph are used to model the relative location of the various jets. Since the jets represent the underlying image characteristics, it is desirable to place them on ducial points on the face. This is achieved by manually marking the locations of the facial ducial points using a small set of controlled graphs that represent general face knowledge, which represents an average geometry for the human face. In our work, a genetic algorithm is used to obtain the spatial location of the ducial points. Besides automating the process of locating these points, our work identi es spatial locations on the face image that are unique to every single person, rather than relying on an average geometry. Closely following the work of Wiskott et al., Lyons et al. [22] proposed a technique that uses Gabor lter coef cients extracted at (1) automatically located rectangular grid points or (2) manually selected image feature points. These coef cients are then used to bin face images based on sex, race, and expression. The technique relies on a combined principal component analysis (PCA) dimensionality reduction and linear discriminant analysis (LDA) classi cation over the extracted Gabor coef cients, to achieve a pooling of images. While the classi cation task is not related directly to identifying individuals from face images, this technique also demonstrates the ability of Gabor lters to extract features that can encode subtle variations on facial images, providing a basis for face identi cation.
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Gabor Filters
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Mathematically, Gabor lters can be de ned as follows:
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(x, y) =
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1 G (x, y) S , (x, y) , 2 x y ,
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(5.1)
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G (x, y) = exp
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(x cos + y sin )2 ( x sin + y cos )2 + 2 2 2 x 2 y 2 2 2 ,
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S , (x, y) = exp {i ( x cos + y sin )} exp
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(5.3)
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Person-Speci c Characteristic Feature Selection for Face Recognition
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where r G (x, y) represents a Gaussian function.
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r S , (x, y) represents a sinusoid function. r (x, y) is the spatial location where the lter is centered with respect to the image axis. r is the frequency parameter of a 2D sinusoid. r 2 represents the variance of the Gaussian (and thus the lter) along the dir speci ed direction. dir can be either x or y. The variance controls the region around the center where the lter has in uence.
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From the de nition of Gabor lters, as given in Eq. (5.1), it is seen that the lters are generated by multiplying two components: a Gaussian Function G (x, y) [Eq. (5.2)] and a Sinusoid S , (x, y) [Eq. (5.3)]. The following discussions detail the two components of Eq. (5.1).
Gaussian Function
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The 2D Gaussian function de nes the spatial spread of the Gabor lter. This spread is de ned by the variance parameters of the Gaussian, along the x and y direction together with the orientation parameter . Figure 5.1a shows a 3D representation of the Gaussian mask generated with x = 10 and y = 15 and rotation angle = 0. The image in Figure 5.1b shows the region of spatial in uence of an elliptical mask on an image, where the variance in the x direction is larger than the variance in the y direction. Typically the Gaussian lter has the same variance along both the x and y directions, that is, x = y = . Under such conditions the rotation parameter does not play any role as the spread will be circular.
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