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Topic 14A in .NET Integrating barcode 39 in .NET Topic 14A .net vs 2010 barcode




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Topic 14A using none todisplay none for asp.net web,windows applicationbarcode generation without using components in c#.net Statistical pattern recognition USS 93 14A.1. Matching featur none for none e vectors using statistical methods Statistical pattern recognition, as mentioned above, is a process worthy of an entire book, and in fact many books have been written on the topic. Here, through a simple example [13.17], we will present just a glimpse of what the discipline entails.

Our problem is to recognize faces. Let s rst collect images which contain only faces (and thereby avoid the segmentation problem) by requiring the subjects all wear black clothing and stand against a black wall. We acquire relatively low-resolution images, 180 120 pixels.

We then scan over the image with a collection of feature extractors, shown in Fig. 14.5.

Each feature extractor operates on the neighborhood of each pixel, in much the same way that a kernel operator does, but instead of a sum of products, this operator returns the product of the image pixels corresponding to the black pixels in the kernel. First, we observe that each kernel, used in this way, is returning a very local autocorrelation of the image, in a particular direction. Denote the result of applying kernel i to the neighborhood of pixel j by i j .

Then, the sum. Fig. 14.5. The collection of 25 kernels used to extract a 25-element feature vector from an image. xi = i j (14.58). is computed, producing a 25-element vector which in some sense describes the image. Statistical pattern recognition So for every im age, we have a vector consisting of 25 numbers. Using that 25-vector, the challenge is to properly make a decision. The rst step is to reduce the dimensionality to something more manageable than 25.

We look for a method for reducing the dimensionality from, in general, d dimensions, to c 1 dimensions, where we are hoping to classify the data into c classes. (Somehow, we must know c, which in this example is the number of individual faces.) The following strategy is an extension of a method known in the literature as Fisher s linear discriminant.

Assume we have c different classes, and a training set, X i of examples from each class. Thus, this is a supervised learning problem. De ne the within-class scatter matrix to be.

SW = (14.59). where Si = x X i 2 3. Fig. 14.6.

The none for none between-class scatter is a measure of the total distance between the class means and the overall mean.. (x i )(x (14.60). and i is the me none none an of class i. Thus, Si is a measure of how much each class varies from its average. .

1 x. n i x X i (14.61). We de ne the between-class scatter matrix as SB = ni (. )(. )T ,. (14.62). where is the me an of all the points in all the training sets and n i is the number of samples in class i. To see what this means, consider Fig. 14.

6. The between-class scatter is a measure of the sum of the distances between each of the class means and the overall sample mean. Maximization of some measure of SB will push the class means apart, away from the overall mean.

The idea is to nd some projection of each data vector x onto a vector y, y = Wx (14.63). such that rst, none none y is of lower dimension than x, and second, the classes are better separated after they are projected. The projection from d-dimensional space to c 1 dimensional space is accomplished by c 1 linear discriminant functions yi = wiT x. (14.

64). If we view the yi as components of a vector, and the vectors wi as columns of a matrix W, we can describe all the discriminant functions by a single matrix equation y = W T x. (14.65).

We now de ne a none for none criterion function which is a function of W and measures the ratio of betweenclass scatter to within-class scatter. That is, we want to maximize SB relative to SW , or rather,. Topic 14A Statistical pattern recognition 1 1 1 to max none none imize some measure of SW SB . The trace of SW SB is the sum of the spreads of SW SB 1 in the direction of the principal components of SW SB . We can see clearly what this means in the two-class case.

1 J = trSW SB =.
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