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Adaptive CoDT Feature Space

To combine the strengths of generative and discriminative approaches for image classification, we characterize our proposed CoDT features of a HEp-2 cell image by a gradient vector derived from a generative model of the training data to model the generation process of the features, and then we feed the output image representations into a discriminative classifier for the identification of HEp-2 cells.

Let X = {xn, n = 1,2,N} be a set of samples from the CoDT feature space of one HEp-2 cell image. The probability density distribution of the CoDT feature, which is used to model the generative process of elements in the feature space, is described by a GMM. Let X = {wt, pt, %t, t = 1,2,..., T} denote the parameters of the GMM, where wt, /ut and Xt respectively denotes the mixture weight, mean vector and covariance matrix of Gaussian t. Then we can formulate

and pt (xn |X) is the Gaussian t defined as

where D is the dimension of the CoDT feature. Actually, the GMM, which models the generation process of the CoDT features, can be regarded as a probabilistic codebook/vocabulary [21]. The parameters of GMM can be adaptively estimated by the Expectation Maximization (EM) algorithm [22] based on the training CoDT feature space. Briefly, EM algorithm can be implemented by the following two steps: Expectation step (E step): the posteriori probability for each training data xn is given by

Maximization step (M step): the means, variances and mixture weights are updated by

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Each Gaussian component can be treated as a micro-texton word of the micro- texton vocabulary while wt corresponds to the relative frequency of word t, represents the mean of the word and Et is the variation around the mean. In the followings, the covariance matrices are assumed to be diagonal and denoted by ot = diag(Et).

 
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