χ2 test for feature detection

摘要

In this paper, χ2 tests are applied to detect local visual features. Each feature and its noise is modeled by a random vector Y with a multivariate normal distribution, denoted by Y ∼ N(μy,∑y). The mean vector μy and the variance-covariance matrix ∑y characterize the structure of the feature. Blurring in real images is modeled by Gaussian distribution. The variance vector in the blur is obtained by simulated annealing, and estimated by a linear matrix B. Then B is used to blur each feature Y. Let Z = BY + N1, where N1 is a random vector for noise, then Z ∼ N(μz, ∑z) = N(Bμy, B1∑yB + ∑N). After the transformation f(Z):(Z-μz)t ∑z−1 (Z-μz), the random vector Z becomes a random variable with χ2 distribution. Therefore, the χ2 test can measure the similarity between data and the expectation vector of each model.