Chi2 Test for Feature Detection

Abstract In this paper, χ 2 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 ( μ y ,∑ y ). The mean vector μ y 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 + N 1 , where N 1 is a random vector for noise, then Z ∼ N ( μ z , ∑ z ) = N ( Bμ y , B 1 ∑ y B + ∑ N ). After the transformation f ( Z ):( Z - μ z ) t ∑ z −1 ( Z - μ z ), the random vector Z becomes a random variable with χ 2 distribution. Therefore, the χ 2 test can measure the similarity between data and the expectation vector of each model.