• Cao, J. and Worsley, K.J. (1999). The geometry of the Hotelling's T^2 field with applications to the detection of shape changes. Technical Report, Bell Labs.

    Abstract

    An exact expression for the expected Euler characteristic (EC) of the excursion set of the Hotelling's T^2 random field is obtained, and the behaviour of the Hotelling's T^2 field near local extrema is studied. This extends previous results for Gaussian random fields (Adler, 1981) and chi^2, t and F fields (Worsley, 1994). The main application is the detection of local changes in the mean of a multivariate Gaussian random field, using a test based on the maximum of a field of Hotelling's T^2 statistics. For large thresholds, the expected EC accurately approximates the P-value of the maximum of a smooth stationary random field. These results are applied to the detection of changes in brain shape using the 3D deformations required to warp brain anatomy to match an atlas standard. These deformations are modelled as a tri-variate Gaussian random field, and the above theory is used to investigate the difference in brain shape between a sample of 29 males and 23 females.

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