Generative modeling of medical images

Probabilistic inference consists of estimating a probability
distribution based on a limited number of randomly sampled
observations. When these observations are images, Euclidean inference
(assuming no prior covariance among voxels) often fails to estimate a
representative distribution of the data. This problem can be overcome
by accounting for two characteristics of images: first, their
intrinsic smoothness, which is captured by a local covariance among
voxels; and second, their topology, which captures the fact that the
objects represented in the images are invariant under some families of
transformations (e.g., multiplicative or additive changes of
appearance, affine or non-linear spatial deformations).

In this talk I will show that a set of images can be described by a
mean and a distribution of transformations (of a given type), such
that a single transformation from the distribution would map the mean
image to a sample from the set of images, and that the particular
transformation type depends on the nature of the variability to be
modeled. I will show two practical applications capitalizing on this
framework: the estimation of sensitivity fields in multi-coil MR
acquisitions, and the estimation of brain templates in computational
anatomy. I will then show that by extending the model of prior
covariance from capturing local smoothness only, to having a
non-stationary form, more structured deviations from the mean image
can be captured. This concept will be applied to the estimation of
shape and appearance variability in the human brain.