Statistical models of shape and appearance (combined appearance models) were introduced by Cootes, Edwards, Lanitis and Taylor [1,2,7], and have since been applied extensively in medical image analysis [9,13,17]. The construction of an appearance model depends on establishing a dense correspondence across a training set of images using a set of landmark points marked consistently on each training image.
Using the notation of Cootes , the shape (configuration of landmark points) can be represented as a vector and the texture (intensity values) represented as a vector .
The shape and texture are controlled by statistical models of the form
where are shape parameters, are texture parameters, and are the mean shape and texture, and and are the principal modes of shape and texture variation respectively.
Since shape and texture are often correlated, we can take this into account in a combined statistical model of the form
where the model parameters control the shape and texture simultaneously and , are matrices describing the modes of variation derived from the training set. The effect of varying one element of for a model built from a set of 2D MR brain image is shown in Fig. 1.
Fig. 1. The effect of varying the first model parameter of a brain appearance model by standard deviations.