Statistical models of shape and appearance (combined appearance models) were introduced by Cootes, Edwards, Lanitis and Taylor [2,3,7], and have since been applied extensively in medical image analysis [9,12,16]. 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.
Fig. 1. The effect of varying the first model
parameter of a brain appearance model by standard deviations.
Using the notation of Cootes [3], 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
![]() |
(3) |
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
![]() |
(4) |
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.