Statistical Shape Analysis of Surfaces in Medical Images Applied to the Tetralogy of Fallot Heart - Modeling in Computational Biology and Biomedicine - page 179

Fig. 5.9 The first five PLS modes of variation that describe 99 % of the observed BSA variability
and 61 % of the observed shape variability in the population

5.3.3.2 Generating a Growth Model Using Canonical Correlation Analysis

Using PLS as described above allows us to predict BSA given the shape, however
what we would like is to estimate the shape given BSA. To reverse the relationship
we use canonical correlation analysis (CCA) on the PLS shape vectors (the t i s of
Algorithm 9 ). CCA computes the vectors r and s that maximize the correlation
between the two sets X and Y

corr ( Xr,Ys ) 2 , max

|r| = |s| =1

(5.10)

where Y is the vector of BSA values and X =[ t 1 ,...t N ] is the matrix of shape

T

descriptors.