ABSTRACT
In this section we present results in Lee et al. (2004) [214]. The landmark data
reduction approach in high level image analysis has led to significant progress
to scene recognition via statistical shape analysis (see Dryden and Mardia
(1998) [91]). While a number of families of similarity shape densities have
proven useful in landmark based data analysis, parametric models have seldom
been considered in the context of projective shape or affine shape (see Mardia
and Patrangenaru (2005) [233]). Sample spaces of interest in Statistics (see
Section 3.5) that have the geometric structure of symmetric spaces (see Sec-
tion 3.2) are spheres (as spaces of directions), real projective spaces as spaces
of axes, complex projective spaces as planar direct similarity shape spaces (see
Kendall (1984) [177]), real Grassmann manifolds as spaces of affine shapes
(see Sparr (1992) [314], and products of real projective spaces as spaces of
projective shapes of configurations of points in general position (see Patrange-
naru (2001) [268], Mardia and Patrangenaru (2005) [233]). Therefore, density
estimation of distributions, regarded as points on such symmetric spaces and
arising from directional data or from digitizing landmarks in images, was nec-
essary.
