Some Major Breakthroughs in Statistics of Shapes and Images
by
Kanti V. Mardia
Centre of Medical Imaging, University of Leeds, Leeds, England

I will describe some key advances related to two modern fields: Shape Analysis and Image Analysis. In shape analysis, the influence of computer technology has been substantial. We can now collect surface data either through laser scan such as for face or we could digitally obtain landmarks through devices such as micro-scribe, for example, for skulls. Indeed we are involved in both projects at data collection as well as at analysis stage.

The significant step forward has been the work of David Kendall who formulated similarity shape definition in early 80's. Bookstein has made substantial contributions to statistical shape analysis since 80's and my group in Leeds have strengthened and complemented his results while developing distribution theory. Lele and C R Rao have motivated distance based methods. Another significant advance has been in shape deformation, where Fred Bookstein, Ulf Grenander and Michael Miller have contributed a quantitative formulation of D'Arcy Thompson's biological grids.

In high level image analysis, there have been advances through deformable templates in object recognition. Ulf Grenander has contributed various new ideas. Images give rise to very large-scale data in Markov Chain Monte Carlo (MCMC) algorithms have led to interpreting and analysing images.

Throughout, I will describe these results with their applications in the foreground.

Date received: October 9, 2000