Kernel Principal Component Analysis and the construction of non-linear Active Shape Models

The use of Kernel Principal Component Analysis (KPCA) to model data distributions in high-dimensional spaces is described. Of the many potential applications, we focus on the problem of modelling the variability in a class of shapes. We show that a previous approach to representing non-linear shape constraints using KPCA is not generally valid, and introduce a new ‘proximity to data’ measure that behaves correctly. This measure is applied to the building of models of both synthetic and real shapes of nematode worms. It is shown that using such a model to impose shape constraints during Active Shape Model (ASM) search gives improved segmentations of worm images than those obtained using linear shape constraints.