Voxel-Wise Gray Scale Invariants for Simultaneous Segmentation and Classification

Abstract: 3D volumetric microscopical techniques (e.g. confocal laser scanning microscopy) have become a standard tool in biomedical applications to record three-dimensional objects with highly anisotropic morphology. To analyze these data in high-throughput experiments, reliable, easy to use and generally applicable pattern recognition tools are required. The major problem of nearly all existing applications is their high specialization to exact one problem, and the their time-consuming adaption to new problems, that has to be done by pattern recognition experts. We therefore search for a tool that can be adapted to new problems just by an interactive training process. Our main idea is therefore to combine object segmentation and recognition into one step by computing voxel-wise gray scale invariants (using nonlinear kernel functions and Haar-integration) on the volumetric multi-channel data set and classify each voxel using support vector machines. After the selection of an appropriate set of nonlinear kernel functions (which allows to integrate previous knowledge, but still needs some expertise), this approach allows a biologist to adapt the recognition system for his problem just by interactively selecting several voxels as training points for each class of objects. Based on these points the classification result is computed and the biologist may refine it by selecting additional training points until the result meets his needs. In this paper we present the theoretical background and a fast approximative algorithm using FFTs for computing Haar-integrals over the very rich class of nonlinear 3-point-kernel functions. The approximation still fulfils the invariance conditions. The experimental application for the recognition of different cell cores of the chorioallantoic membrane is presented in the accompanying paper [1] and in the technical report [2]