Voxel-Wise Gray Scale Invariants for Simultaneous Segmentation and Classification
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  and in the technical report 
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- 1.Fehr, J., Ronneberger, O., Kurz, H., Burkhardt, H.: Self-learning segmentation and classification of cell-nuclei in 3d volumetric data using voxel-wise gray scale invariants. In: Kropatsch, W.G., Sablatnig, R., Hanbury, A. (eds.) DAGM 2005. LNCS, vol. 3663, pp. 377–384. Springer, Heidelberg (2005)CrossRefGoogle Scholar
- 2.Ronneberger, O., Fehr, J., Burkhardt, H.: Voxel-wise gray scale invariants for simultaneous segmentation and classification – theory and application to cell-nuclei in 3d volumetric data. Internal report 2/05, IIF-LMB. University Freiburg (2005)Google Scholar
- 3.Schulz-Mirbach, H.: Invariant features for gray scale images. In: Sagerer, G., Posch, S., Kummert, F. (eds.) 17. DAGM - Symposium “Mustererkennung”, Bielefeld, Reihe Informatik aktuell, pp. 1–14. Springer, Heidelberg (1995)Google Scholar
- 4.Burkhardt, H., Siggelkow, S.: Invariant features in pattern recognition – fundamentals and applications. In: Kotropoulos, C., Pitas, I. (eds.) Nonlinear Model-Based Image/Video Processing and Analysis, pp. 269–307. John Wiley & Sons, Chichester (2001)Google Scholar
- 5.Ronneberger, O., Burkhardt, H., Schultz, E.: General-purpose Object Recognition in 3D Volume Data Sets using Gray-Scale Invariants – Classification of Airborne Pollen-Grains Recorded with a Confocal Laser Scanning Microscope. In: Proceedings of the International Conference on Pattern Recognition, Quebec, Canada (2002)Google Scholar