3D invariants for automated pollen recognition

Abstract: In biomedical research we can see a clear tendency towards the study of cells and whole organisms in their natural 3D environment, away from the studies of isolated flat cells, that were grown in a synthetic 2D environment and were analyzed with 2D techniques. Another trend in biomedical research is the ever increasing need for high-throughput experiments, e. g., to retrieve statistically relevant information. The equipment for the automatic recording of great amounts of 3D volumetric data is available in many research laboratories today, but the recorded 3D data are still manually evaluated which has become the main bottleneck in many applications. In this thesis the development of 3D invariants for the recognition of biological structures is described. These invariants are based on the Haar-integration-framework of Schulz-Mirbach (1995b). The invariance properties are reached by an integration over the desired transformation groups, e. g. rotation and translation. Several important aspects of the application of the Haar-integration framework to 3D volumetric data sets of biological structures are described. The most important extension is the introduction of deformation models such that the resulting features are robust to elastic deformations of the structures. Another important aspect is the reached robustness to even non-linear gray-scale transformations, that allow certain variations of the recording parameters between the training and the test objects. The direct computation of these invariants is computationally very expensive. Several new techniques are introduced that allow a fast computation of the invariants by means of the FFT, by the expansion of the integral into spherical harmonics series or by simultaneous computation of multiple invariants based on invertible vectorial kernel functions. Furthermore voxel-wise invariants are introduced for a simultaneous segmentation and recognition of 3D structures. Vectorial invariants are developed for a fast and reliable detection of spherical objects in cluttered environments. A very challenging application that demands many of the requirements to be fulfilled which are given in the biomedical research is the recognition of pollen grains. The high number of different pollen grains from different plants contain very different kinds of structures that have to be identified. For a part of these structures clear one-to-one correspondences can be identified, while for the other part of these structures only the statistical properties match. In the given application we use microscopically recorded images to recognize a real-world object. For the correct interpretation of the gray values it is important to understand the different effects within a microscope. The main four steps, illumination, interaction of the object with the light, transformation of the emitted light, and the recording of the light are explained. In pollen recognition (as in many other applications) we should differentiate between those results that can be reached within a clean and well-controlled laboratory environment and those results of a real-world routine application. In this thesis two representative data sets for these scenarios are used: The first one (denoted as "confocal data set" here) is a typical laboratory data set: The pollen were collected directly from the corresponding plants. They were carefully prepared on one slide per taxon and were manually recorded as a full 3D volumetric data set with confocal laser scanning microscopy. Due to the high costs of such a system and the time-consuming operation, only a small data set containing 389 pollen grains of 26 different taxa (15 grains per taxon) was recorded. The preparation and recording applied here guarantees a 100% correct labeling of the pollen grains and contains the lowest possible degree of distortion due to optical effects. On the other hand the used samples do not represent all variations within each taxon, such as different genera, species or subspecies, different growth conditions of the plants, etc. Furthermore this data s