Learning with Algebraic Invariances, and the Invariant Kernel Trick

When solving data analysis problems it is important to integrate prior knowledge and/or structural invariances. This paper contributes by a novel framework for incorporating algebraic invariance structure into kernels. In particular, we show that algebraic properties such as sign symmetries in data, phase independence, scaling etc. can be included easily by essentially performing the kernel trick twice. We demonstrate the usefulness of our theory in simulations on selected applications such as sign-invariant spectral clustering and underdetermined ICA

Blood vessel segmentation in the analysis of retinal and diaphragm images

The segmentation and characterization of structures in medical images represents an important part of the diagnostic and research procedures in medicine. This thesis focuses on the characterization methods in two application fields that make use of two imaging modalities. The first topic is the characterization of the blood vessel structure in the human retina and the second is the characterization of diaphragm movement during breathing. The imaged blood vessel structures are considered important landmarks in both applications. The framework for the retinal image processing and analysis starts with the testing of five publicly available blood vessel segmentation methods for retinal images. The parameters of the methods are optimized on five databases with the ground truth for blood vessels. An approach for predicting the method parameters is proposed based on the optimization results. The parameter prediction approach is then applied to obtain vessel segmentation on a new database and an automatic approach to the blood vessel classification and computation of the arteriovenous ratio is proposed and evaluated on the new database. The framework for the diaphragm image processing and analysis is based on the measurement of diaphragm motion. The motion is characterized by a set of features quantifying the amplitude and frequency of the breathing pattern, as well as a portion of the nonharmonic movements that occur. In addition, a set of static features like the diaphragm slope and height are proposed. Two approaches for the motion measurement are proposed and compared. A statistical evaluation of the proposed features is performed by comparing measurements from people with and without spinal findings. The results from the retinal image processing and analysis revealed the possibility of the successful prediction of the parameters of the blood vessel segmentation methods. The automatic approach for the automatic arteriovenous ratio estimation revealed a stronger association with blood pressure than the manually estimated ratio. The results from the diaphragm image processing and analysis confirmed differences in the position, shape and breathing patterns between the healthy people and people suffering from spinal findings. The blood vessel structure was shown to be a reliable marker for characterizing the diaphragm motion.Katedra kybernetik