Image Similarity based on the Discrepancy Norm

In computer vision, or image processing, among the most common tasks are image registration and tracking. Their applications are manifold and can be found in industry, medicine and entertainment. Particular applications include automatic quality control, stress analysis, surveillance, video compression, fusion of aerial or satellite images, fusion of medical scans of different modalities, special effects in movies, football player tracking etc. These problems are in general quite easy for a human observer but highly non-trivial for a machine. For all of these tasks one needs to measure the similarity of two images (respectively patches of images). Measuring the similarity can be done by a huge number of methods, which however suffer mostly of one or another deficiency. E.g. most of them are either non-monotonous wrt. small image deviations like shifts, i.e. coming closer to the optimal location does not necessarily lower the distance. Others are so robust wrt. image transformations, that one gets minimal distances in a rather big neighbourhood and hence cannot exactly align the images. Also the performance in presence of noise is sometimes rather poor. The discrepancy norm is a novel similarity measure by the proposer. It provides some significantly better properties than the state-of-the-art measures - such as proven monotonicity for shifted signals, or robustness in the face of noise. Furthermore, there already exist quick evaluation schemes. However, it is currently still constrained to translational alignment without illumination changes. The proposed work is aimed at better understanding the discrepancy norm, both from the theoretical and practical perspective. In order to perform the working program we ask for two PhD. positions along with necessary support. The first student will be mostly concerned with the theoretical issues and the expansion to general image transformations. The second one will closely examine the interaction of the discrepancy norm with optimization schemes and its limitations in the face of noisy data. Both of them will apply their results to appropriate problems originating from practice. The supervision will be performed jointly by the proposer and the national research partner. Dissemination of the results on international conferences and in high quality international journals is planned.

This fundamental research project picks up a mathematical concept for measuring irregularities of distributions which dates back to Hermann Weyl 1916. While this so-called discrepancy measure is still an active field of research in the original context of probability distributions and pseudo random numbers, this FWF project is based on the hypothesis that this discrepancy measure holds mathematical properties which are of interest for a broader field of research topics. Particularly, this FWF project addresses signal and image processing problems and underpins this hypothesis by mathematical analysis. It has been demonstrated that the discrepancy measure distinguishes above all by its robustness and stability properties which makes this measure interesting for pattern recognition. Moreover, it has been shown that the discrepancy measure is related to other fields of mathematics like discrete geometry and combinatorics. Particularly it turns out that this measure shows unique properties in the context of on-delta-send sampling, which is an alternative bio-inspired signal sampling approach with application potentials in the field of wireless sensor networks, neuro-informatics and, particularly, neuromorphic sensors like Silicon Retina and Silicon Cochlea. These sensors offer very attractive features for real world application such as sub-millisecond latencies, high dynamic range, and sparse output. However, compared to conventional machine vision and audition, the development of algorithms using this asynchronous sensor output has been hampered by a lack of a comprehensive mathematical basis for event-driven signal processing and solutions have been developed entirely in an ad-hoc fashion. As result it was shown that on-delta-send sampling can cause instability effects which cannot be avoided by state-of-the-art distance measures while mathematical results prove the discrepancy measures guarantees the required stability criteria.A further example where the discrepancy measure has been found to show advantages is in the context nearly regular textures which are encountered in visual quality inspection. One result refers to the robust and efficient characterization of the basic texture pattern (texel) by which nearly regular textures are built up. This is necessary for reasonable and efficient image post processing e.g. to robustly detect structural deviations in woven fabrics as defects.