Using Mathematical Morphology for Geometric Music Retrieval

The usual task in music information retrieval (MIR) is to find occurrences of a monophonic query pattern within a music database, which can contain both monophonic and polyphonic content. The so-called query-by-humming systems are a famous instance of content-based MIR. In such a system, the user's hummed query is converted into symbolic form to perform search operations in a similarly encoded database. The symbolic representation (e.g., textual, MIDI or vector data) is typically a quantized and simplified version of the sampled audio data, yielding to faster search algorithms and space requirements that can be met in real-life situations. In this thesis, we investigate geometric approaches to MIR. We first study some musicological properties often needed in MIR algorithms, and then give a literature review on traditional (e.g., string-matching-based) MIR algorithms and novel techniques based on geometry. We also introduce some concepts from digital image processing, namely the mathematical morphology, which we will use to develop and implement four algorithms for geometric music retrieval. The symbolic representation in the case of our algorithms is a binary 2-D image. We use various morphological pre- and post-processing operations on the query and the database images to perform template matching / pattern recognition for the images. The algorithms are basically extensions to classic image correlation and hit-or-miss transformation techniques used widely in template matching applications. They aim to be a future extension to the retrieval engine of C-BRAHMS, which is a research project of the Department of Computer Science at University of Helsinki.

Disturbance in boreal spruce forest - immediate dynamics from stand to understorey level

The immediate effects of two human-related vegetation disturbances, (1) green tree retention (GTR) patch felling and scarification by harrowing and (2) experimental understorey vegetation layer removal, were examined in boreal forest stands in Finland. Effects of GTR patch felling and scarification on tree uprootings, on coarse woody debris (CWD) and on epixylic plant community were followed in upland and in paludified forest types. Uprootings increased considerably during 2-3 years after the fellings and were more frequent (47%) in the paludified than in the upland forest (13%). Scarification reduced 68% of the CWD in the felling area. Cover and especially species richness of epixylics declined in the both areas during 1-2 years after the felling. The increasing size of GTR patch correlated positively with the species richness. Regeneration of understorey vegetation community and Vaccinium myrtillus and Vaccinium vitis-idaea after different removals of vegetation layers in an old-growth forest took four years. The regeneration occurred mainly by vegetative means and it was faster in the terms of species richness than in the cover. In the most severe treatment, recovery occurred merely by sexual reproduction. V. myrtillus recovered mainly by producing new shoots. V. vitis-idaea recovered faster than V. myrtillus, mainly by increasing length growth. For ecological reasons, use of larger GTR patches on paludified biotope would be recommendable. In felling areas, scarification by harrowing could be replaced with some other spot-wise method. After moderate intensity level disturbance, recovery occurs rapidly by vegetative regrowth of the dominating species. High level of intensity may prevent the recovery of vegetation community for years, while enabling also the genetic regeneration of the initial species. Local anthropogenic-related disturbances are currently increasing and they can interact during temporally short times, which should be taken in to account in the future forest management plans.

Geometric Characterizations for Patterson-Sullivan Measures of Geometrically Finite Kleinian Groups

The main results of this thesis show that a Patterson-Sullivan measure of a non-elementary geometrically finite Kleinian group can always be characterized using geometric covering and packing constructions. This means that if the standard covering and packing constructions are modified in a suitable way, one can use either one of them to construct a geometric measure which is identical to the Patterson-Sullivan measure. The main results generalize and modify results of D. Sullivan which show that one can sometimes use the standard covering construction to construct a suitable geometric measure and sometimes the standard packing construction. Sullivan has shown also that neither or both of the standard constructions can be used to construct the geometric measure in some situations. The main modifications of the standard constructions are based on certain geometric properties of limit sets of Kleinian groups studied first by P. Tukia. These geometric properties describe how closely the limit set of a given Kleinian group resembles euclidean planes or spheres of varying dimension on small scales. The main idea is to express these geometric properties in a quantitative form which can be incorporated into the gauge functions used in the modified covering and packing constructions. Certain estimation results for general conformal measures of Kleinian groups play a crucial role in the proofs of the main results. These estimation results are generalizations and modifications of similar results considered, among others, by B. Stratmann, D. Sullivan, P. Tukia and S. Velani. The modified constructions are in general defined without reference to Kleinian groups, so they or their variants may prove useful in some other contexts in addition to that of Kleinian groups.