5 research outputs found
Topological descriptors for 3D surface analysis
We investigate topological descriptors for 3D surface analysis, i.e. the
classification of surfaces according to their geometric fine structure. On a
dataset of high-resolution 3D surface reconstructions we compute persistence
diagrams for a 2D cubical filtration. In the next step we investigate different
topological descriptors and measure their ability to discriminate structurally
different 3D surface patches. We evaluate their sensitivity to different
parameters and compare the performance of the resulting topological descriptors
to alternative (non-topological) descriptors. We present a comprehensive
evaluation that shows that topological descriptors are (i) robust, (ii) yield
state-of-the-art performance for the task of 3D surface analysis and (iii)
improve classification performance when combined with non-topological
descriptors.Comment: 12 pages, 3 figures, CTIC 201
SuPP & MaPP: Adaptable Structure-Based Representations For Mir Tasks
Accurate and flexible representations of music data are paramount to addressing MIR tasks, yet many of the existing approaches are difficult to interpret or rigid in nature. This work introduces two new song representations for structure-based retrieval methods: Surface Pattern Preservation (SuPP), a continuous song representation, and Matrix Pattern Preservation (MaPP), SuPP’s discrete counterpart. These representations come equipped with several user-defined parameters so that they are adaptable for a range of MIR tasks. Experimental results show MaPP as successful in addressing the cover song task on a set of Mazurka scores, with a mean precision of 0.965 and recall of 0.776. SuPP and MaPP also show promise in other MIR applications, such as novel-segment detection and genre classification, the latter of which demonstrates their suitability as inputs for machine learning problems
Adaptive Topological Feature via Persistent Homology: Filtration Learning for Point Clouds
Machine learning for point clouds has been attracting much attention, with
many applications in various fields, such as shape recognition and material
science. To enhance the accuracy of such machine learning methods, it is known
to be effective to incorporate global topological features, which are typically
extracted by persistent homology. In the calculation of persistent homology for
a point cloud, we need to choose a filtration for the point clouds, an
increasing sequence of spaces. Because the performance of machine learning
methods combined with persistent homology is highly affected by the choice of a
filtration, we need to tune it depending on data and tasks. In this paper, we
propose a framework that learns a filtration adaptively with the use of neural
networks. In order to make the resulting persistent homology
isometry-invariant, we develop a neural network architecture with such
invariance. Additionally, we theoretically show a finite-dimensional
approximation result that justifies our architecture. Experimental results
demonstrated the efficacy of our framework in several classification tasks.Comment: 17 pages with 4 figure