Asymmetric Feature Maps with Application to Sketch Based Retrieval

We propose a novel concept of asymmetric feature maps (AFM), which allows to evaluate multiple kernels between a query and database entries without increasing the memory requirements. To demonstrate the advantages of the AFM method, we derive a short vector image representation that, due to asymmetric feature maps, supports efficient scale and translation invariant sketch-based image retrieval. Unlike most of the short-code based retrieval systems, the proposed method provides the query localization in the retrieved image. The efficiency of the search is boosted by approximating a 2D translation search via trigonometric polynomial of scores by 1D projections. The projections are a special case of AFM. An order of magnitude speed-up is achieved compared to traditional trigonometric polynomials. The results are boosted by an image-based average query expansion, exceeding significantly the state of the art on standard benchmarks.Comment: CVPR 201

Discovering Regularity in Point Clouds of Urban Scenes

Despite the apparent chaos of the urban environment, cities are actually replete with regularity. From the grid of streets laid out over the earth, to the lattice of windows thrown up into the sky, periodic regularity abounds in the urban scene. Just as salient, though less uniform, are the self-similar branching patterns of trees and vegetation that line streets and fill parks. We propose novel methods for discovering these regularities in 3D range scans acquired by a time-of-flight laser sensor. The applications of this regularity information are broad, and we present two original algorithms. The first exploits the efficiency of the Fourier transform for the real-time detection of periodicity in building facades. Periodic regularity is discovered online by doing a plane sweep across the scene and analyzing the frequency space of each column in the sweep. The simplicity and online nature of this algorithm allow it to be embedded in scanner hardware, making periodicity detection a built-in feature of future 3D cameras. We demonstrate the usefulness of periodicity in view registration, compression, segmentation, and facade reconstruction. The second algorithm leverages the hierarchical decomposition and locality in space of the wavelet transform to find stochastic parameters for procedural models that succinctly describe vegetation. These procedural models facilitate the generation of virtual worlds for architecture, gaming, and augmented reality. The self-similarity of vegetation can be inferred using multi-resolution analysis to discover the underlying branching patterns. We present a unified framework of these tools, enabling the modeling, transmission, and compression of high-resolution, accurate, and immersive 3D images

Revealing the state space of turbulent pipe flow by symmetry reduction

Symmetry reduction by the method of slices is applied to pipe flow in order to quotient the stream-wise translation and azimuthal rotation symmetries of turbulent flow states. Within the symmetry-reduced state space, all travelling wave solutions reduce to equilibria, and all relative periodic orbits reduce to periodic orbits. Projections of these solutions and their unstable manifolds from their $\infty$-dimensional symmetry-reduced state space onto suitably chosen 2- or 3-dimensional subspaces reveal their interrelations and the role they play in organising turbulence in wall-bounded shear flows. Visualisations of the flow within the slice and its linearisation at equilibria enable us to trace out the unstable manifolds, determine close recurrences, identify connections between different travelling wave solutions, and find, for the first time for pipe flows, relative periodic orbits that are embedded within the chaotic attractor, which capture turbulent dynamics at transitional Reynolds numbers.Comment: 24 pages, 12 figure

A machine learning route between band mapping and band structure

The electronic band structure (BS) of solid state materials imprints the multidimensional and multi-valued functional relations between energy and momenta of periodically confined electrons. Photoemission spectroscopy is a powerful tool for its comprehensive characterization. A common task in photoemission band mapping is to recover the underlying quasiparticle dispersion, which we call band structure reconstruction. Traditional methods often focus on specific regions of interests yet require extensive human oversight. To cope with the growing size and scale of photoemission data, we develop a generic machine-learning approach leveraging the information within electronic structure calculations for this task. We demonstrate its capability by reconstructing all fourteen valence bands of tungsten diselenide and validate the accuracy on various synthetic data. The reconstruction uncovers previously inaccessible momentum-space structural information on both global and local scales in conjunction with theory, while realizing a path towards integrating band mapping data into materials science databases