Rotationally Invariant Image Representation for Viewing Direction Classification in Cryo-EM

We introduce a new rotationally invariant viewing angle classification method for identifying, among a large number of Cryo-EM projection images, similar views without prior knowledge of the molecule. Our rotationally invariant features are based on the bispectrum. Each image is denoised and compressed using steerable principal component analysis (PCA) such that rotating an image is equivalent to phase shifting the expansion coefficients. Thus we are able to extend the theory of bispectrum of 1D periodic signals to 2D images. The randomized PCA algorithm is then used to efficiently reduce the dimensionality of the bispectrum coefficients, enabling fast computation of the similarity between any pair of images. The nearest neighbors provide an initial classification of similar viewing angles. In this way, rotational alignment is only performed for images with their nearest neighbors. The initial nearest neighbor classification and alignment are further improved by a new classification method called vector diffusion maps. Our pipeline for viewing angle classification and alignment is experimentally shown to be faster and more accurate than reference-free alignment with rotationally invariant K-means clustering, MSA/MRA 2D classification, and their modern approximations

An Affine-Invariant Sampler for Exoplanet Fitting and Discovery in Radial Velocity Data

Markov Chain Monte Carlo (MCMC) proves to be powerful for Bayesian inference and in particular for exoplanet radial velocity fitting because MCMC provides more statistical information and makes better use of data than common approaches like chi-square fitting. However, the non-linear density functions encountered in these problems can make MCMC time-consuming. In this paper, we apply an ensemble sampler respecting affine invariance to orbital parameter extraction from radial velocity data. This new sampler has only one free parameter, and it does not require much tuning for good performance, which is important for automatization. The autocorrelation time of this sampler is approximately the same for all parameters and far smaller than Metropolis-Hastings, which means it requires many fewer function calls to produce the same number of independent samples. The affine-invariant sampler speeds up MCMC by hundreds of times compared with Metropolis-Hastings in the same computing situation. This novel sampler would be ideal for projects involving large datasets such as statistical investigations of planet distribution. The biggest obstacle to ensemble samplers is the existence of multiple local optima; we present a clustering technique to deal with local optima by clustering based on the likelihood of the walkers in the ensemble. We demonstrate the effectiveness of the sampler on real radial velocity data.Comment: 24 pages, 7 figures, accepted to Ap

A fuzzy clustering algorithm to detect planar and quadric shapes

In this paper, we introduce a new fuzzy clustering algorithm to detect an unknown number of planar and quadric shapes in noisy data. The proposed algorithm is computationally and implementationally simple, and it overcomes many of the drawbacks of the existing algorithms that have been proposed for similar tasks. Since the clustering is performed in the original image space, and since no features need to be computed, this approach is particularly suited for sparse data. The algorithm may also be used in pattern recognition applications

FastJet user manual

FastJet is a C++ package that provides a broad range of jet finding and analysis tools. It includes efficient native implementations of all widely used 2-to-1 sequential recombination jet algorithms for pp and e+e- collisions, as well as access to 3rd party jet algorithms through a plugin mechanism, including all currently used cone algorithms. FastJet also provides means to facilitate the manipulation of jet substructure, including some common boosted heavy-object taggers, as well as tools for estimation of pileup and underlying-event noise levels, determination of jet areas and subtraction or suppression of noise in jets.Comment: 69 pages. FastJet 3 is available from http://fastjet.fr

Progress in jet reconstruction and heavy ion collisions

We review recent developments related to jet clustering algorithms and jet reconstruction, with particular emphasis on their implications in heavy ion collisions. These developments include fast implementations of sequential recombination algorithms, new IRC safe algorithms, quantitative determination of jet areas and quality measures for jet finding, among many others. We also show how jet reconstruction provides a useful tool to probe the characteristics of the hot and dense medium created in heavy ion collisions, which allows one to distinguish between different models of parton-medium interaction.Comment: 7 pages, 4 figures, to appear in the proceedings of the 13th International Conference on Elastic & Diffractive Scattering, CERN, 29th June - 3rd July 200

Stereo image processing system for robot vision

More and more applications (path planning, collision avoidance methods) require 3D description of the surround world. This paper describes a stereo vision system that uses 2D (grayscale or color) images to extract simple 2D geometric entities (points, lines) applying a low-level feature detector. The features are matched across views with a graph matching algorithm. During the projective reconstruction the 3D description of the scene is recovered. The developed system uses uncalibrated cameras, therefore only projective 3D structure can be detected defined up to a collineation. Using the Euclidean information about a known set of predefined objects stored in database and the results of the recognition algorithm, the description can be updated to a metric one