Dongryeol Lee

Gaussian process regression flow for analysis of motion trajectories

Recognition of motions and activities of objects in videos requires effective representations for analysis and matching of motion trajectories. In this paper, we introduce a new representation specifically aimed at matching motion trajectories. We model a trajectory as a continuous dense flow field from a sparse set of vector sequences using Gaussian Process Regression. Furthermore, we introduce a random sampling strategy for learning stable classes of motions from limited data. Our representation allows for incrementally predicting possible paths and detecting anomalous events from online trajectories. This representation also supports matching of complex motions with acceleration changes and pauses or stops within a trajectory. We use the proposed approach for classifying and predicting motion trajectories in traffic monitoring domains and test on several data sets. We show that our approach works well on various types of complete and incomplete trajectories from a variety of video data sets with different frame rates.

Hydrodynamics and heat transfer in sphere assemblages—cylindrical cell models

Abstract In order to evaluate interactions between vaporizing fuel droplets, a cylindrical cell model based on a single sphere has been suggested by the authors in previous works as a replacement for the existing spherical cell model. Since wake effects are important, a multisphere cylindrical cell model has been developed in the present work. The Navier-Stokes and energy equations have been solved numerically within the representative cells for intermediate Reynolds numbers. Using a nonuniform mesh suited for the problem, several spheres in tandem are considered and the importance of wake effects in considerably reducing the drag and Nusselt number in the bulk is discussed. The quasiperiodic features of the results are indicated and compared favorably with a model assuming periodicity a priori.

Numerical optimization studies of axisymmetric unsteady sprays

A hybrid numerical technique is developed for the treatment of axisymmetric unsteady spray equations. An Eulerian mesh is employed for the parabolic gas-phase subsystem of equations while a Lagrangian scheme (or method of characteristics) is utilized for the droplet equations. The integration schemes and the scheme for interpolation between the two meshes are demonstrated to be second-order accurate. The approach is shown to be especially useful in situations where a multivaluedness of the droplet properties occurs due to the crossing of particle paths. A set of model equations are studied but the technique is applicable to a more general and more physically correct set of equations. The effects of interesting numerical parameters such as mesh size, number of droplet characteristics, time step, and the injection pulse time are determined via a parameter study. In addition to confirming quadratic convergence, the results indicate slightly more sensitivity to grid spacing than to the number of characteristics.

Detecting regions of interest in dynamic scenes with camera motions

We present a method to detect the regions of interests in moving camera views of dynamic scenes with multiple moving objects. We start by extracting a global motion tendency that reflects the scene context by tracking movements of objects in the scene. We then use Gaussian process regression to represent the extracted motion tendency as a stochastic vector field. The generated stochastic field is robust to noise and can handle a video from an uncalibrated moving camera. We use the stochastic field for predicting important future regions of interest as the scene evolves dynamically. We evaluate our approach on a variety of videos of team sports and compare the detected regions of interest to the camera motion generated by actual camera operators. Our experimental results demonstrate that our approach is computationally efficient and provides better predictions than previously proposed RBF-based approaches.

Optimizing the computation of n-point correlations on large-scale astronomical data

The n-point correlation functions (npcf) are powerful statistics that are widely used for data analyses in astronomy and other fields. These statistics have played a crucial role in fundamental physical breakthroughs, including the discovery of dark energy. Unfortunately, directly computing the npcf at a single value requires O(Nn) time for N points and values of n of 2, 3, 4, or even larger. Astronomical data sets can contain billions of points, and the next generation of surveys will generate terabytes of data per night. To meet these computational demands, we present a highly-tuned npcf computation code that show an order-of-magnitude speedup over current state-of-the-art. This enables a much larger 3-point correlation computation on the galaxy distribution than was previously possible. We show a detailed performance evaluation on many different architectures.

Multibody multipole methods

A three-body potential function can account for interactions among triples of particles which are uncaptured by pairwise interaction functions such as Coulombic or Lennard-Jones potentials. Likewise, a multibody potential of order n can account for interactions among n-tuples of particles uncaptured by interaction functions of lower orders. To date, the computation of multibody potential functions for a large number of particles has not been possible due to its O ( N n ) scaling cost. In this paper we describe a fast tree-code for efficiently approximating multibody potentials that can be factorized as products of functions of pairwise distances. For the first time, we show how to derive a Barnes-Hut type algorithm for handling interactions among more than two particles. Our algorithm uses two approximation schemes: (1) a deterministic series expansion-based method; (2) a Monte Carlo-based approximation based on the central limit theorem. Our approach guarantees a user-specified bound on the absolute or relative error in the computed potential with an asymptotic probability guarantee. We provide speedup results on a three-body dispersion potential, the Axilrod-Teller potential.