UCLA has an ongoing project
developing algorithms for tracking objects and devloping
control algorithms for autonomous vehicles. This year there will be at
least two projects in this area.
tracking: A team of students will
learn about real time video tracking algorithms. The goal
will be to implement these methods on a platform with a real video
camera and streaming data. The goal will be to
track people walking across the field of view of the camera.
robots: a team of students will help to design, build,
and implement a tracking algorithm
using autonomous robots. The robots will be equipped
with sensors to measure local environmental changes.
The goal of the algorithm is to map out the environment
using sensor data.
the Epidemiology of Crime
Projects on the modeling and analysis of automobile
theft, residential break-ins, and gang activity are open
for undergraduate research participation. These projects will
involve use of actual crime data from
Los Angeles and Long Beach. The student will work on the mathematics of
propagation. A better quantitative understanding of both of these
processes will help with designing crime prevention strategies.
Auto Theft Hot Spots in
from May 2003 to April 2004
Image Processing and Inpainting
UCLA has several ongoing projects studying image processing and
inpainting of images (i.e. filling in missing information in partial
- Hyperspectral Imaging: This project involves remote
sensing from satellites and airplanes. Objects
on the ground are imaged using very fine scale information
in the electromagnetic spectrum. The result
is large volumes of data with spectral information about
the materials on the ground. The project will design
algorithms to identify the objects based on their
spatial shape and high dimensional spectral data.
- Image inpainting: This project involves testing
and design of algorithms for filling in missing information
on images. Applications include text reconstruction,
aerial imagery, and Hollywood special effects.
Mudslides, Slurry Flows and Particle Tracking
Slurry flows are models of mudlslides; UCLA has on ongoing numerical,
experimental and theoretical study of slurry flows. The experiment to
produce behavior like the photos (below) obtained
in Peko Hosoi's lab at MIT.
Glass beads of a uniform size are mixed into a less dense viscous
resulting slurry is poured into a reservoir at the top of an inclined
plane. A controlled amount of the slurry is allowed to flow through a
down the incline. At low inclination angles and concentrations,
the particles tend to settle out of the mixture and stick to the
of the incline, leaving a clear fluid to flow down the slope (left
At intermediate angles and concentrations, a well-mixed slurry flows
down the slope (middle panel) producing the characteristic fingering
pattern seen in visous films. At high inclination angles and particle
concentrations (right panel) the beads tend to collect at the front
of the film; their presence drastically changes the dynamics of
the contact line, supressing fingering and producing a pronounced
experimental apparatus for studying these flows is under
development at UCLA; one project is to refine particle tracking
software that allows one to determine the flow velocity in the fluid
from experimental observation.
* Department of
Mathematics * Harvey
Maintained by Andrew Bernoff
March 6th, 2007