SE263 Video Analytics
Course Project Initial Report
X. Mei and H. Ling, ICCV’09
Presented by M. Aravind Krishnan, SERC, IISc
AIM of the course project is to implement and if possible, improve the work done by
Xue Mei and Haibin Ling in visual tracking, as explained in their paper Robust Visual
Tracking using l1 minimization.
By ‘improve’ it is meant to ‘accelerate’ the speed of execution using special
processing hardware called Graphics Processing Units.
OVERVIEW
1. I will begin by explaining the work done in the paper, and the various mathematical
tools used in achieving the desired results.
1. Bayesian state inference framework, used to predict the affine state of the object.
(Called the particle filter)
2. Sparse representation of the Tracking target.
3. Non-negativity constraints
4. l1 minimization
5. Template update
2. This will be followed by a brief overview of Graphics processing Units, and how they
can be used for general purpose computation.
3. Finally the parts of the algorithm most suited for being executed in a GPU is
proposed.
Templates
• Sample/collection of possible views of the object, whose linear
combination can be used to represent the tracked object in the
frame.
• Two types of templates are considered in this paper, Target
templates and Trivial templates.
• Target templates to deal with various lighting conditions, poses, etc.
• Trivial templates to deal with occlusions, noise, bacckground clutter,
etc.
Templates continued
• Target templates are densely used to
represent, and hence are less in number.
• Trivial templates are sparsely used to
represent, and hence can be large in number.
State of object being tracked
Xt =
2D deformation parameters
2D translation parameters
If zt is the observed distribution of the state of the object at time t, then the
predicted distribution of the object xt is given by the recursive computation
"filtering" refers to determining the distribution of a latent variable at a specific time, given all
observations up to that time; particle filters are so named because they allow for approximate
"filtering" using a set of "particles" (differently-weighted samples of the distribution). -Wikipedia
l1 minimization
Non negativity
Optimization
Convex Optimization – Interior point method
The method uses the preconditioned conjugate gradients (PCG) algorithm to
compute the search direction and the run time is determined by the product of
the total number of PCG steps required over all iterations and the cost of a PCG
step. This process can be accelerated by GPUs.
Algorithm for template update
Review of Algorithm
1
2
3
4
5
Frame 1
1. Manually detect object to be tracked
2. Initialize Target Templates with random variations of
object
Generate a set of N states around current state Xt, with each of
the 6 affine parameters being modeled as an independent
gaussian variable.
Represent each of the N generated states as a sparse linear
combination of target and trivial templates by solving the l1
minimization problem min||Bc-y||22+λ||c||1
Calculate p(Xt|Z1:t ) by determining the Bayesian weights of
the importance wi = p(zt|xt), in turn determined from the
errors/residuals in projecting the tracked object onto each of
the solutions of 3.
Update templates if the highest similarity of the templates with
newly tracked object is less than a threshold. Do by replacing
lowest similarity template with the newly tracked object.
Working of a GPU
• Consists of a lot ALUs.
Banks of ALUs with shared memory are called
cores.
• An average CPU consists of upto 4 SIMD units.
• A GPU consists of 32-128 SIMD units
• A tesla C1060 unit available in SERC will be
used to try and speed up the optimization
process, and hence the whole algorithm.
The functionality of GPUs – Data
Parallelism
• GPUs are extremely good at executing the same
instruction across bulky data.
Eg. Vector addition, Matrix Vector Multiplication,
BLAS routines, etc.
• The major bottle-neck of this algorithm is the
convex optimization performed using Interior
point method. It involves some matrix vector
operations over the same matrix and around N
different vectors. This can be readily and trivially
parallelized, and great speedup can be achieved if
done carefully.
Architecture of GPU
Goals and tasks of project
• Dividing the minimization algorithm amongst the cores
of the GPU, and figuring out optimal grid configuration.
• Optimizing to perform the whole task with minimal
data transfer from CPU to GPU and performing the
algorithm in real time using just one kernel invocation,
for a long video.
• Achieve a frame rate > 30 fps on Tesla C1060.
• Achieve frame rate of 18 fps or more using ATI mobility
Radeon HD 5650 graphics processor with 1Gb internal
memory available in my laptop. (requires transcription
to OpenCL. Under constraints of time)
Thank you