Spatiograms Versus Histograms for Region-Based Tracking

1
Spatiograms Versus Histograms for Region-Based
Tracking STAN BIRCHFIELD AND SRIRAM
RANGARAJAN CLEMSON UNIVERSITY
An illustrative insight
Abstract
Tracking results
We introduce the concept of a spatiogram, which
is a generalization of a histogram that includes
potentially higher order moments. A histogram is
a zeroth-order spatiogram, while second-order
spatiograms contain spatial means and covariances
for each histogram bin. This spatial information
still allows quite general transformations, as in
a histogram, but captures a richer description of
the target to increase robustness in tracking. We
show how to use spatiograms in kernel-based
trackers, deriving a mean shift procedure in
which individual pixels vote not only for the
amount of shift but also for its direction.
Experiments show improved tracking results
compared with histograms, using both mean shift
and exhaustive local search.
To compare histograms and spatiograms, three
experiments were conducted.
Three poses of a head
Image generated from histogram
Histograms and spatiograms
Experiment 1 Using mean shift. Spatiogram is
slightly better, but both lose the target when
the head jerks quickly.
SPATIOGRAM
HISTOGRAM
A discrete function (an image)
Image generated from spatiogram
Binary 2D formulation
The i th moment
Tracking by mean shift
Experiment 2 Using local exhaustive search (6 x
6 x 1 in x, y, and scale), with gradient dot
product. Spatiogram is less distracted by the
background, but both succeed in maintaining the
target.
Histogram (no spatial information)
HISTOGRAMS
SPATIOGRAMS
S
Likelihood function
Spatiogram (some spatial Information)
number of bins

µ
Experiment 2 Using local exhaustive search (6 x
6 x 1 in x, y, and scale), with gradient dot
product. Spatiogram succeeds, while histogram
fails.

• The spatial histogram, or spatiogram, captures
  some spatial information about the target
• m is the spatial mean of all the pixels that
  contribute to the bin
• S is the spatial covariance matrix of all the
  pixels that contribute to the bin
• Spatiograms are between histograms (which
  contain no spatial information) and specific
  geometric models like SSD-based translation or
  affine (which maintain precise spatial
  information)

Conclusion
model
target
target location

• Introduction of a novel concept a higher-order
  histogram that captures a limited amount of
  spatial information (spatiogram)
• Derivation of a mean shift procedure for
  spatiograms
• Demonstration of improved tracking results when
  compared to histograms

Mean shift update