1. Spatiograms Versus Histograms for Region-Based Tracking
STAN BIRCHFIELD AND SRIRAM RANGARAJAN
CLEMSON UNIVERSITY
Abstract
An illustrative insight
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
Histogram
(no spatial information)
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.
HISTOGRAMS
SPATIOGRAMS Σ
Spatiogram
(some spatial
Information)
Likelihood function:
number of bins
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)
target location
model
target
Conclusion
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: