detection using our Difference of B-spline (DoB) detector,
computed efficiently using the generalized integral image.
The integral image
representation (known in graphics as summed area tables) popularized
by Viola and Jones in the computer vision literature represents an
efficient/fast manner for computing space variant box filter related
features. Briefly, the integral image representation is
by a running sum image (i.e., the integral image) and the features are
computed by linear weighted samples of the integral image.
generally, by preintegrating the image n times and taking appropriate
linear weighted samples one can generate the family of B-spline filters
(see figure below), where
the first order
integral image realizes the zero order B-spline (box) filter.
call this family of representations, the generalized integral image.
filters from orders zero to three (top to bottom) and their respective
derivaties from zero to three (left to right)
The generalized integral image formulation allows for the efficient
formulation of a multitude of multi-scale feature representations, such
as, interest point detectors (example
figure shown at top)
and smoothed differential filters. The main advantages of
the integral order of the representation salient are two-fold: (1)
it allows for reducing the introduction of spurious
structures common to box filter-based approaches (filter smoothness
increases as the B-spline order is increased) and (2) it allows for the
reduction in the degree of anisotropicity in the filters which in
turn results in the improvement in the rotation invariance of
filter responses. Importantly, these advantages are realized
while still retaining the efficiency aspect of the original integral
image formulation. Ultimately, the selection of the integral
image order is application dependent; a trade-off between speed in
feature computation and accuracy in feature representation must be made.
K.G., Leung, E.T.H. and Sizintsev, M.,
Fast Scale-space Feature Representations by Generalized Integral Images,
Conference on Image Processing, 2007. (short version)
Derpanis, K.G., Leung, E.T.H. and Sizintsev, M., Fast Scale-space Feature Representations by
Generalized Integral Images,
University, Technical Report CSE-2007-01, 2007. (long version)
Derpanis, K.G., Integral
, York University, memo, 2007.
Generalized integral image C++ code
Last updated: Seotember 30, 2007.