Fast, robust estimation of translational offset between a pair of images.
Approximates the translational offset between two images by assuming the
images lie on linear manifold. Specifically, assumes that if I0 and I1
are a pair of images related by a translation [dx dy], then (I0+I1)/2 is
the image exactly halfway between I0 and I1 (ie I0 translated by [dx/2
dy/2]). The above only holds for small translations and spatially smooth
images. As such the input images typically need to be spatially smoothed
first, the amount of necessary smoothing will increase as the size of
translation increases (experiment for best results). The code is quite
fast, the bottleneck is the spatial smoothing. More accurate results can
be optained by iterating between estimating the translation and applying
the resulting translation.
The actual computation is performed as follows. First we generate an
artificial translation of I0 by 1 pixel in x and y, and store the results
in Tx and Ty respectively. The linearity assumption then tells us that:
I1 = I0 + (I0-Tx) * dx + (I0-Ty) * dy
Only dx and dy are unknown in the resulting overcomplete set of linear
equations, least squares is then used. The error of the estimate can be
used as a measure of the quality of the linear fit.
This function was inspired by the beautiful work ok Yang et al.:
H. Yang, M. Pollefeys, G. Welch, J. Frahm, and A. Ilie. Differential
camera tracking through linearizing the local appearance manifold.
CVPR, 2007.
USAGE
[delta,err] = diffTracker( I0, I1, sigma )
INPUTS
I0 - reference grayscale double image
I1 - translated version of I0
sigma - amount of Gaussian spatial smoothing to apply
OUTPUTS
delta - estimated dx/dy
err - squared error of estimate
EXAMPLE
I = imread('cameraman.tif'); dx=3; dy=5;
I0=I(1+dy:end,1+dx:end); figure(1); im(I0);
I1=I(1:end-dy,1:end-dx); figure(2); im(I1);
tic, [delta,err] = diffTracker( I0, I1, 10 ), toc
See also
Piotr's Image&Video Toolbox Version 2.31
Copyright 2009 Piotr Dollar. [pdollar-at-caltech.edu]
Please email me if you find bugs, or have suggestions or questions!
Licensed under the Lesser GPL [see external/lgpl.txt]