Fast and robust estimation of homography relating two images.
The algorithm for image alignment is a simple but effective variant of
the inverse compositional algorithm. For a thorough overview, see:
"Lucas-kanade 20 years on A unifying framework,"
S. Baker and I. Matthews. IJCV 2004.
The implementation is optimized and can easily run at 20-30 fps.
type may take on the following values:
'translation' - translation only
'rigid' - translation and rotation
'similarity' - translation, rotation and scale
'affine' - 6 parameter affine transform
'rotation' - pure rotation (about x, y and z)
'projective' - full 8 parameter homography
Alternatively, type may be a vector of ids between 1 and 8, specifying
exactly the types of transforms allowed. The ids correspond, to: 1:
translate-x, 2: translate-y, 3: uniform scale, 4: shear, 5: non-uniform
scale, 6: rotate-z, 7: rotate-x, 8: rotate-y. For example, to specify
translation use type=[1,2]. If the transforms don't form a group, the
returned homography may have more degrees of freedom than expected.
Parameters (in rough order of importance): [resample] controls image
downsampling prior to computing H. Runtime is proportional to area, so
using resample<1 can dramatically speed up alignment, and in general not
degrade performance much. [sig] controls image smoothing, sig=2 gives
good performance, setting sig too low causes loss of information and too
high will violate the linearity assumption. [epsilon] defines the
stopping criteria, use to adjust performance versus speed tradeoff.
[lambda] is a regularization term that causes small transforms to be
favored, in general any small non-zero setting of lambda works well.
[outThr] is a threshold beyond which pixels are considered outliers, be
careful not to set too low. [minArea] determines coarsest scale beyond
which the image is not downsampled (should not be set too low). [H0] can
be used to specify an initial alignment. Use [show] to display results.
USAGE
[H,Ip] = imagesAlign( I, Iref, varargin )
INPUTS
I - transformed version of I
Iref - reference grayscale double image
varargin - additional params (struct or name/value pairs)
.type - ['projective'] see above for options
.resample - [1] image resampling prior to homography estimation
.sig - [2] amount of Gaussian spatial smoothing to apply
.epsilon - [1e-3] stopping criteria (min change in error)
.lambda - [1e-6] regularization term favoring small transforms
.outThr - [inf] outlier threshold
.minArea - [4096] minimum image area in coarse to fine search
.H0 - [eye(3)] optional initial homography estimate
.show - [0] optionally display results in figure show
OUTPUTS
H - estimated homography to transform I into Iref
Ip - tranformed version of I (slow to compute)
EXAMPLE
Iref = double(imread('cameraman.tif'))/255;
H0 = [eye(2)+randn(2)*.1 randn(2,1)*10; randn(1,2)*1e-3 1];
I = imtransform2(Iref,H0^-1,'pad','replicate');
o=50; P=ones(o)*1; I(150:149+o,150:149+o)=P;
prmAlign={'outThr',.1,'resample',.5,'type',1:8,'show'};
[H,Ip]=imagesAlign(I,Iref,prmAlign{:},1);
tic, for i=1:30, H=imagesAlign(I,Iref,prmAlign{:},0); end;
t=toc; fprintf('average fps: %f\n',30/t)
See also imTransform2
Piotr's Computer Vision Matlab Toolbox Version 2.61
Copyright 2014 Piotr Dollar. [pdollar-at-gmail.com]
Licensed under the Simplified BSD License [see external/bsd.txt]