outlier, robust statistics

[P. Anandan x3249]

Hi Terry,

It may be worth mentioning that a simple extension of your "fixed velocity"
formulation leads to something quite powerful and is a decent approximation for
many real situations.  This is to look formulate the hypothesis space as 2-D
affine transforms of the image plane.  Most of the references below have not
used robust estimators but have focussed on the layered representation problem.
However, recent extensions of all these algorithms at Sarnoff have included
several different types of robust estimators as options.  One noteworthy
omission (simply because I have not yet updated my bib file, is the paper by
Black and Jepson, CVPR93.)   I also did not inlude the paper by Wang and
Adelson at CVPR93, because that can be viewed as falling into either category
(affine hypotheses or object hypotheses).

In general, when you use a parametric motion model (translation, affine,
8-parameter quadratic for planar surface motion), you have the choice of
working with motion-parameters as hypotheses or the objects as hypotheses. But
if you are working with non-parametric motion fields (e.g., smooth flow), it is
not obvious how to work with motion parameters as hypotheses.  

Last but not least, I should mention a recent paper that we have written which
is under review that goes beyond parametric layers to include residual flow to
fully account for the scene motion.  This is an alternative approach to the
standard formulation of the spatial-coherence assumption as a "smoothness"
constraint (e.g., minimum quadratic variation, etc.).  This paper also
describes a computational framework that identifies the critical choice points
for layered motion estimation and shows how different algorithms fit into that
framework.   I should be in a position to send you a copy of the paper in a
couple of weeks or so.

-- anandan

@article{Irani-Peleg:IJCV,
	author =	{M. Irani and S. Peleg},
	title =		{Computing Occluding and Transparent Motions},
	journal =	IJCV,
	year =		{accepted for publication, 1993},
}


@inproceedings{Bergen-etal:AICV91,
        author =	{J.R. Bergen and P.J. Burt and K. Hanna and
			R. Hingorani and P. Jeanne and S. Peleg},
        title =         {Dynamic Multiple-Motion Computation},
        booktitle =     {Artificial Intelligence and Computer Vision:
                         Proceedings of the Israeli Conference},
	publisher =	{Elsevier},
	editor =	{Y.A. Feldman and A. Bruckstein},
        year =          {1991},
	pages =		{147--156}
}

@inproceedings{Burt-etal:WVM89,
	title =	{Object tracking with a moving camera, an application of
		dynamic motion analysis},
	author ={P.J. Burt and J.R. Bergen and R. Hingorani and R. Kolczynski and W.A. Lee and A. Leung and J. Lubin and H. Shvaytser},
	booktitle = WVM,
	address =	{Irvine, CA},
	month =		{March},
	year =		{1989},
	pages =		{2--12}
}


@article{Bergen-etal:PAMI92,
        author =   {J.R. Bergen and P.J. Burt and R. Hingorani and S. Peleg},
        title =    {A Three Frame Algorithm for Estimating Two-Component Image 
              Motion}, 
        journal =       PAMI,
        month =         {September},
        year =          {1992},
        volume =        {14},
        pages =         {886--896}
}