Optical Flow Estimation

Reference Paper

Performance of optical flow techniques

J. L. BarronD. J. FleetS. S. Beauchemin

International Journal of Computer Vision, 1994, Volume 12, Issue 1, pp 43–77

Secrets of optical flow estimation and their principles

Sun, D., Roth, S., and Black, M. J.,

IEEE Conf. on Computer Vision and Pattern Recog., CVPR, June 2010.

　　A Quantitative Analysis of Current Practices in Optical Flow Estimation and The Principles Behind Them

Sun, D.; Roth, S. & Black, M. J.

Technical Report Brown-CS-10-03, 2010

 

A Database and Evaluation Methodology for Optical Flow

Simon BakerDaniel ScharsteinEmail, J. P. LewisStefan RothMichael J. BlackRichard Szeliski

International Journal of Computer Vision, March 2011, Volume 92, Issue 1, pp 1–31

Source Code by Brown University

Link: http://cs.brown.edu/~black/code.html

From "The most recent and most accurate optical flow code in Matlab", I select the part they use for estimation for research purpose, which is shown below,

function [mang, stdang, mepe]=flowAngErr(tu, tv, u, v, bord, varargin)
% return the Barron et al angular error.  bord is the pixel width of the
% border to be ingnored.
%
%   Author:  Stefan Roth, Department of Computer Science, TU Darmstadt
%   Contact: sroth@cs.tu-darmstadt.de
%   $Date: 2007-03-27 14:09:11 -0400 (Tue, 27 Mar 2007) $
%   $Revision: 252 $

% Copyright 2004-2007, Brown University, Providence, RI. USA
% Copyright 2007-2010 TU Darmstadt, Darmstadt, Germany.
% 
%                          All Rights Reserved
% 
% All commercial use of this software, whether direct or indirect, is
% strictly prohibited including, without limitation, incorporation into in
% a commercial product, use in a commercial service, or production of other
% artifacts for commercial purposes.     
%
% Permission to use, copy, modify, and distribute this software and its
% documentation for research purposes is hereby granted without fee,
% provided that the above copyright notice appears in all copies and that
% both that copyright notice and this permission notice appear in
% supporting documentation, and that the name of the author and Brown
% University not be used in advertising or publicity pertaining to
% distribution of the software without specific, written prior permission.        
%
% For commercial uses contact the Technology Venture Office of Brown University
% 
% THE AUTHOR AND BROWN UNIVERSITY DISCLAIM ALL WARRANTIES WITH REGARD TO
% THIS SOFTWARE, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND
% FITNESS FOR ANY PARTICULAR PURPOSE.  IN NO EVENT SHALL THE AUTHOR OR
% BROWN UNIVERSITY BE LIABLE FOR ANY SPECIAL, INDIRECT OR CONSEQUENTIAL
% DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR
% PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS
% ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF
% THIS SOFTWARE.        

smallflow=0.0;

% if length(varargin) == 1
%     % mask
%     tu(~varargin{1}) = 0;
%     tv(~varargin{1}) = 0;
% end;
    
stu=tu(bord+1:end-bord,bord+1:end-bord);
stv=tv(bord+1:end-bord,bord+1:end-bord);
su=u(bord+1:end-bord,bord+1:end-bord);
sv=v(bord+1:end-bord,bord+1:end-bord);

% ignore a pixel if both u and v are zero 
%ind2=find((stu(:).*stv(:)|sv(:).*su(:))~=0);
ind2=find(abs(stu(:))>smallflow|abs(stv(:)>smallflow)); 
%length(ind2)
n=1.0./sqrt(su(ind2).^2+sv(ind2).^2+1);
un=su(ind2).*n;
vn=sv(ind2).*n;
tn=1./sqrt(stu(ind2).^2+stv(ind2).^2+1);
tun=stu(ind2).*tn;
tvn=stv(ind2).*tn;
ang=acos(un.*tun+vn.*tvn+(n.*tn));
mang=mean(ang);
mang=mang*180/pi;

if nargout >= 2
    stdang = std(ang*180/pi);
end;

if nargout == 3
    epe = sqrt((stu-su).^2 + (stv-sv).^2);
    epe = epe(ind2);
    mepe = mean(epe(:));
end;

% show which pixels were ignored
% tmp=zeros(size(su));
% tmp(ind2)=1;
% imagesc(tmp)

Among the input parameters, u is the horizontal flow and v is the vertical flow.

Related Datasets

To find ground truth results for performance analysis of optical flow algorithms, these datasets below are quite useful:

• Middlebury Optical Flow Evaluation: The classic optical flow evaluation benchmark, featuring eight test images, with very accurate ground truth from a shape from UV light pattern system. 24 image pairs are provided in total.
• KITTI vision benchmark
  • Optical Flow Evaluation 2015
• UCL Ground Truth Optical Flow Dataset v1.2