HornSchunck.m

function [u, v] = HornSchunck(im1, im2, alpha, ite, uInitial, vInitial, displayFlow)
% Horn-Schunck optical flow method
% Horn, B.K.P., and Schunck, B.G., Determining Optical Flow, AI(17), No.
% 1-3, August 1981, pp. 185-203 http://dspace.mit.edu/handle/1721.1/6337
%
% Usage:
% [u, v] = HS(im1, im2, alpha, ite, uInitial, vInitial, displayFlow)
% For an example, run this file from the menu Debug->Run or press (F5)
%
% -im1,im2 : two subsequent frames or images.
% -alpha : a parameter that reflects the influence of the smoothness term.
% -ite : number of iterations.
% -uInitial, vInitial : initial values for the flow. If available, the
% flow would converge faster and hence would need less iterations ; default is zero.
% -displayFlow : 1 for display, 0 for no display ; default is 1.
% -displayImg : specify the image on which the flow would appear ( use an
% empty matrix "[]" for no image. )
%
% Author: Mohd Kharbat at Cranfield Defence and Security
% mkharbat(at)ieee(dot)org , http://mohd.kharbat.com
% Published under a Creative Commons Attribution-Non-Commercial-Share Alike
% 3.0 Unported Licence http://creativecommons.org/licenses/by-nc-sa/3.0/
%
% October 2008
% Rev: Jan 2009

%% Default parameters
arguments
  im1 (:,:) {mustBeNumeric}
  im2 (:,:) {mustBeNumeric}
  alpha (1,1) {mustBeNumeric} = 1
  ite (1,1) {mustBePositive,mustBeInteger} = 100
  uInitial (:,:) {mustBeNumeric} = zeros(size(im1(:,:,1)))
  vInitial (:,:) {mustBeNumeric} = zeros(size(im2(:,:,1)))
  displayFlow (1,1) = false
end

im1=smoothImg(im1,1);
im2=smoothImg(im2,1);

tic;

%%
% Set initial value for the flow vectors
u = uInitial;
v = vInitial;

% Estimate spatiotemporal derivatives
[fx, fy, ft] = computeDerivatives(im1, im2);

% Averaging kernel
kernel_1=[1/12 1/6 1/12;1/6 0 1/6;1/12 1/6 1/12];

% Iterations
for i=1:ite
    % Compute local averages of the flow vectors
    uAvg=conv2(u,kernel_1,'same');
    vAvg=conv2(v,kernel_1,'same');
    % Compute flow vectors constrained by its local average and the optical flow constraints
    der = ( fx.*uAvg + fy.*vAvg + ft ) ./ ( alpha^2 + fx.^2 + fy.^2);
    u = uAvg - fx .* der;
    v = vAvg - fy .* der;
end

u(isnan(u))=0;
v(isnan(v))=0;

%% Plotting
if displayFlow
    plotFlow(u, v, im1, 5, 5);
end