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function [us,vs] = HSoptflow(Xrgb,n)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Author: Gregory Power gregory.power@wpafb.af.mil

% This MATLAB code shows a Motion Estimation map created by % using a Horn and Schunck motion estimation technique on two % consecutive frames. Input requires.

% Xrgb(h,w,d,N) where X is a frame sequence of a certain % height(h), width (w), depth (d=3 for color), % and number of frames (N).

% n= is the starting frame number which is less than N % V= the output variable which is a 2D velocity array %

% Sample Call: V=HSoptflow(X,3);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

[h,w,d,N]=size(Xrgb); if n>N-1

error(1,'requested file greater than frame number required'); end;

%get two image frames if d==1

Xn=double(Xrgb(:,:,1,n));

Xnp1=double(Xrgb(:,:,1,n+1)); elseif d==3

Xn=double(Xrgb(:,:,1,n)*0.299+Xrgb(:,:,2,n)*0.587+Xrgb(:,:,3,n)*0.114);

Xnp1=double(Xrgb(:,:,1,n+1)*0.299+Xrgb(:,:,2,n+1)*0.587+Xrgb(:,:,3,n+1)*0.114); else

error(2,'not an RGB or Monochrome image file'); end;

%get image size and adjust for border size(Xn);

hm5=h-5; wm5=w-5;

z=zeros(h,w); v1=z; v2=z;

%initialize

dsx2=v1; dsx1=v1; dst=v1; alpha2=625; imax=20;

êlculate gradients

dst(5:hm5,5:wm5) = ( Xnp1(6:hm5+1,6:wm5+1)-Xn(6:hm5+1,6:wm5+1) + Xnp1(6:hm5+1,5:wm5)-Xn(6:hm5+1,5:wm5)+ Xnp1(5:hm5,6:wm5+1)-Xn(5:hm5,6:wm5+1) +Xnp1(5:hm5,5:wm5)-Xn(5:hm5,5:wm5))/4;

dsx2(5:hm5,5:wm5) = ( Xnp1(6:hm5+1,6:wm5+1)-Xnp1(5:hm5,6:wm5+1) + Xnp1(6:hm5+1,5:wm5)-Xnp1(5:hm5,5:wm5)+ Xn(6:hm5+1,6:wm5+1)-Xn(5:hm5,6:wm5+1) +Xn(6:hm5+1,5:wm5)-Xn(5:hm5,5:wm5))/4;

dsx1(5:hm5,5:wm5) = ( Xnp1(6:hm5+1,6:wm5+1)-Xnp1(6:hm5+1,5:wm5) + Xnp1(5:hm5,6:wm5+1)-Xnp1(5:hm5,5:wm5)+ Xn(6:hm5+1,6:wm5+1)-Xn(6:hm5+1,5:wm5) +Xn(5:hm5,6:wm5+1)-Xn(5:hm5,5:wm5))/4;

for i=1:imax

delta=(dsx1.*v1+dsx2.*v2+dst)./(alpha2+dsx1.^2+dsx2.^2); v1=v1-dsx1.*delta; v2=v2-dsx2.*delta; end;

u=z; u(5:hm5,5:wm5)=v1(5:hm5,5:wm5); v=z; v(5:hm5,5:wm5)=v2(5:hm5,5:wm5);

xskip=round(h/64);

[hs,ws]=size(u(1:xskip:h,1:xskip:w)) us=zeros(hs,ws); vs=us;

N=xskip^2; for i=1:hs-1 for j=1:ws-1

hk=i*xskip-xskip+1; hl=i*xskip;

wk=j*xskip-xskip+1; wl=j*xskip;

us(i,j)=sum(sum(u(hk:hl,wk:wl)))/N; vs(i,j)=sum(sum(v(hk:hl,wk:wl)))/N; end; end;

figure(1); quiver(us,vs);

colormap('default'); axis ij; axis tight; axis equal;

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