TLD之L-K光流算法代码篇

代码是国外的大神Musawir Ali Shah 写的，我拿过来研究了一下，代码原理和步骤都明白了，代码里面都有我个人参考的资料名称或者链接，以及我个人的注释，这次就先上代码！下一次上原理！

主函数： main.m

clc;
clear all;
close all;
file1='yos9.tif';
file2='yos10.tif';
density=10;
%% Read Images %%
img1 = im2double (imread (file1));
%% Take alternating rows and columns %%
[odd1, even1] = split (img1); %在行方向分解成奇数行和偶数行
img2 = im2double (imread (file2));
[odd2, even2] = split (img2);
%% Run Lucas Kanade %%
[Dx, Dy] = Estimate (odd1, odd2);
%% Plot %%
figure;
[maxI,maxJ]=size(Dx);
Dx=Dx(1:density:maxI,1:density:maxJ);
Dy=Dy(1:density:maxI,1:density:maxJ);
quiver(1:density:maxJ,(maxI):(-density):1,Dx,-Dy,1);
axis square;

Estimate.m

<span style="font-size:18px;">% Run Lucas Kanade on all levels and interpolate（插入） %%
function [Dx, Dy] = Estimate (img1, img2)
%[Dx, Dy] = Estimate (odd1, odd2);   img1=odd1;  img2=odd2;
level = 4;
half_window_size=2;
[m, n] = size (img1);
G00 = img1; G10 = img2;
if (level>0)
G01 = reduce (G00); G11 = reduce (G10); %进行的是高斯金字塔分解算法。
end
if (level>1)
G02 = reduce (G01); G12 = reduce (G11);
end
if (level>2)
G03 = reduce (G02); G13 = reduce (G12);
end
if (level>3)
G04 = reduce (G03); G14 = reduce (G13);
end
subplot(2,2,1);
imshow(G00)
subplot(2,2,2);
imshow(G01)
subplot(2,2,3);
imshow(G02)
subplot(2,2,4);
imshow(G03)

l = level;

for i=level:-1:0,
if (l == level)
switch (l)
case 4, Dx = zeros (size (G04)); Dy = zeros (size (G04));
case 3, Dx = zeros (size (G03)); Dy = zeros (size (G03));
case 2, Dx = zeros (size (G02)); Dy = zeros (size (G02));
case 1, Dx = zeros (size (G01)); Dy = zeros (size (G01));
case 0, Dx = zeros (size (G00)); Dy = zeros (size (G00));
end
else
Dx = expand (Dx); Dy = expand (Dy);
Dx = Dx .* 2; Dy = Dy .* 2;
end
switch (l)
case 4,
W = warp (G04, Dx, Dy);
[Vx, Vy] = EstimateMotion (W, G14, half_window_size);
case 3,
W = warp (G03, Dx, Dy);
[Vx, Vy] = EstimateMotion (W, G13, half_window_size);
case 2,
W = warp (G02, Dx, Dy);
[Vx, Vy] = EstimateMotion (W, G12, half_window_size);
case 1,
W = warp (G01, Dx, Dy);
[Vx, Vy] = EstimateMotion (W, G11, half_window_size);
case 0,
W = warp (G00, Dx, Dy);
[Vx, Vy] = EstimateMotion (W, G10, half_window_size);
end
[m, n] = size (W);
Dx(1:m, 1:n) = Dx(1:m,1:n) + Vx; Dy(1:m, 1:n) = Dy(1:m, 1:n) + Vy;
smooth (Dx); smooth (Dy);
l = l - 1;
end
</span>

算法的核心函数：EstimateMotion.m

<span style="font-size:18px;">% Lucas Kanade on the image sequence at pyramid step %%
function [Vx, Vy] = EstimateMotion (W, G1, half_window_size) % [Vx, Vy] = EstimateMotion (W, G14, half_window_size);G1=G14
[m, n] = size (W);
Vx = zeros (size (W)); Vy = zeros (size (W));%初始化
N = zeros (2*half_window_size+1, 5);%为空间邻域5*5   此处参考的是：基于光流场的视频运动检测
for i = 1:m,
l = 0;
for j = 1-half_window_size:1+half_window_size,
l = l + 1;
N (l,:) = getSlice (W, G1, i, j, half_window_size);%求出想，方向的偏导数
end
replace = 1;
for j = 1:n,
t = sum (N);
[v, d] = eig ([t(1) t(2);t(2) t(3)]);%梯度矩阵
namda1 = d(1,1); namda2 = d(2,2);
if (namda1 > namda2)
tmp = namda1; namda1 = namda2; namda2 = tmp;
tmp1 = v (:,1); v(:,1) = v(:,2); v(:,2) = tmp1;
end
if (namda2 < 0.001)%不满足
Vx (i, j) = 0; Vy (i, j) = 0;
elseif (namda2 > 100 * namda1)%不满足
n2 = v(1,2) * t(4) + v(2,2) * t(5);
Vx (i,j) = n2 * v(1,2) / namda2;
Vy (i,j) = n2 * v(2,2) / namda2;
else%执行
n1 = v(1,1) * t(4) + v(2,1) * t(5);%计算的是图像的光流（inv(G)*b）  t(4)和t(5)表示的是图像的比匹配向量
n2 = v(1,2) * t(4) + v(2,2) * t(5);
Vx (i,j) = n1 * v(1,1) / namda1 + n2 * v(1,2) / namda2;%就这个地方的公式仅仅针对半正定（类似于[a,b;b,c]的形式）的矩阵可以有如下的计算：这4行等价于inv(G)*b  即inv([t(1) t(2);t(2) t(3)])*[t(4,t(5))]'
Vy (i,j) = n1 * v(2,1) / namda1 + n2 * v(2,2) / namda2;%代码的结尾后面有相关的举例说明。
end
N (replace, :) = getSlice (W, G1, i, j+half_window_size+1, half_window_size);
replace = replace + 1;
if (replace == 2 * half_window_size + 2)
replace = 1;
end
end
end

%%解释那个不清楚的公式：只有在半正定的情况下才能使用：
% 计算方法一“
% a=[1,2;2,3];
% t=[2,3]';
% inv(a)*t
% 计算方法二
% %仅仅只有在半正定的情况下才能使用
% [v,d]=eig(a);
% namda1 = d(1,1); namda2 = d(2,2);
% n1 = v(1,1) * t(1) + v(2,1) * t(2);
% n2 = v(1,2) * t(1) + v(2,2) * t(2);
% n1 * v(1,1) / namda1 + n2 * v(1,2) / namda2
% n1 * v(2,1) / namda1 + n2 * v(2,2) / namda2</span>

getSlice.m

<span style="font-size:18px;">%计算图像的不匹配向量
function
= getSlice (W, G1, i, j, half_window_size) %  N (l,:) = getSlice (W, G1, i, j, half_window_size)
N = zeros (1, 5);
[m, n] = size (W);
for y=-half_window_size:half_window_size,
Y1 = y +i;
if (Y1 < 1)
Y1 = Y1 + m;
elseif (Y1 > m)
Y1 = Y1 - m;
end
X1 = j;
if (X1 < 1)
X1 = X1 + n;
elseif (X1 > n)
X1 = X1 - n;
end
DeriX = Derivative (G1, X1, Y1, 'x'); DeriY = Derivative (G1, X1, Y1, 'y');
N = N + [ DeriX * DeriX, ...
DeriX * DeriY, ...
DeriY * DeriY, ...
DeriX * (G1 (Y1, X1) - W (Y1, X1)), ... %G1 (Y1, X1) - W (Y1, X1)计算的是图像的像素差   DeriX * (G1 (Y1, X1) - W (Y1, X1))求和后就是算的是图像的不匹配向量
DeriY * (G1 (Y1, X1) - W (Y1, X1))]; %
end </span>

Derivative.m

<span style="font-size:18px;">% Calculates the Fx Fy %%  DeriX = Derivative (G1, X1, Y1, 'x');
function result = Derivative (img, x, y, direction)
[m, n] = size (img);
switch (direction)
case 'x',
if (x == 1)
result = img (y, x+1) - img (y, x);
elseif (x == n)
result = img (y, x) - img (y, x-1);
else
result = 0.5 * (img (y, x+1) - img (y, x-1));
end
case 'y',
if (y == 1)
result = img (y+1, x) - img (y, x);
elseif (y == m)
result = img (y, x) - img (y-1, x);
else
result = 0.5 * (img (y+1, x) - img (y-1, x));
end
end</span>

smooth.m

<span style="font-size:18px;">function result = smooth (img)
result = expand (reduce (img)); </span>

expand.m

<span style="font-size:18px;">% The Expansion Function for pyramid %%
function result = expand (ori)
[m,n] = size (ori);
mid = zeros (m, n);
m1 = m * 2; n1 = n * 2;
result = zeros (m1, n1);
w = generateFilter (0.4);
for j=1:m,
t = zeros (1, n1);
t(1:2:n1-1) = ori (j,1:n);
tmp = conv ([ori(j,n) 0 t ori(j,1) 0], w); %tmp长度为：n1+5+4-1
mid(j,1:n1) = 2 .* tmp (5:n1+4);
end
for i=1:n1,
t = zeros (1, m1);
t(1:2:m1-1) = mid (1:m,i)';
tmp = conv([mid(m,i) 0 t mid(1,i) 0], w);
result(1:m1,i) = 2 .* tmp (5:m1+4)';
end
</span>

Warp.m

<span style="font-size:18px;">% Interpolation %%
function result = warp (img, Dx, Dy) % W = warp (G04, Dx, Dy);  img=G04;
[m, n] = size (img);
[x,y] = meshgrid (1:n, 1:m); %x,y均是m*n的矩阵
x = x + Dx (1:m, 1:n); y = y + Dy (1:m,1:n);
for i=1:m,
for j=1:n,
if x(i,j)>n
x(i,j) = n;
end
if x(i,j)<1
x(i,j) = 1;
end
if y(i,j)>m
y(i,j) = m;
end
if y(i,j)<1
y(i,j) = 1;
end
end
end
result = interp2 (img, x, y, 'linear');%看帮助文档  surf(x,y,result);</span>

reduce.m

<span style="font-size:18px;">% The Reduce Function for pyramid %%
function result = reduce (ori)
[m,n] = size (ori);
mid = zeros (m, n);
m1 = round (m/2); n1 = round (n/2);
result = zeros (m1, n1);
w = generateFilter (0.4); %产生的是一个长度为5的滤波器。窗口函数
for j=1:m, %行方向的线性卷积
tmp = conv([ori(j,n-1:n) ori(j,1:n) ori(j,1:2)], w); %计算的是两个向量的线性卷积（长度为2+n+2+4-1=n+7）：http://blog.csdn.net/styxqdz/article/details/4943089
mid(j,1:n1) = tmp(5:2:n+4);
end
for i=1:n1, %列方向的线性卷积
tmp = conv([mid(m-1:m,i); mid(1:m,i); mid(1:2,i)]', w);
result(1:m1,i) = tmp(5:2:m+4)';
end </span>

generateFilter .m

<span style="font-size:18px;">function filter = generateFilter (alpha)
filter = [0.25-alpha/2 0.25 alpha 0.25 0.25-alpha/2]; %0.25=1/4（4表示的是滤波器的长度）</span>

split .m

<span style="font-size:18px;">function [odd, even] = split (img);
[m, n] = size (img);
odd = img (1:2:m, :);
even = img (2:2:m, :); </span>

运行结果：



这幅是通过高斯金字塔获得的图像（层数分别为：1,2,3,4）