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SIFT_feature.m
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SIFT_feature.m
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function [feature] = SIFT_feature(img)
img=rgb2gray(img);
[row,colum] = size(img);
img=im2double(img);
origin=img;
%% Scale-Space Extrema Detection
tic
% original sigma and the number of actave can be modified. the larger
% sigma0, the more quickly-smooth images
sigma0=sqrt(2);
octave=3;%6*sigma*k^(octave*level)<=min(m,n)/(2^(octave-2))
level=3;
D=cell(1,octave);
for i=1:octave
D(i)=mat2cell(zeros(row*2^(2-i)+2,colum*2^(2-i)+2,level),row*2^(2-i)+2,colum*2^(2-i)+2,level);
end
% first image in first octave is created by interpolating the original one.
temp_img=kron(img,ones(2));
temp_img=padarray(temp_img,[1,1],'replicate');
figure(2)
subplot(1,2,1);
imshow(origin)
%create the DoG pyramid.
for i=1:octave
temp_D=D{i};
for j=1:level
scale=sigma0*sqrt(2)^(1/level)^((i-1)*level+j);
p=(level)*(i-1);
figure(1);
subplot(octave,level,p+j);
f=fspecial('gaussian',[1,floor(6*scale)],scale);
L1=temp_img;
if(i==1&&j==1)
L2=conv2(temp_img,f,'same');
L2=conv2(L2,f','same');
temp_D(:,:,j)=L2-L1;
imshow(uint8(255 * mat2gray(temp_D(:,:,j))));
L1=L2;
else
L2=conv2(temp_img,f,'same');
L2=conv2(L2,f','same');
temp_D(:,:,j)=L2-L1;
L1=L2;
if(j==level)
temp_img=L1(2:end-1,2:end-1);
end
imshow(uint8(255 * mat2gray(temp_D(:,:,j))));
end
end
D{i}=temp_D;
temp_img=temp_img(1:2:end,1:2:end);
temp_img=padarray(temp_img,[1,1],'both','replicate');
end
toc
%% Keypoint Localistaion
% search each pixel in the DoG map to find the extreme point
tic
interval=level-1;
number=0;
for i=2:octave+1
number=number+(2^(i-octave)*colum)*(2*row)*interval;
end
extrema=zeros(1,4*number);
flag=1;
for i=1:octave
[m,n,~]=size(D{i});
m=m-2;
n=n-2;
volume=m*n/(4^(i-1));
for k=2:interval
for j=1:volume
% starter=D{i}(x+1,y+1,k);
x=ceil(j/n);
y=mod(j-1,m)+1;
sub=D{i}(x:x+2,y:y+2,k-1:k+1);
large=max(max(max(sub)));
little=min(min(min(sub)));
if(large==D{i}(x+1,y+1,k))
temp=[i,k,j,1];
extrema(flag:(flag+3))=temp;
flag=flag+4;
end
if(little==D{i}(x+1,y+1,k))
temp=[i,k,j,-1];
extrema(flag:(flag+3))=temp;
flag=flag+4;
end
end
end
end
idx= extrema==0;
extrema(idx)=[];
toc
[m,n]=size(img);
x=floor((extrema(3:4:end)-1)./(n./(2.^(extrema(1:4:end)-2))))+1;
y=mod((extrema(3:4:end)-1),m./(2.^(extrema(1:4:end)-2)))+1;
ry=y./2.^(octave-1-extrema(1:4:end));
rx=x./2.^(octave-1-extrema(1:4:end));
figure(2)
subplot(1,2,2);
imshow(origin)
hold on
plot(ry,rx,'r+');
%% accurate keypoint localization
%eliminate the point with low contrast or poorly localised on an edge
% x:|,y:-- x is for vertial and y is for horizontal
% value comes from the paper.
tic
threshold=0.1;
r=10;
extr_volume=length(extrema)/4;
[m,n]=size(img);
secondorder_x=conv2([-1,1;-1,1],[-1,1;-1,1]);
secondorder_y=conv2([-1,-1;1,1],[-1,-1;1,1]);
for i=1:octave
for j=1:level
test=D{i}(:,:,j);
temp=-1./conv2(test,secondorder_y,'same').*conv2(test,[-1,-1;1,1],'same');
D{i}(:,:,j)=temp.*conv2(test',[-1,-1;1,1],'same')*0.5+test;
end
end
for i=1:extr_volume
x=floor((extrema(4*(i-1)+3)-1)/(n/(2^(extrema(4*(i-1)+1)-2))))+1;
y=mod((extrema(4*(i-1)+3)-1),m/(2^(extrema(4*(i-1)+1)-2)))+1;
rx=x+1;
ry=y+1;
rz=extrema(4*(i-1)+2);
z=D{extrema(4*(i-1)+1)}(rx,ry,rz);
if(abs(z)<threshold)
extrema(4*(i-1)+4)=0;
end
end
idx=find(extrema==0);
idx=[idx,idx-1,idx-2,idx-3];
extrema(idx)=[];
extr_volume=length(extrema)/4;
x=floor((extrema(3:4:end)-1)./(n./(2.^(extrema(1:4:end)-2))))+1;
y=mod((extrema(3:4:end)-1),m./(2.^(extrema(1:4:end)-2)))+1;
ry=y./2.^(octave-1-extrema(1:4:end));
rx=x./2.^(octave-1-extrema(1:4:end));
figure(2)
subplot(2,2,3);
imshow(origin)
hold on
plot(ry,rx,'g+');
for i=1:extr_volume
x=floor((extrema(4*(i-1)+3)-1)/(n/(2^(extrema(4*(i-1)+1)-2))))+1;
y=mod((extrema(4*(i-1)+3)-1),m/(2^(extrema(4*(i-1)+1)-2)))+1;
rx=x+1;
ry=y+1;
rz=extrema(4*(i-1)+2);
Dxx=D{extrema(4*(i-1)+1)}(rx-1,ry,rz)+D{extrema(4*(i-1)+1)}(rx+1,ry,rz)-2*D{extrema(4*(i-1)+1)}(rx,ry,rz);
Dyy=D{extrema(4*(i-1)+1)}(rx,ry-1,rz)+D{extrema(4*(i-1)+1)}(rx,ry+1,rz)-2*D{extrema(4*(i-1)+1)}(rx,ry,rz);
Dxy=D{extrema(4*(i-1)+1)}(rx-1,ry-1,rz)+D{extrema(4*(i-1)+1)}(rx+1,ry+1,rz)-D{extrema(4*(i-1)+1)}(rx-1,ry+1,rz)-D{extrema(4*(i-1)+1)}(rx+1,ry-1,rz);
deter=Dxx*Dyy-Dxy*Dxy;
R=(Dxx+Dyy)/deter;
R_threshold=(r+1)^2/r;
if(deter<0||R>R_threshold)
extrema(4*(i-1)+4)=0;
end
end
idx=find(extrema==0);
idx=[idx,idx-1,idx-2,idx-3];
extrema(idx)=[];
extr_volume=length(extrema)/4;
x=floor((extrema(3:4:end)-1)./(n./(2.^(extrema(1:4:end)-2))))+1;
y=mod((extrema(3:4:end)-1),m./(2.^(extrema(1:4:end)-2)))+1;
ry=y./2.^(octave-1-extrema(1:4:end));
rx=x./2.^(octave-1-extrema(1:4:end));
figure(2)
subplot(2,2,4);
imshow(origin)
hold on
plot(ry,rx,'b+');
toc
%% Orientation Assignment(Multiple orientations assignment)
tic
kpori=zeros(1,36*extr_volume);
minor=zeros(1,36*extr_volume);
f=1;
flag=1;
for i=1:extr_volume
%search in the certain scale
scale=sigma0*sqrt(2)^(1/level)^((extrema(4*(i-1)+1)-1)*level+(extrema(4*(i-1)+2)));
width=2*round(3*1.5*scale);
count=1;
x=floor((extrema(4*(i-1)+3)-1)/(n/(2^(extrema(4*(i-1)+1)-2))))+1;
y=mod((extrema(4*(i-1)+3)-1),m/(2^(extrema(4*(i-1)+1)-2)))+1;
%make sure the point in the searchable area
if(x>(width/2)&&y>(width/2)&&x<(m/2^(extrema(4*(i-1)+1)-2)-width/2-2)&&y<(n/2^(extrema(4*(i-1)+1)-2)-width/2-2))
rx=x+1;
ry=y+1;
rz=extrema(4*(i-1)+2);
reg_volume=width*width;%3? thereom
% make weight matrix
weight=fspecial('gaussian',width,1.5*scale);
%calculate region pixels' magnitude and region orientation
reg_mag=zeros(1,count);
reg_theta=zeros(1,count);
for l=(rx-width/2):(rx+width/2-1)
for k=(ry-width/2):(ry+width/2-1)
reg_mag(count)=sqrt((D{extrema(4*(i-1)+1)}(l+1,k,rz)-D{extrema(4*(i-1)+1)}(l-1,k,rz))^2+(D{extrema(4*(i-1)+1)}(l,k+1,rz)-D{extrema(4*(i-1)+1)}(l,k-1,rz))^2);
reg_theta(count)=atan2((D{extrema(4*(i-1)+1)}(l,k+1,rz)-D{extrema(4*(i-1)+1)}(l,k-1,rz)),(D{extrema(4*(i-1)+1)}(l+1,k,rz)-D{extrema(4*(i-1)+1)}(l-1,k,rz)))*(180/pi);
count=count+1;
end
end
%make histogram
mag_counts=zeros(1,36);
for x=0:10:359
mag_count=0;
for j=1:reg_volume
c1=-180+x;
c2=-171+x;
if(c1<0||c2<0)
if(abs(reg_theta(j))<abs(c1)&&abs(reg_theta(j))>=abs(c2))
mag_count=mag_count+reg_mag(j)*weight(ceil(j/width),mod(j-1,width)+1);
end
else
if(abs(reg_theta(j)>abs(c1)&&abs(reg_theta(j)<=abs(c2))))
mag_count=mag_count+reg_mag(j)*weight(ceil(j/width),mod(j-1,width)+1);
end
end
end
mag_counts(x/10+1)=mag_count;
end
% find the max histogram bar and the ones higher than 80% max
[maxvm,~]=max(mag_counts);
kori=find(mag_counts>=(0.8*maxvm));
kori=(kori*10+(kori-1)*10)./2-180;
kpori(f:(f+length(kori)-1))=kori;
f=f+length(kori);
temp_extrema=[extrema(4*(i-1)+1),extrema(4*(i-1)+2),extrema(4*(i-1)+3),extrema(4*(i-1)+4)];
temp_extrema=padarray(temp_extrema,[0,length(temp_extrema)*(length(kori)-1)],'post','circular');
long=length(temp_extrema);
minor(flag:flag+long-1)=temp_extrema;
flag=flag+long;
end
end
idx= minor==0;
minor(idx)=[];
extrema=minor;
% delete unsearchable points and add minor orientation points
idx= kpori==0;
kpori(idx)=[];
extr_volume=length(extrema)/4;
toc
%% keypoint descriptor
tic
d=4;% In David G. Lowe experiment,divide the area into 4*4.
pixel=4;
feature=zeros(d*d*8,extr_volume);
for i=1:extr_volume
descriptor=zeros(1,d*d*8);% feature dimension is 128=4*4*8;
width=d*pixel;
%x,y centeral point and prepare for location rotation
x=floor((extrema(4*(i-1)+3)-1)/(n/(2^(extrema(4*(i-1)+1)-2))))+1;
y=mod((extrema(4*(i-1)+3)-1),m/(2^(extrema(4*(i-1)+1)-2)))+1;
z=extrema(4*(i-1)+2);
if((m/2^(extrema(4*(i-1)+1)-2)-pixel*d*sqrt(2)/2)>x&&x>(pixel*d/2*sqrt(2))&&(n/2^(extrema(4*(i-1)+1)-2)-pixel*d/2*sqrt(2))>y&&y>(pixel*d/2*sqrt(2)))
sub_x=(x-d*pixel/2+1):(x+d*pixel/2);
sub_y=(y-d*pixel/2+1):(y+d*pixel/2);
sub=zeros(2,length(sub_x)*length(sub_y));
j=1;
for p=1:length(sub_x)
for q=1:length(sub_y)
sub(:,j)=[sub_x(p)-x;sub_y(q)-y];
j=j+1;
end
end
distort=[cos(pi*kpori(i)/180),-sin(pi*kpori(i)/180);sin(pi*kpori(i)/180),cos(pi*kpori(i)/180)];
%accordinate after distort
sub_dis=distort*sub;
fix_sub=ceil(sub_dis);
fix_sub=[fix_sub(1,:)+x;fix_sub(2,:)+y];
patch=zeros(1,width*width);
for p=1:length(fix_sub)
patch(p)=D{extrema(4*(i-1)+1)}(fix_sub(1,p),fix_sub(2,p),z);
end
temp_D=(reshape(patch,[width,width]))';
%create weight matrix.
mag_sub=temp_D;
temp_D=padarray(temp_D,[1,1],'replicate','both');
weight=fspecial('gaussian',width,width/1.5);
mag_sub=weight.*mag_sub;
theta_sub=atan((temp_D(2:end-1,3:1:end)-temp_D(2:end-1,1:1:end-2))./(temp_D(3:1:end,2:1:end-1)-temp_D(1:1:end-2,2:1:end-1)))*(180/pi);
% create orientation histogram
for area=1:d*d
cover=pixel*pixel;
ori=zeros(1,cover);
magcounts=zeros(1,8);
for angle=0:45:359
magcount=0;
for p=1:cover;
x=(floor((p-1)/pixel)+1)+pixel*floor((area-1)/d);
y=mod(p-1,pixel)+1+pixel*(mod(area-1,d));
c1=-180+angle;
c2=-180+45+angle;
if(c1<0||c2<0)
if (abs(theta_sub(x,y))<abs(c1)&&abs(theta_sub(x,y))>=abs(c2))
ori(p)=(c1+c2)/2;
magcount=magcount+mag_sub(x,y);
end
else
if(abs(theta_sub(x,y))>abs(c1)&&abs(theta_sub(x,y))<=abs(c2))
ori(p)=(c1+c2)/2;
magcount=magcount+mag_sub(x,y);
end
end
end
magcounts(angle/45+1)=magcount;
end
descriptor((area-1)*8+1:area*8)=magcounts;
end
descriptor=normr(descriptor);
% cap 0.2
for j=1:numel(descriptor)
if(abs(descriptor(j))>0.2)
descriptor(j)=0.2;
end
end
descriptor=normr(descriptor);
else
continue;
end
feature(:,i)=descriptor';
end
index=find(sum(feature));
feature=feature(:,index);
toc