FAST means Features from Accelerated Segment Test. FAST use a circle around the central pixel as a base of computation. Let's take the next pixels as an example where pc is the central pixel.
A circle of radius 3 give us a vecteur of 16 pixels:
We compute for each pixel f the vector the difference between itself and the central pixel. A high and low threshold is then choose aroundthe value of the central pixel. We define 3 states according to the result of the difference:
If we apply the previous algorythm, we find the next vector:
We can note that to detect corner, sequence of eleven 1 (or -1) must be contain in the vector. To render the detection more flexible, the algorythm detects sequence from 10 to 12 points.
clear all;
close all;
[filename, pathname] = uigetfile({'*.jpg;*.tif;*.png;*.gif;*.bmp','All Image Files';...
'*.*','All Files' },'mytitle',...
'C:\Work\myfile.jpg')
img = imread(filename);
if length(size(img))>2
img=mean(img,3);
end
[ligneorigine colonneorigine]=size(img);
%effet de bord
taille=3;
img = wextend(2,'zpd',img,taille);
dolong=0;
[ligne colonne]=size(img);
resultat = zeros(ligne,colonne);
for i = taille+1 : ligne-(taille+1)
for j = taille+1 : colonne -(taille+1)
p = img(i,j);
threshold_haut = p+50;
threshold_haut(threshold_haut>255)=255;
threshold_bas = p-50;
threshold_bas(threshold_bas<0)=0;
v=[img(i-3,j) img(i-3,j+1) img(i-2,j+2) img(i-1,j+3) img(i,j+3) img(i+1,j+3) img(i+2,j+2) img(i+3,j+1) ...
img(i+3,j) img(i+3,j-1) img(i+2,j-2) img(i+1,j-3) img(i,j-3) img(i-1,j-3) img(i-2,j-2) img(i-3,j-1)] ;
v(v<threshold_bas)=-1;
v(threshold_bas<=v & v<=threshold_haut)=0;
v(threshold_haut<v)=1;
v2=[v v];
v=[img(i-3,j) img(i-3,j+1) img(i-2,j+2) img(i-1,j+3) img(i,j+3) img(i+1,j+3) img(i+2,j+2) img(i+3,j+1) ...
img(i+3,j) img(i+3,j-1) img(i+2,j-2) img(i+1,j-3) img(i,j-3) img(i-1,j-3) img(i-2,j-2) img(i-3,j-1)] ;
for ilong = 1 : 16
if (sum(v2(ilong:ilong+9)) == 10) && (sum(v2(ilong:ilong+10)) ~= 11)
resultat(i,j)= 1;
elseif (sum(v2(ilong:ilong+10)) == 11) && (sum(v2(ilong:ilong+11)) ~= 12)
resultat(i,j)= 1;
elseif (sum(v2(ilong:ilong+11)) == 12) && (sum(v2(ilong:ilong+12)) ~= 13)
resultat(i,j)= 1;
elseif (sum(v2(ilong:ilong+9)) == -10) && (sum(v2(ilong:ilong+10)) ~= -11)
resultat(i,j)= 1;
elseif (sum(v2(ilong:ilong+10)) == -11) && (sum(v2(ilong:ilong+11)) ~= -12)
resultat(i,j)= -1;
elseif (sum(v2(ilong:ilong+11)) == -12) && (sum(v2(ilong:ilong+12)) ~= -13)
resultat(i,j)= -1;
end
end
end
i
end
resultat = resultat(taille:end-taille-1,taille:end-taille-1);
img = img(taille:end-taille-1,taille:end-taille-1);
figure( 'Name','corner detection FAST',...
'NumberTitle','off',...
'color',[0.3137 0.3137 0.5098]);
imshow(uint8(img))
hold on
[ligne colonne]=size(img);
for i = 1 : ligne
for j = 1 : colonne
if resultat(i,j)==1
plot([j-2 j-2 j+2 j+2 j-2],...
[i-2 i+2 i+2 i-2 i-2] ,'r','LineWidth',1)
elseif resultat(i,j)==-1
plot([j-2 j-2 j+2 j+2 j-2],...
[i-2 i+2 i+2 i-2 i-2] ,'g','LineWidth',1)
end
end
end
Here is an example 
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