matlab - How does the Gabor filter work? -

i have found gabor filter source code this link. code clean , well-documented.

my question here,

for = 1:u         ...............     ...............     ...............             j = 1:v         tetav = ((j-1)/v)*pi;         .....................                     x = 1:m             y = 1:n                 xprime = ........                 yprime = ........                 gfilter(x,y) = ........             end         end         gaborarray{i,j} = gfilter;             end end 

what mean tetav = ((j-1)/v)*pi;? radian or degree? if radian, why wasn't divided 180?

why kernel computation go 1 m or n? why not -(m/2) (m+1)/2?

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source code

gaborfeatures.m

function gaborresult = gaborfeatures(img,gaborarray,d1,d2)  if (nargin ~= 4)        % check correct number of arguments     error('please use correct number of input arguments!') end  if size(img,3) == 3     % check if input image grayscale     warning('the input rgb image converted grayscale!')     img = rgb2gray(img); end  img = double(img);   % filter input image each gabor filter [u,v] = size(gaborarray); gaborresult = cell(u,v); = 1:u     j = 1:v         gaborresult{i,j} = imfilter(img, gaborarray{i,j});     end end 

gaborfilterbank.m

function gaborarray = gaborfilterbank(u,v,m,n)     if (nargin ~= 4)    % check correct number of arguments     error('there must 4 input arguments (number of scales , orientations , 2-d size of filter)!') end   % create u*v gabor filters each being m n matrix  gaborarray = cell(u,v); fmax = 0.25; gama = sqrt(2); eta = sqrt(2);  = 1:u      fu = fmax/((sqrt(2))^(i-1));     alpha = fu/gama;     beta = fu/eta;      j = 1:v         tetav = ((j-1)/v)*pi;         gfilter = zeros(m,n);          x = 1:m             y = 1:n                 xprime = (x-((m+1)/2))*cos(tetav)+(y-((n+1)/2))*sin(tetav);                 yprime = -(x-((m+1)/2))*sin(tetav)+(y-((n+1)/2))*cos(tetav);                 gfilter(x,y) = (fu^2/(pi*gama*eta))*exp(-((alpha^2)*(xprime^2)+(beta^2)*(yprime^2)))*exp(1i*2*pi*fu*xprime);             end         end         gaborarray{i,j} = gfilter;             end end 

what mean tetav = ((j-1)/v)*pi;?

this means tetav take on increasingly larger pieces of pi; starting 0 , increasing whole thing (i.e. 3.14159...). there 180 degrees or pi radians in half circle. tetav taking on increasingly portions of half circle.

is radian or degree?

it radians.

if radian, why wasn't divided 180?

radians desired unit here (for whoever programmed this). have instead multiplied pi if wanted in degrees. if, hypothetically, thinking expression ((j-1)/v) in degrees , needed converted radians multiplication of pi/180, mean function cover, @ most, 1 degree of circle.

why kernel computation go 1 m or n? why not -(m/2) (m+1)/2?

it because chose instead handle -(m/2) (m+1)/2 inside loop. in code posted gaborfilterbank.m file:

xprime = (x-((m+1)/2))*cos(tetav)+(y-((n+1)/2))*sin(tetav); yprime = -(x-((m+1)/2))*sin(tetav)+(y-((n+1)/2))*cos(tetav); 

since sin , cosine being combined, you'll getting full circle covered gabor filter. , offset adjusted x , y center points -((m+1)/2) calls. example, when x = 1 expression (x-((m+1)/2)) becomes -(m+1)/2+1 or -m/2+0.5 , when x = m, same expression becomes m/2+0.5, still covering range wondering about.