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 ```function gauss=gauss2D(sigma,orient,aspect,norm,pxsize,cntr,order) ``` ```%function gauss=gauss2D(sigma,orient,aspect,norm,pxsize,cntr,order) ``` ```% ``` ```% This function produces a numerical approximation to Gaussian function with ``` ```% variable aspect ratio. ``` ```% Parameters: ``` ```% sigma = standard deviation of Gaussian envelope, this in-turn controls the ``` ```% size of the result (pixels) ``` ```% orient = orientation of the Gaussian clockwise from the vertical (degrees) ``` ```% Optional, if not specified orient=0. ``` ```% aspect = aspect ratio of Gaussian envelope (0 = no "length" to envelope, ``` ```% 1 = circular symmetric envelope) ``` ```% Optional, if not specified aspect=1. ``` ```% norm = 1 to normalise the gaussian so that it sums to 1 ``` ```% = 0 for no normalisation (gaussian has max value of 1) ``` ```% Optional, default value is 1. ``` ```% pxsize = the size of the filter. ``` ```% Optional, if not specified size is 6*sigma*max(1,aspect) ``` ```% cntr = location of the centre of the gaussian. ``` ```% Optional, if not specified gaussian is centred in the middle of image. ``` ```% order = order of differential. Differential is calculated in the y direction. ``` ```% Valid values are whole numbers from 0 (output is not differentiated) ``` ```% to 4 (output is the 4th differential of a gaussian). ``` ```% Optional, if not specified default is 0. ``` ``` ``` ```if nargin<2 || isempty(orient), orient=0; end ``` ```if nargin<3 || isempty(aspect), aspect=1; end ``` ```if nargin<4 || isempty(norm), norm=1; end ``` ```if nargin<5 || isempty(pxsize), pxsize=[1,1].*odd(6*sigma*max(1,aspect)); end ``` ```if nargin<6 || isempty(cntr), cntr=0.5+pxsize./2; end ``` ```if nargin<7 || isempty(order), order=0; end ``` ``` ``` ```scale=1; %0.2;0.04 ``` ``` ``` ```%define grid of x,y coodinates at which to define function ``` ```[x y]=meshgrid(1-0.5+scale/2:scale:pxsize(1)+0.5-scale/2,... ``` ``` 1-0.5+scale/2:scale:pxsize(2)+0.5-scale/2); ``` ``` ``` ```%rotate ``` ```orient=-orient*pi/180; ``` ```x_theta=(x-cntr(1))*cos(orient)+(y-cntr(2))*sin(orient); ``` ```y_theta=-(x-cntr(1))*sin(orient)+(y-cntr(2))*cos(orient); ``` ``` ``` ```%avoid division by zero errors ``` ```sigma=max(1e-15,sigma); ``` ``` ``` ```%define gaussian ``` ```gauss=exp(-.5*( ((x_theta.^2)./((sigma*aspect).^2)) ... ``` ``` + ((y_theta.^2)./(sigma.^2)) )); ``` ```gauss=gauss./(sigma*sqrt(2*pi)); ``` ``` ``` ```%differentiate gaussian, if requested ``` ```if order==0 ``` ``` %do nothing ``` ```elseif order==1 ``` ``` gauss=gauss.*(-y_theta./(sigma^2)); ``` ```elseif order==2 ``` ``` gauss=gauss.*(((y_theta.^2)-(sigma^2))./(sigma^4)); ``` ```elseif order==3 ``` ``` gauss=gauss.*(-y_theta.*((y_theta.^2)-(3*sigma^2))./(sigma^6)); ``` ```elseif order==4 ``` ``` gauss=gauss.*(((y_theta.^4)-(6.*y_theta.^2.*sigma^2)+(3*sigma^4))./(sigma^8)); ``` ```else ``` ``` disp('ERROR: order of differential applied to gaussian, not defined'); ``` ```end ``` ```gauss=imresize(gauss,scale); ``` ``` ``` ```%normalise ``` ```if norm, ``` ``` gauss=gauss./sum(sum(abs(gauss))); ``` ```else ``` ``` gauss=gauss./max(max(abs(gauss))); ``` ```end ```