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68 lines
2.4 KiB
Matlab
68 lines
2.4 KiB
Matlab
function gauss=gauss2D(sigma,orient,aspect,norm,pxsize,x0,y0,order)
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%function gauss=gauss2D(sigma,orient,aspect,norm,pxsize,x0,y0,order)
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%
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% This function produces a numerical approximation to Gaussian function with
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% variable aspect ratio.
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% Parameters:
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% sigma = standard deviation of Gaussian envelope, this in-turn controls the
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% size of the result (pixels)
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% orient = orientation of the Gaussian clockwise from the vertical (degrees)
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% Optional, if not specified orient=0.
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% aspect = aspect ratio of Gaussian envelope (0 = no "length" to envelope,
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% 1 = circular symmetric envelope)
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% Optional, if not specified aspect=1.
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% norm = 1 to normalise the gaussian so that it sums to 1
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% = 0 for no normalisation (gaussian has max value of 1)
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% Optional, default value is 1.
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% pxsize = the size of the filter.
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% Optional, if not specified size is 5*sigma.
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% x0,y0 = location of the centre of the gaussian.
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% Optional, if not specified gaussian is centred in the middle of image.
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% order = order of differential. Differential is calculated in the y direction.
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% Valid values are whole numbers from 0 (output is not differentiated)
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% to 2 (output is 2nd differential of a gaussian).
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% Optional, if not specified default is 0.
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if nargin<2 || isempty(orient), orient=0; end
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if nargin<3 || isempty(aspect), aspect=1; end
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if nargin<4 || isempty(norm), norm=1; end
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if nargin<5 || isempty(pxsize), pxsize=odd(5*sigma); end
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if nargin<6 || isempty(x0), x0=0; end
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if nargin<7 || isempty(y0), y0=0; end
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if nargin<8 || isempty(order), order=0; end
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%define grid of x,y coodinates at which to define function
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pxrange=(pxsize-1)/2;
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[x y]=meshgrid(-pxrange:pxrange,-pxrange:pxrange);
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%rotate
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orient=-orient*pi/180;
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x_theta=(x-x0)*cos(orient)+(y-y0)*sin(orient);
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y_theta=-(x-x0)*sin(orient)+(y-y0)*cos(orient);
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%avoid division by zero errors
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sigma=max(1e-15,sigma);
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%define gaussian
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gauss=exp(-.5*( ((x_theta.^2)./((sigma*aspect).^2)) ...
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+ ((y_theta.^2)./(sigma.^2)) ));
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gauss=gauss./(sigma*sqrt(2*pi));
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%differentiate gaussian, if requested
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if order==0
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%do nothing
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elseif order==1
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gauss=gauss.*(-y_theta./(sigma^2));
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elseif order==2
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gauss=gauss.*((y_theta.^2-sigma^2)./(sigma^4));
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else
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disp('ERROR: order of differential applied to gaussian, not defined');
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end
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%normalise
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if norm,
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gauss=gauss./sum(sum(abs(gauss)));
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else
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gauss=gauss./max(max(abs(gauss)));
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end
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