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- % IM = mkGaussian(SIZE, COVARIANCE, MEAN, AMPLITUDE)
- %
- % Compute a matrix with dimensions SIZE (a [Y X] 2-vector, or a
- % scalar) containing a Gaussian function, centered at pixel position
- % specified by MEAN (default = (size+1)/2), with given COVARIANCE (can
- % be a scalar, 2-vector, or 2x2 matrix. Default = (min(size)/6)^2),
- % and AMPLITUDE. AMPLITUDE='norm' (default) will produce a
- % probability-normalized function. All but the first argument are
- % optional.
- % Eero Simoncelli, 6/96.
- function [res] = mkGaussian(sz, cov, mn, ampl)
- sz = sz(:);
- if (size(sz,1) == 1)
- sz = [sz,sz];
- end
- %------------------------------------------------------------
- %% OPTIONAL ARGS:
- if (exist('cov') ~= 1)
- cov = (min(sz(1),sz(2))/6)^2;
- end
- if ( (exist('mn') ~= 1) | isempty(mn) )
- mn = (sz+1)/2;
- else
- mn = mn(:);
- if (size(mn,1) == 1)
- mn = [mn, mn];
- end
- end
- if (exist('ampl') ~= 1)
- ampl = 'norm';
- end
- %------------------------------------------------------------
- [xramp,yramp] = meshgrid([1:sz(2)]-mn(2),[1:sz(1)]-mn(1));
- if (sum(size(cov)) == 2) % scalar
- if (strcmp(ampl,'norm'))
- ampl = 1/(2*pi*cov(1));
- end
- e = (xramp.^2 + yramp.^2)/(-2 * cov);
- elseif (sum(size(cov)) == 3) % a 2-vector
- if (strcmp(ampl,'norm'))
- ampl = 1/(2*pi*sqrt(cov(1)*cov(2)));
- end
- e = xramp.^2/(-2 * cov(2)) + yramp.^2/(-2 * cov(1));
- else
- if (strcmp(ampl,'norm'))
- ampl = 1/(2*pi*sqrt(det(cov)));
- end
- cov = -inv(cov)/2;
- e = cov(2,2)*xramp.^2 + (cov(1,2)+cov(2,1))*(xramp.*yramp) ...
- + cov(1,1)*yramp.^2;
- end
-
- res = ampl .* exp(e);
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