load_image.m

This document is intended to serve as an introduction to Wavelet processing through a set of Matlab

function M = load_image(type, n, options)

% load_image - load benchmark images.
%
%   M = load_image(name, n, options);
%
%   name can be:
%   Synthetic images:
%       'chessboard1', 'chessboard', 'square', 'disk', 'quaterdisk', '3contours', 'line',
%       'line_vertical', 'line_horizontal', 'line_diagonal', 'line_circle',
%       'parabola', 'sin', 'phantom', 'circ_oscil',
%       'fnoise' (1/f^alpha noise).
%   Natural images:
%       'boat', 'lena', 'goldhill', 'mandrill', 'maurice', 'polygons_blurred', or your own.
%   
%   Copyright (c) 2004 Gabriel Peyr?

if nargin<2
    n = 512;
end
options.null = 0;

type = lower(type);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% parameters for geometric objects
eta = 0.1;              % translation
gamma = 1/sqrt(2);      % slope
if isfield( options, 'eta' )
    eta = options.eta;
end
if isfield( options, 'gamma' )
    eta = options.gamma;
end
if isfield( options, 'radius' )
    radius = options.radius;
end
if isfield( options, 'center' )
    center = options.center;
end
if isfield( options, 'center1' )
    center1 = options.center1;
end


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% for the line, can be vertical / horizontal / diagonal / any
if strcmp(type, 'line_vertical')
    eta = 0.5;              % translation
    gamma = 0;      % slope
elseif strcmp(type, 'line_horizontal')
    eta = 0.5;              % translation
    gamma = Inf;      % slope
elseif strcmp(type, 'line_diagonal')
    eta = 0;              % translation
    gamma = 1;      % slope
end


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% for some blurring
sigma = 0;
if isfield(options, 'sigma')
    sigma = options.sigma;
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
switch type
    case 'chessboard1'
        x = -1:2/(n-1):1;
        [Y,X] = meshgrid(x,x);
        M = (2*(Y>=0)-1).*(2*(X>=0)-1);
        
    case 'chessboard'
        if ~isfield( options, 'width' )
            width = round(n/16);
        else
            width = options.width;
        end
        [Y,X] = meshgrid(0:n-1,0:n-1);
        M = mod( floor(X/width)+floor(Y/width), 2 ) == 0;
        
    case 'square'
        if ~isfield( options, 'radius' )
            radius = 0.6;
        end
        x = -1:2/(n-1):1;
        [Y,X] = meshgrid(x,x);
        M = max( abs(X),abs(Y) )<radius;
        
    case 'square_texture'
        M = load_image('square',n);
        M = rescale(M);
        % make a texture patch
        x = linspace(0,1,n);
        [Y,X] = meshgrid(x,x);
        theta = pi/3;
        x = cos(theta)*X + sin(theta)*Y;
        c = [0.3,0.4]; r = 0.2;
        I = find( (X-c(1)).^2 + (Y-c(2)).^2 < r^2 );
        eta = 3/n; lambda = 0.3;
        M(I) = M(I) + lambda * sin( x(I) * 2*pi / eta ); 
        
        
    case 'oscillatory_texture'
        x = linspace(0,1,n);
        [Y,X] = meshgrid(x,x);
        theta = pi/3;
        x = cos(theta)*X + sin(theta)*Y;
        c = [0.3,0.4]; r = 0.2;
        I = find( (X-c(1)).^2 + (Y-c(2)).^2 < r^2 );
        eta = 3/n; lambda = 0.3;
        M = sin( x * 2*pi / eta ); 
        
    case {'line', 'line_vertical', 'line_horizontal', 'line_diagonal'}
        x = 0:1/(n-1):1;
        [Y,X] = meshgrid(x,x);
        if gamma~=Inf
            M = (X-eta) - gamma*Y < 0;
        else
            M = (Y-eta) < 0;
        end
        
    case 'grating'
        x = linspace(-1,1,n);
        [Y,X] = meshgrid(x,x);
        if isfield(options, 'theta')
            theta = options.theta;
        else
            theta = 0.2;
        end
        if isfield(options, 'freq')
            freq = options.freq;
        else
            freq = 0.2;
        end
        X = cos(theta)*X + sin(theta)*Y;
        M = sin(2*pi*X/freq);
        
    case 'disk'
        if ~isfield( options, 'radius' )
            radius = 0.35;
        end
        if ~isfield( options, 'center' )
            center = [0.5, 0.5];    % center of the circle
        end
        x = 0:1/(n-1):1;
        [Y,X] = meshgrid(x,x);
        M = (X-center(1)).^2 + (Y-center(2)).^2 < radius^2;
        
    case 'quarterdisk'
        if ~isfield( options, 'radius' )
            radius = 0.95;
        end
        if ~isfield( options, 'center' )
            center = -[0.1, 0.1];    % center of the circle
        end
        x = 0:1/(n-1):1;
        [Y,X] = meshgrid(x,x);
        M = (X-center(1)).^2 + (Y-center(2)).^2 < radius^2;
        
    case 'fading_contour'
        if ~isfield( options, 'radius' )
            radius = 0.95;
        end
        if ~isfield( options, 'center' )
            center = -[0.1, 0.1];    % center of the circle
        end
        x = 0:1/(n-1):1;
        [Y,X] = meshgrid(x,x);
        M = (X-center(1)).^2 + (Y-center(2)).^2 < radius^2;
        theta = 2/pi*atan2(Y,X);
        h = 0.5;
        M = exp(-(1-theta).^2/h^2).*M;
        
    case '3contours'        
        radius = 1.3;
        center = [-1, 1];
        radius1 = 0.8;
        center1 = [0, 0];
        x = 0:1/(n-1):1;
        [Y,X] = meshgrid(x,x);
        f1 = (X-center(1)).^2 + (Y-center(2)).^2 < radius^2;
        f2 = (X-center1(1)).^2 + (Y-center1(2)).^2 < radius1^2;
        M = f1 + 0.5*f2.*(1-f1);
        
    case 'line_circle'

        gamma = 1/sqrt(2);

        x = linspace(-1,1,n);
        [Y,X] = meshgrid(x,x);
        M1 = double( X>gamma*Y+0.25 );
        M2 = X.^2 + Y.^2 < 0.6^2;
        M = 20 + max(0.5*M1,M2) * 216;
        
    case 'fnoise'
        
        % generate an image M whose Fourier spectrum amplitude is 
        %   |M^(omega)| = 1/f^{omega}
        if isfield(options, 'alpha')
            alpha = options.alpha;
        else
            alpha = 1;
        end
        M = gen_noisy_image(n,alpha);
        
        
    case 'gaussiannoise'
        % generate an image of filtered noise with gaussian
        if isfield(options, 'sigma')
            sigma = options.sigma;
        else
            sigma = 10;
        end
        M = randn(n);
        m = 51;
        h = build_gaussian_filter([m m],sigma/(4*n),[n n]);
        M = perform_convolution(M,h);
        return;
    
    case {'bwhorizontal','bwvertical','bwcircle'}
        
        [Y,X] = meshgrid(0:n-1,0:n-1);
        if strcmp(type, 'bwhorizontal')
            d = X;
        elseif strcmp(type, 'bwvertical')
            d = Y;
        elseif strcmp(type, 'bwcircle')
            d = sqrt( (X-(n-1)/2).^2 + (Y-(n-1)/2).^2 );
        end
        if isfield(options, 'stripe_width')
            stripe_width = options.stripe_width;
        else
            stripe_width = 5;
        end
        if isfield(options, 'black_prop')
            black_prop = options.black_prop;
        else
            black_prop = 0.5;
        end
        M = double( mod( d/(2*stripe_width),1 )>=black_prop );
        
    case 'parabola'
        
        % curvature
        if isfield(options, 'c')
            c = options.c;
        else
            c = 0.1;
        end
        % angle
        if isfield(options, 'theta');
            theta = options.theta;
        else
            theta = pi/sqrt(2);
        end
        x = -0.5:1/(n-1):0.5;
        [Y,X] = meshgrid(x,x);
        Xs = X*cos(theta) + Y*sin(theta);
        Y =-X*sin(theta) + Y*cos(theta); X = Xs;
        M = Y>c*X.^2; 
        
    case 'sin'
        
        [Y,X] = meshgrid(-1:2/(n-1):1, -1:2/(n-1):1);
        M = Y >= 0.6*cos(pi*X);
        M = double(M);
        
    case 'circ_oscil'

        x = linspace(-1,1,n);
        [Y,X] = meshgrid(x,x);
        R = sqrt(X.^2+Y.^2);
        M = cos(R.^3*50);

    case 'phantom'
        
        M = phantom(n);
        
    case 'periodic_bumps'
        
        if isfield(options, 'nbr_periods')
            nbr_periods = options.nbr_periods;
        else
            nbr_periods = 8;
        end
        if isfield(options, 'theta')
            theta = options.theta;
        else
            theta = 1/sqrt(2);
        end
        if isfield(options, 'skew')
            skew = options.skew;
        else
            skew = 1/sqrt(2);
        end
        
        A = [cos(theta), -sin(theta); sin(theta), cos(theta)];
        B = [1 skew; 0 1];
        T = B*A;
        x = (0:n-1)*2*pi*nbr_periods/(n-1);
        [Y,X] = meshgrid(x,x);
        pos = [X(:)'; Y(:)'];
        pos = T*pos;
        X = reshape(pos(1,:), n,n);
        Y = reshape(pos(2,:), n,n);
        M = cos(X).*sin(Y);      
        
    case 'noise'
        if isfield(options, 'sigma')
            sigma = options.sigma;
        else
            sigma = 1;
        end
        M = randn(n);
        
    otherwise
        ext = {'gif', 'png', 'jpg', 'bmp', 'tiff', 'pgm'};
        for i=1:length(ext)
            name = [type '.' ext{i}];
            if( exist(name) )
                M = imread( name );
                M = double(M);
                if n~=size(M, 1) && nargin>=2
                    M = image_resize(M,n,n);
                end
                return;
            end
        end
        error( ['Image ' type ' does not exists.'] );
end

M = double(M);

if sigma>0
    h = ones(sigma);
    h = conv2(h,h);
    h = h/sum(h(:));
    M = conv2(M, h, 'same');
end

M = rescale(M) * 256;



function M = gen_noisy_image(n,alpha)

% gen_noisy_image - generate a noisy cloud-like image.
%
%   M = gen_noisy_image(n,alpha);
%
% generate an image M whose Fourier spectrum amplitude is 
%   |M^(omega)| = 1/f^{omega}
%
%   Copyright (c) 2004 Gabriel Peyr?

if nargin<1
    n = 128;
end
if nargin<2
    alpha = 1.5;
end

if mod(n(1),2)==0
    x = -n/2:n/2-1;
else
    x = -(n-1)/2:(n-1)/2;
end

[Y,X] = meshgrid(x,x);
d = sqrt(X.^2 + Y.^2) + 0.1;
f = rand(n)*2*pi;

M = (d.^(-alpha)) .* exp(f*1i);
% M = real(ifft2(fftshift(M)));

M = ifftshift(M);
M = real( ifft2(M) );


function y = gen_signal_2d(n,alpha)

% gen_signal_2d -  generate a 2D C^\alpha signal of length n x n.
%   gen_signal_2d(n,alpha) generate a 2D signal C^alpha. 
%
%   The signal is scale in [0,1].
%   
%   Copyright (c) 2003 Gabriel Peyr?



% new new method

[Y,X] = meshgrid(0:n-1, 0:n-1);

A = X+Y+1;
B = X-Y+n+1;

a = gen_signal(2*n+1, alpha);
b = gen_signal(2*n+1, alpha);
y = a(A).*b(B);
% M = a(1:n)*b(1:n)';

return;


% new method
h = (-n/2+1):(n/2); h(n/2)=1;
[X,Y] = meshgrid(h,h);
h = sqrt(X.^2+Y.^2+1).^(-alpha-1/2);
h = h .* exp( 2i*pi*rand(n,n) );
h = fftshift(h);
y = real( ifft2(h) );

m1 = min(min(y));
m2 = max(max(y));
y = (y-m1)/(m2-m1);

return;

%% old code

y = rand(n,n); 
y = y - mean(mean(y));
for i=1:alpha
    y = cumsum(cumsum(y)')';
    y = y - mean(mean(y));
end
m1 = min(min(y));
m2 = max(max(y));
y = (y-m1)/(m2-m1);



function newimg = image_resize(img,p1,q1,r1)

% image_resize - resize an image using bicubic interpolation
%
%   newimg = image_resize(img,nx,ny,nz);
% or
%   newimg = image_resize(img,newsize);
%
%   Works for 2D, 2D 2 or 3 channels, 3D images.
%
%   Copyright (c) 2004 Gabriel Peyr