MATLAB.rar_hpfilter.m_matlab intrans

function [c, s] = wavefast(x, n, varargin) %WAVEFAST Perform multi-level 2-dimensional fast wavelet transform. % [C, L] = WAVEFAST(X, N, LP, HP) performs a 2D N-level FWT of % image (or matrix) X with respect to decomposition filters LP and % HP. % % [C, L] = WAVEFAST(X, N, WNAME) performs the same operation but % fetches filters LP and HP for wavelet WNAME using WAVEFILTER. % % Scale parameter N must be less than or equal to log2 of the % maximum image dimension. Filters LP and HP must be even. To % reduce border distortion, X is symmetrically extended. That is, % if X = [c1 c2 c3 ... cn] (in 1D), then its symmetric extension % would be [... c3 c2 c1 c1 c2 c3 ... cn cn cn-1 cn-2 ...]. % % OUTPUTS: % Matrix C is a coefficient decomposition vector: % % C = [ a(n) h(n) v(n) d(n) h(n-1) ... v(1) d(1) ] % % where a, h, v, and d are columnwise vectors containing % approximation, horizontal, vertical, and diagonal coefficient % matrices, respectively. C has 3n + 1 sections where n is the % number of wavelet decompositions. % % Matrix S is an (n+2) x 2 bookkeeping matrix: % % S = [ sa(n, :); sd(n, :); sd(n-1, :); ... ; sd(1, :); sx ] % % where sa and sd are approximation and detail size entries. % % See also WAVEBACK and WAVEFILTER. % Copyright 2002-2004 R. C. Gonzalez, R. E. Woods, & S. L. Eddins % Digital Image Processing Using MATLAB, Prentice-Hall, 2004 % $Revision: 1.5 $ $Date: 2003/10/13 01:14:17 $ % Check the input arguments for reasonableness. error(nargchk(3, 4, nargin)); if nargin == 3 if ischar(varargin{1}) [lp,hp]=wavefilter(varargin{1},'d'); else error('Missing wavelet name.'); end else lp = varargin{1}; hp = varargin{2}; end fl = length(lp); sx = size(x); if (ndims(x) ~= 2) | (min(sx) < 2) | ~isreal(x) | ~isnumeric(x) error('X must be a real, numeric matrix.'); end if (ndims(lp) ~= 2) | ~isreal(lp) | ~isnumeric(lp) ... | (ndims(hp) ~= 2) | ~isreal(hp) | ~isnumeric(hp) ... | (fl ~= length(hp)) | rem(fl, 2) ~= 0 error(['LP and HP must be even and equal length real, ' ... 'numeric filter vectors.']); end if ~isreal(n) | ~isnumeric(n) | (n < 1) | (n > log2(max(sx))) error(['N must be a real scalar between 1 and ' ... 'log2(max(size((X))).']); end % Init the starting output data structures and initial approximation. c = []; s = sx; app = double(x); % For each decomposition ... for i = 1:n % Extend the approximation symmetrically. [app, keep] = symextend(app, fl); % Convolve rows with HP and downsample. Then convolve columns % with HP and LP to get the diagonal and vertical coefficients. rows = symconv(app, hp, 'row', fl, keep); coefs = symconv(rows, hp, 'col', fl, keep); c = [coefs(:)' c]; s = [size(coefs); s]; coefs = symconv(rows, lp, 'col', fl, keep); c = [coefs(:)' c]; % Convolve rows with LP and downsample. Then convolve columns % with HP and LP to get the horizontal and next approximation % coeffcients. rows = symconv(app, lp, 'row', fl, keep); coefs = symconv(rows, hp, 'col', fl, keep); c = [coefs(:)' c]; app = symconv(rows, lp, 'col', fl, keep); end % Append final approximation structures. c = [app(:)' c]; s = [size(app); s]; %-------------------------------------------------------------------% function [y, keep] = symextend(x, fl) % Compute the number of coefficients to keep after convolution % and downsampling. Then extend x in both dimensions. keep = floor((fl + size(x) - 1) / 2); y = padarray(x, [(fl - 1) (fl - 1)], 'symmetric', 'both'); %-------------------------------------------------------------------% function y = symconv(x, h, type, fl, keep) % Convolve the rows or columns of x with h, downsample, % and extract the center section since symmetrically extended. if strcmp(type, 'row') y = conv2(x, h); y = y(:, 1:2:end); y = y(:, fl / 2 + 1:fl / 2 + keep(2)); else y = conv2(x, h'); y = y(1:2:end, :); y = y(fl / 2 + 1:fl / 2 + keep(1), :); end