REDUCE2D - Reduce an image by a factor of 2 in each dimension.

Contents

Description

Wrapper for the reduce2D function of the [BIG] Spline Pyramids Software that reduces an image by a factor of 2 in each dimension using the algorithm described in [Unser99]; it also includes the code for reduction through the classical Laplacian Pyramid of [BA83].

Syntax

  Ir = REDUCE2D(I);
  [Ir, Er] = REDUCE2D(I, filter, order);

Inputs

I : input image, possibly multispectral.

filter : (optional) name of the filter; it is either:

for standard spline pyramids ('spl', 'spl2'), the coarser grid points are at the even integers; for centered pyramids ('cspl', 'cspl2'), the coarser grid points are placed in-between their two closest finer grid predecessors [BMIU99]; default: filter='cspl'.

order : (optional) order for the filters based on splines; it is either:

in the case filter='lpl', this parameter is ignored; default: order=3, with filter='cspl'.

Outputs

Ir : image reduced by a factor 2.

Er : (optional) error image, computed as error=signal­EXPAND2D(Ir); it gives the loss of information due to image reduction.

Acknowledgment

This software package implements the basic REDUCE and EXPAND operators for the reduction and enlargement of signals and images by factors of two. A signal is represented by a polynomial spline which is a continuously- defined function [Unser99]; the model is interpolating and is unambiguously defined by the sample values. The spline model specifies the enlargement mechanism (spline interpolation), as well as the reduction algorithm which is optimal in the least squares sense.

References

[BA83] P.J. Burt and E.H. Adelson: "The Laplacian Pyramid as a Compact Image Code", IEEE Transactions on Commununication, 31(4):337-345, 1983. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1095851&tag=1

[Unser99] M. Unser: "Splines: a perfect fit for signal and image processing", IEEE Signal Processing Magazine, 16(6):22-38, 1999. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=799930

[BMIU99] P. Brigger, F. Muller, K. Illgner and M. Unser: "Centered pyramids," IEEE Transactions on Image Processing, 8(9):1254-1264, 1999. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=784437

[BIG] Software available at: http://bigwww.epfl.ch/sage/pyramids/. See README at: http://bigwww.epfl.ch/sage/pyramids/README.TXT

See also

Ressembles: PYRDOWN, EXPAND2D, DOWNSCALEXY. Requires: REDUCE2D_BASE, EXPAND2D_BASE.

Function implementation

function [Ir,varargout] = reduce2d(I, varargin)

check if possible

error(nargchk(1, 11, nargin, 'struct'));
error(nargoutchk(1, 2, nargout, 'struct'));

if ~isnumeric(I)
    error('reduce2d:inputparameter','a matrix is required in input');
end

parsing parameters

p = createParser('REDUCE2D');
p.addOptional('filter','cspl', @(x)ischar(x) && ...
    any(strcmpi(x,{'spl','spl2','cspl','cspl2'})));
p.addOptional('order',[], @(x)isempty(x) || (isscalar(x) && x>0 && x<=5));

% parse and validate all input arguments
p.parse(varargin{:});
p = getvarParser(p);

checking parameters

if any(strcmpi(p.filter,{'cspl','cspl2''spl''spl2'}))
    if ~exist('reduce2d_mex','file')
        error('reduce2d:errorlibrary', ...
            'mex file reduce2d_mex required for spline based pyramid');
    elseif isempty(p.order)
        p.order = 3;
    end
elseif ~isempty(p.order)
    warning('reduce2d:warninginput', ...
        'input variable ''order'' ignored with Laplacian pyramid');
    p.order = [];
end

if (any(strcmpi(p.filter,{'cspl','cspl2'})) && ~ismember(p.order,[0,1,2,3,4])) || ...
        (strcmpi(p.filter,'spl') && ~ismember(p.order,[0,1,2,3])) || ...
        (strcmpi(p.filter,'spl2') && ~ismember(p.order,[0,1,3,5]))
    error('reduce2d:inputerror', ...
        'check compatibility of filter and order variables');
end

main calculation

Ir = reduce2d_base(I, p.filter, p.order);

if nargout==2
    J = expand2d_base(Ir, p.filter, p.order);
    varargout{1} = abs(I - J);
end

display

if p.disp
    figure, subplot(1,nargout,1)
    imagesc(rescale(Ir,0,1)), axis image off, title('reduced image');
    if size(I,3)==1, colormap gray;  end;
    if nargout==2
        subplot(1,2,2)
        imagesc(rescale(varargout{1},0,1)), axis image off, title('error image');
        if size(I,3)==1, colormap gray;  end;
    end
end

end % end of reduced2d