phasecong2.m

hopfield neural network for binary image recognition

% PHASECONG2 - Computes edge and corner phase congruency in an image.
%
% This function calculates the PC_2 measure of phase congruency.  
% This function supersedes PHASECONG
%
% There are potentially many arguments, here is the full usage:
%
%   [M m or ft pc EO] = phasecong2(im, nscale, norient, minWaveLength, ...
%                         mult, sigmaOnf, dThetaOnSigma, k, cutOff, g)
%
% However, apart from the image, all parameters have defaults and the
% usage can be as simple as:
%
%    M = phasecong2(im);
% 
% Arguments:
%              Default values      Description
%
%    nscale           4    - Number of wavelet scales, try values 3-6
%    norient          6    - Number of filter orientations.
%    minWaveLength    3    - Wavelength of smallest scale filter.
%    mult             2.1  - Scaling factor between successive filters.
%    sigmaOnf         0.55 - Ratio of the standard deviation of the Gaussian 
%                            describing the log Gabor filter's transfer function 
%                            in the frequency domain to the filter center frequency.
%    dThetaOnSigma    1.2  - Ratio of angular interval between filter orientations
%                            and the standard deviation of the angular Gaussian
%                            function used to construct filters in the
%                            freq. plane.
%    k                2.0  - No of standard deviations of the noise energy beyond
%                            the mean at which we set the noise threshold point.
%                            You may want to vary this up to a value of 10 or
%                            20 for noisy images 
%    cutOff           0.5  - The fractional measure of frequency spread
%                            below which phase congruency values get penalized.
%    g                10   - Controls the sharpness of the transition in
%                            the sigmoid function used to weight phase
%                            congruency for frequency spread.                        
%
% Returned values:
%    M          - Maximum moment of phase congruency covariance.
%                 This is used as a indicator of edge strength.
%    m          - Minimum moment of phase congruency covariance.
%                 This is used as a indicator of corner strength.
%    or         - Orientation image in integer degrees 0-180,
%                 positive anticlockwise.
%                 0 corresponds to a vertical edge, 90 is horizontal.
%    ft         - *Not correctly implemented at this stage*
%                 A complex valued image giving the weighted mean 
%                 phase angle at every point in the image for each
%                 orientation. 
%    pc         - Cell array of phase congruency images (values between 0 and 1)   
%                 for each orientation
%    EO         - A 2D cell array of complex valued convolution results
%
%   EO{s,o} = convolution result for scale s and orientation o.  The real part
%   is the result of convolving with the even symmetric filter, the imaginary
%   part is the result from convolution with the odd symmetric filter.
%
%   Hence:
%       abs(EO{s,o}) returns the magnitude of the convolution over the
%       image at scale s and orientation o.
%       angle(EO{s,o}) returns the phase angles.
%   
% Notes on specifying parameters:  
%
% The parameters can be specified as a full list eg.
%  >> [M m or ft pc EO] = phasecong2(im, 5, 6, 3, 2.5, 0.55, 1.2, 2.0, 0.4, 10);
%
% or as a partial list with unspecified parameters taking on default values
%  >> [M m or ft pc EO] = phasecong2(im, 5, 6, 3);
%
% or as a partial list of parameters followed by some parameters specified via a
% keyword-value pair, remaining parameters are set to defaults, for example:
%  >> [M m or ft pc EO] = phasecong2(im, 5, 6, 3, 'cutOff', 0.3, 'k', 2.5);
% 
% The convolutions are done via the FFT.  Many of the parameters relate to the
% specification of the filters in the frequency plane.  The values do not seem
% to be very critical and the defaults are usually fine.  You may want to
% experiment with the values of 'nscales' and 'k', the noise compensation factor.
%
% Notes on filter settings to obtain even coverage of the spectrum
% dthetaOnSigma 1.2    norient 6
% sigmaOnf       .85   mult 1.3
% sigmaOnf       .75   mult 1.6     (filter bandwidth ~1 octave)
% sigmaOnf       .65   mult 2.1  
% sigmaOnf       .55   mult 3       (filter bandwidth ~2 octaves)
%
% For maximum speed the input image should have dimensions that correspond to
% powers of 2, but the code will operate on images of arbitrary size.
%
% See Also:  PHASECONG, PHASESYM, GABORCONVOLVE, PLOTGABORFILTERS

% References:
%
%     Peter Kovesi, "Image Features From Phase Congruency". Videre: A
%     Journal of Computer Vision Research. MIT Press. Volume 1, Number 3,
%     Summer 1999 http://mitpress.mit.edu/e-journals/Videre/001/v13.html
%
%     Peter Kovesi, "Phase Congruency Detects Corners and
%     Edges". Proceedings DICTA 2003, Sydney Dec 10-12

% April 1996     Original Version written 
% August 1998    Noise compensation corrected. 
% October 1998   Noise compensation corrected.   - Again!!!
% September 1999 Modified to operate on non-square images of arbitrary size. 
% May 2001       Modified to return feature type image. 
% July 2003      Altered to calculate 'corner' points. 
% October 2003   Speed improvements and refinements. 
% July 2005      Better argument handling, changed order of return values
% August 2005    Made Octave compatible
% May 2006       Bug in checkargs fixed
% Jan 2007       Bug in setting radius to 0 for odd sized images fixed.

% Copyright (c) 1996-2005 Peter Kovesi
% School of Computer Science & Software Engineering
% The University of Western Australia
% http://www.csse.uwa.edu.au/
% 
% Permission is hereby  granted, free of charge, to any  person obtaining a copy
% of this software and associated  documentation files (the "Software"), to deal
% in the Software without restriction, subject to the following conditions:
% 
% The above copyright notice and this permission notice shall be included in all
% copies or substantial portions of the Software.
% 
% The software is provided "as is", without warranty of any kind.

function [M, m, or, featType, PC, EO]=phasecong2(varargin)
    
% Get arguments and/or default values    
[im, nscale, norient, minWaveLength, mult, sigmaOnf, ...
                  dThetaOnSigma,k, cutOff, g] = checkargs(varargin(:));     

Octave = exist('OCTAVE_VERSION') ~= 0;  % Are we running under Octave?

epsilon         = .0001;                % Used to prevent division by zero.

thetaSigma = pi/norient/dThetaOnSigma;  % Calculate the standard deviation of the
                                        % angular Gaussian function used to
                                        % construct filters in the freq. plane.

[rows,cols] = size(im);
imagefft = fft2(im);              % Fourier transform of image

zero = zeros(rows,cols);
totalEnergy = zero;               % Total weighted phase congruency values (energy).
totalSumAn  = zero;               % Total filter response amplitude values.
orientation = zero;               % Matrix storing orientation with greatest
                                  % energy for each pixel.
EO = cell(nscale, norient);       % Array of convolution results.                                 
covx2 = zero;                     % Matrices for covariance data
covy2 = zero;
covxy = zero;

estMeanE2n = [];
ifftFilterArray = cell(1,nscale); % Array of inverse FFTs of filters

% Pre-compute some stuff to speed up filter construction

% Set up X and Y matrices with ranges normalised to +/- 0.5
% The following code adjusts things appropriately for odd and even values
% of rows and columns.
if mod(cols,2)
    xrange = [-(cols-1)/2:(cols-1)/2]/(cols-1);
else
    xrange = [-cols/2:(cols/2-1)]/cols;	
end

if mod(rows,2)
    yrange = [-(rows-1)/2:(rows-1)/2]/(rows-1);
else
    yrange = [-rows/2:(rows/2-1)]/rows;	
end

[x,y] = meshgrid(xrange, yrange);

radius = sqrt(x.^2 + y.^2);       % Matrix values contain *normalised* radius from centre.
theta = atan2(-y,x);              % Matrix values contain polar angle.
                                  % (note -ve y is used to give +ve
                                  % anti-clockwise angles)
				  
radius = ifftshift(radius);       % Quadrant shift radius and theta so that filters
theta  = ifftshift(theta);        % are constructed with 0 frequency at the corners.
radius(1,1) = 1;                  % Get rid of the 0 radius value at the 0
                                  % frequency point (now at top-left corner)
                                  % so that taking the log of the radius will 
                                  % not cause trouble.

sintheta = sin(theta);
costheta = cos(theta);
clear x; clear y; clear theta;    % save a little memory

% Filters are constructed in terms of two components.
% 1) The radial component, which controls the frequency band that the filter
%    responds to
% 2) The angular component, which controls the orientation that the filter
%    responds to.
% The two components are multiplied together to construct the overall filter.

% Construct the radial filter components...

% First construct a low-pass filter that is as large as possible, yet falls
% away to zero at the boundaries.  All log Gabor filters are multiplied by
% this to ensure no extra frequencies at the 'corners' of the FFT are
% incorporated as this seems to upset the normalisation process when
% calculating phase congrunecy.
lp = lowpassfilter([rows,cols],.45,15);   % Radius .45, 'sharpness' 15

logGabor = cell(1,nscale);

for s = 1:nscale
    wavelength = minWaveLength*mult^(s-1);
    fo = 1.0/wavelength;                  % Centre frequency of filter.
    logGabor{s} = exp((-(log(radius/fo)).^2) / (2 * log(sigmaOnf)^2));  
    logGabor{s} = logGabor{s}.*lp;        % Apply low-pass filter
    logGabor{s}(1,1) = 0;                 % Set the value at the 0 frequency point of the filter
                                          % back to zero (undo the radius fudge).
end

% Then construct the angular filter components...

spread = cell(1,norient);

for o = 1:norient
  angl = (o-1)*pi/norient;           % Filter angle.

  % For each point in the filter matrix calculate the angular distance from
  % the specified filter orientation.  To overcome the angular wrap-around
  % problem sine difference and cosine difference values are first computed
  % and then the atan2 function is used to determine angular distance.

  ds = sintheta * cos(angl) - costheta * sin(angl);    % Difference in sine.
  dc = costheta * cos(angl) + sintheta * sin(angl);    % Difference in cosine.
  dtheta = abs(atan2(ds,dc));                          % Absolute angular distance.
  spread{o} = exp((-dtheta.^2) / (2 * thetaSigma^2));  % Calculate the
                                                       % angular filter component.
end

% The main loop...

for o = 1:norient                    % For each orientation.
  fprintf('Processing orientation %d\r',o);
  if Octave fflush(1); end

  angl = (o-1)*pi/norient;           % Filter angle.
  sumE_ThisOrient   = zero;          % Initialize accumulator matrices.
  sumO_ThisOrient   = zero;       
  sumAn_ThisOrient  = zero;      
  Energy            = zero;      

  for s = 1:nscale,                  % For each scale.
    filter = logGabor{s} .* spread{o};   % Multiply radial and angular
                                         % components to get the filter. 

%    if o == 1   % accumulate filter info for noise compensation (nominally the same 
                 % for all orientations, hence it is only done once)
        ifftFilt = real(ifft2(filter))*sqrt(rows*cols);  % Note rescaling to match power
        ifftFilterArray{s} = ifftFilt;                   % record ifft2 of filter
%    end

    % Convolve image with even and odd filters returning the result in EO
    EO{s,o} = ifft2(imagefft .* filter);      

    An = abs(EO{s,o});                         % Amplitude of even & odd filter response.