phasecong2.m

hopfield neural network for binary image recognition

    sumAn_ThisOrient = sumAn_ThisOrient + An;  % Sum of amplitude responses.
    sumE_ThisOrient = sumE_ThisOrient + real(EO{s,o}); % Sum of even filter convolution results.
    sumO_ThisOrient = sumO_ThisOrient + imag(EO{s,o}); % Sum of odd filter convolution results.

    if s==1                                 % Record mean squared filter value at smallest
      EM_n = sum(sum(filter.^2));           % scale. This is used for noise estimation.
      maxAn = An;                           % Record the maximum An over all scales.
    else
      maxAn = max(maxAn, An);
    end

  end                                       % ... and process the next scale

  % Get weighted mean filter response vector, this gives the weighted mean
  % phase angle.

  XEnergy = sqrt(sumE_ThisOrient.^2 + sumO_ThisOrient.^2) + epsilon;   
  MeanE = sumE_ThisOrient ./ XEnergy; 
  MeanO = sumO_ThisOrient ./ XEnergy; 

  % Now calculate An(cos(phase_deviation) - | sin(phase_deviation)) | by
  % using dot and cross products between the weighted mean filter response
  % vector and the individual filter response vectors at each scale.  This
  % quantity is phase congruency multiplied by An, which we call energy.

  for s = 1:nscale,       
      E = real(EO{s,o}); O = imag(EO{s,o});    % Extract even and odd
                                               % convolution results.
      Energy = Energy + E.*MeanE + O.*MeanO - abs(E.*MeanO - O.*MeanE);
  end

  % Compensate for noise
  % We estimate the noise power from the energy squared response at the
  % smallest scale.  If the noise is Gaussian the energy squared will have a
  % Chi-squared 2DOF pdf.  We calculate the median energy squared response
  % as this is a robust statistic.  From this we estimate the mean.
  % The estimate of noise power is obtained by dividing the mean squared
  % energy value by the mean squared filter value

  medianE2n = median(reshape(abs(EO{1,o}).^2,1,rows*cols));
  meanE2n = -medianE2n/log(0.5);
  estMeanE2n(o) = meanE2n;

  noisePower = meanE2n/EM_n;                       % Estimate of noise power.

%  if o == 1
  % Now estimate the total energy^2 due to noise
  % Estimate for sum(An^2) + sum(Ai.*Aj.*(cphi.*cphj + sphi.*sphj))

  EstSumAn2 = zero;
  for s = 1:nscale
    EstSumAn2 = EstSumAn2 + ifftFilterArray{s}.^2;
  end

  EstSumAiAj = zero;
  for si = 1:(nscale-1)
    for sj = (si+1):nscale
      EstSumAiAj = EstSumAiAj + ifftFilterArray{si}.*ifftFilterArray{sj};
    end
  end
  sumEstSumAn2 = sum(sum(EstSumAn2));
  sumEstSumAiAj = sum(sum(EstSumAiAj));

%  end % if o == 1

  EstNoiseEnergy2 = 2*noisePower*sumEstSumAn2 + 4*noisePower*sumEstSumAiAj;

  tau = sqrt(EstNoiseEnergy2/2);                     % Rayleigh parameter
  EstNoiseEnergy = tau*sqrt(pi/2);                   % Expected value of noise energy
  EstNoiseEnergySigma = sqrt( (2-pi/2)*tau^2 );

  T =  EstNoiseEnergy + k*EstNoiseEnergySigma;       % Noise threshold

  % The estimated noise effect calculated above is only valid for the PC_1 measure. 
  % The PC_2 measure does not lend itself readily to the same analysis.  However
  % empirically it seems that the noise effect is overestimated roughly by a factor 
  % of 1.7 for the filter parameters used here.

  T = T/1.7;        % Empirical rescaling of the estimated noise effect to 
                    % suit the PC_2 phase congruency measure

  Energy = max(Energy - T, zero);          % Apply noise threshold

  % Form weighting that penalizes frequency distributions that are
  % particularly narrow.  Calculate fractional 'width' of the frequencies
  % present by taking the sum of the filter response amplitudes and dividing
  % by the maximum amplitude at each point on the image.

  width = sumAn_ThisOrient ./ (maxAn + epsilon) / nscale;    

  % Now calculate the sigmoidal weighting function for this orientation.

  weight = 1.0 ./ (1 + exp( (cutOff - width)*g)); 

  % Apply weighting to energy and then calculate phase congruency

  PC{o} = weight.*Energy./sumAn_ThisOrient;   % Phase congruency for this orientation
  featType{o} = E+i*O;

  % Build up covariance data for every point
  covx = PC{o}*cos(angl);
  covy = PC{o}*sin(angl);
  covx2 = covx2 + covx.^2;
  covy2 = covy2 + covy.^2;
  covxy = covxy + covx.*covy;

end  % For each orientation

fprintf('                                          \r');

% Edge and Corner calculations

% The following is optimised code to calculate principal vector
% of the phase congruency covariance data and to calculate
% the minimumum and maximum moments - these correspond to
% the singular values.

% First normalise covariance values by the number of orientations/2

covx2 = covx2/(norient/2);
covy2 = covy2/(norient/2);
covxy = covxy/norient;   % This gives us 2*covxy/(norient/2)

denom = sqrt(covxy.^2 + (covx2-covy2).^2)+epsilon;
sin2theta = covxy./denom;
cos2theta = (covx2-covy2)./denom;
or = atan2(sin2theta,cos2theta)/2;    % Orientation perpendicular to edge.
or = round(or*180/pi);                % Return result rounded to integer
                                      % degrees.
neg = or < 0;                                 
or = ~neg.*or + neg.*(or+180);        % Adjust range from -90 to 90
                                      % to 0 to 180.

M = (covy2+covx2 + denom)/2;          % Maximum moment
m = (covy2+covx2 - denom)/2;          % ... and minimum moment




    
%------------------------------------------------------------------
% CHECKARGS
%
% Function to process the arguments that have been supplied, assign
% default values as needed and perform basic checks.
    
function [im, nscale, norient, minWaveLength, mult, sigmaOnf, ...
          dThetaOnSigma,k, cutOff, g] = checkargs(arg); 

    nargs = length(arg);
    
    if nargs < 1
        error('No image supplied as an argument');
    end    
    
    % Set up default values for all arguments and then overwrite them
    % with with any new values that may be supplied
    im              = [];
    nscale          = 4;     % Number of wavelet scales.    
    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. 
    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.                      
    
    % Allowed argument reading states
    allnumeric   = 1;       % Numeric argument values in predefined order
    keywordvalue = 2;       % Arguments in the form of string keyword
                            % followed by numeric value
    readstate = allnumeric; % Start in the allnumeric state
    
    if readstate == allnumeric
        for n = 1:nargs
            if isa(arg{n},'char')
                readstate = keywordvalue;
                break;
            else
                if     n == 1, im            = arg{n}; 
                elseif n == 2, nscale        = arg{n};              
                elseif n == 3, norient       = arg{n};
                elseif n == 4, minWaveLength = arg{n};
                elseif n == 5, mult          = arg{n};
                elseif n == 6, sigmaOnf      = arg{n};
                elseif n == 7, dThetaOnSigma = arg{n};
                elseif n == 8, k             = arg{n};              
                elseif n == 9, cutOff        = arg{n}; 
                elseif n == 10,g             = arg{n};                                                    
                end
            end
        end
    end

    % Code to handle parameter name - value pairs
    if readstate == keywordvalue
        while n < nargs
            
            if ~isa(arg{n},'char') | ~isa(arg{n+1}, 'double')
                error('There should be a parameter name - value pair');
            end
            
            if     strncmpi(arg{n},'im'      ,2), im =        arg{n+1};
            elseif strncmpi(arg{n},'nscale'  ,2), nscale =    arg{n+1};
            elseif strncmpi(arg{n},'norient' ,2), norient =   arg{n+1};
            elseif strncmpi(arg{n},'minWaveLength',2), minWaveLength = arg{n+1};
            elseif strncmpi(arg{n},'mult'    ,2), mult =      arg{n+1};
            elseif strncmpi(arg{n},'sigmaOnf',2), sigmaOnf =  arg{n+1};
            elseif strncmpi(arg{n},'dThetaOnSigma',2), dThetaOnSigma =  arg{n+1};
            elseif strncmpi(arg{n},'k'       ,1), k =         arg{n+1};
            elseif strncmpi(arg{n},'cutOff'  ,2), cutOff   =  arg{n+1};
            elseif strncmpi(arg{n},'g'       ,1), g        =  arg{n+1};         
            else   error('Unrecognised parameter name');
            end

            n = n+2;
            if n == nargs
                error('Unmatched parameter name - value pair');
            end
            
        end
    end
    
    if isempty(im)
        error('No image argument supplied');
    end

    if ~isa(im, 'double')
        im = double(im);
    end
    
    if nscale < 1
        error('nscale must be an integer >= 1');
    end
    
    if norient < 1 
        error('norient must be an integer >= 1');
    end    

    if minWaveLength < 2
        error('It makes little sense to have a wavelength < 2');
    end          

    if cutOff < 0 | cutOff > 1
        error('Cut off value must be between 0 and 1');
    end