HISTCORRELATION - Correlation feature derived from (co)occurrence matrices.

Description
Syntax
References
See also
Function implementation

Description

Calculate the correlation feature defined in [HSD73] from (co)occurrence matrices.

This feature measures the correlation C of pixel pairs on greylevels as [ST99]:

GLCM case - with the local statistics $\mu_i = \sum_{i,j} i \cdot P_{ij}$ , $\mu_j = \sum_{i,j} j \cdot P_{ij}$ , $\sigma_i = \sum_{i,j} (i-\mu_i)^2 \cdot P_{ij}$ and $\sigma_j = \sum_{i,j} (j-\mu_j)^2 \cdot P_{ij}$ based on the greylevel joint probability $P_{ij}$ of the greylevel pair : $$ C = \sum_{i,j} ((i-\mu_i) \cdot (j-\mu_j) \cdot P_{ij}) ) / (\sigma_i \cdot \sigma_j)

GLSDV case - with the local statistics $\mu_d = \sum_d d \cdot P_d$ , $\mu_s = \sum_s s \cdot P_s$ and $\sigma = \sum_s (s-\mu_s)^2 \cdot P_s + \sum_d (d-\mu_d)^2 \cdot P_d$ based on the probabilities and of the greylevel sum and difference respectively : $C = \frac{(\sum_s(s-\mu_s)^2 \cdot P_s - \sum_d (d-\mu_d)^2 \cdot P_d)}{\sigma^2}$

Syntax

   C = HISTCORRELATION(pD, D);
   C = HISTCORRELATION(pIJ, I, J);

References

See HISTCONTRAST.

Function implementation

function C = histcorrelation(pIJ,I,varargin)

muI = sum(I .* pIJ);
sI = sum((I-muI).^2 .* pIJ);

if nargin>2
    J = varargin{1};
    muJ = sum(J .* pIJ);
    sJ = sum((J-muJ).^2 .* pIJ);
else % J = I = D
    J = I;
    muJ = muI;
    sJ = sI;
end

% Correlation = sum_i( sum_j( ((ij)p(i,j) - u_x.u_y) / (s_x.s_y) ) ) (p[2])
% C = sum (I .* J .* pIJ - muI .* muJ) / sqrt(sI * sJ);
% Correlation = sum_i( sum_j( (i - u_i)(j - u_j)p(i,j)/(s_i.s_j) ) ) (m)
C = sum ((I - muI) .* (J - muJ) .* pIJ) / sqrt(sI * sJ);

end % end of histcorrelation

HISTCORRELATION - Correlation feature derived from (co)occurrence matrices.

Contents

Description

Syntax

References

See also

Function implementation