WEIGHTFILT_BASE - Matrix functional filter.

Description
Syntax
Inputs
Outputs
Function implementation
Subfunctions

Description

Filter a matrix with the functional transform of another matrix.

Syntax

   k = WEIGHTFILT_BASE(Awin, Dwin, wei);

Inputs

Awin : input window to filter.

Dwin : input window which functional transform is used to filter Awin; it should be of same size as Awin.

wei : weighting functional F(Awin,Dwin); it is either:

a scalar <0 if the transform is a scale function with exponent wei, applied on Dwin ie. $x \rightarrow 1/ (x^{-\mbox{wei}})$ ,
0 if a weighted median filter is to be applied on Dwin using the weights given by the window Dwin,
a scalar >0 if a gaussian weighting with standard deviation 1 and factor wei is applied on Dwin, ie. it takes the form $x \rightarrow e^{(x \cdot \mbox{wei})}$ .

Outputs

k : scalar value obtained as an output of F(Awin,Dwin).

Function implementation

function k = weightfilt_base(Awin, Dwin, wei)

% if wei==0,     weighting = @wmedweight;
% elseif wei>0,  weighting = @gaussweight;
% else           weighting = @scaleweight;
% end
if wei==0,
    k = wmedweight(Awin, Dwin);
elseif wei>0,
    k = gaussweight(Awin, Dwin, wei);
else
    k = scaleweight(Awin, Dwin, wei);
end

end % end of weightfilt_base

Subfunctions

GAUSSWEIGHT - Gaussian-based weighting function

%--------------------------------------------------------------------------
function k = gaussweight(Awin, Dwin, a)
Dwin = exp( - a * Dwin );
t = sum(Dwin);
if(t>0),    Dwin = Dwin/t;  end
k = sum(Awin.*Dwin);

end % end of gaussweight

WMEDWEIGHT - Weighted median-based weighting function. For n numbers $x_1, \cdots, x_n$ with positive weights $w_1, \cdots, w_n$ (sum of all weights equal to one) the weighted median is defined as the element $x_k$ , such that: $\frac{1}{2} \geq \sum_{x_i < x_k} \quad \& \quad \frac{1}{2} \geq \sum_{x_i > x_k}$

%--------------------------------------------------------------------------
function k = wmedweight(Awin, Dwin)

Dwin = Dwin / max(Dwin(:));

% (line by line) transformation of the input-matrices to line-vectors
d = reshape(Awin',1,[]);
w = reshape(Dwin',1,[]);

% sort the vectors
A = [d' w'];
ASort = sortrows(A,1);

dSort = ASort(:,1)';
wSort = ASort(:,2)';

l = length(wSort);
sumVec = zeros(1,l);    % vector for cumulative sums of the weights
for i = 1:l
    sumVec(i) = sum(wSort(1:i));
end

k = [];     j = 0;

while isempty(k)
    j = j + 1;
    if sumVec(j) >= 0.5
        k = dSort(j);    % value of the weighted median
    end
end

end % end of wmedweight

SCALEWEIGHT - Scale-based weighting function.

%--------------------------------------------------------------------------
function k = scaleweight(Awin, Dwin, a)
Dwin = rescale(Dwin,eps,1) .^ a;
t = sum(Dwin);
if(t>0),    Dwin = Dwin/t;  end
k = sum(Awin.*Dwin);

end % end of scaleweight