D = VL_ALLDIST2(X,Y) returns the pairwise distance matrix D of the columns of S1 and S2, yielding
D(i,j) = sum (X(:,i) - Y(:,j)).^2
VL_ALLDIST2(X) returns the pairwise distance matrix fo the columns of S, yielding
D(i,j) = sum (X(:,i) - X(:,j)).^2
VL_ALLDIST2(...,'METRIC') changes the computed distance. Supported values for METRIC are
METRIC D(i,j) -------------------------------------------------------- LINF max |X - Y| L2 sum (X - Y).^2 L1 sum |X - Y| L0 sum (X ~= Y) CHI2 sum (X - Y).^2 ./ (X + Y) HELL sum (X^.5 - Y^.5) .^ 2
(Notice that the standard definition of chi2 is half of what is computed here).
VL_ALLDIST2(...,'KERNEL') computes the following 'kernels' K:
KERNEL K(i,j) --------------------------------------------------------- KL2 sum X .* Y KL1 sum min (X, Y) KCHI2 2 * sum (X .* Y) ./ (X + Y) KHELL (X .* Y) .^ 0.5
The constant are chosen so that D(i,j) = K(i,i) + K(j,j) - 2 K(i,j) where D is the metric corresponding to the kenrel (if the arguments are non-negative vectors). Each kernel can be interpreted as the inner product inducing the corresponding metric in an embedding of the real space into an approrpiate reproducing Kenrel Hilbert space.
VL_ALLDIST2() supports several storage classes. X and Y must have the same storage class. The sotrage class of D is promoted to reduce the chance of overvlow, but this is not checked.
X & Y class D class --------------------------- UINT8 UINT32 INT8 INT32 UINT16 UINT32 INT16 INT32 UINT32 UINT32 INT32 INT32 SINGLE SINGLE DOUBLE DOUBLE
Warning: Both chi2 and kchi2 use integer math when presented with integer data types. This can easily result in zeros where you did not expect them.
See also: VL_HELP().