# normxcorrn

## PURPOSE

Normalized n-dimensional cross-correlation.

## SYNOPSIS

function C = normxcorrn( T, A, shape, Tm )

## DESCRIPTION

     Normalized n-dimensional cross-correlation.

     For 2 dimensional inputs this function is exactly the same as normxcorr2,
     but also works in higher dimensions.   For more information see help on
     normxcorr2.m.  Also see Forsyth & Ponce 11.3.1 (p241).

     Also, it can take an additional argument that specifies a figure ground
     mask for the T.  That is Tm must be of the same dimensions as T, with
     each entry being 0 or 1, where zero specifies regions to ignore (the
     ground) and 1 specifies interesting regions (the figure).  Essentially Tm
     specifies regions in T that are interesting and should be taken into
     account when doing normalized cross correlation. This allows for
     templates of arbitrary shape, and not just squares. Note: with a mask,
     this function is approximately 3 times slower because it cannot use the
     trick of precomputing running sums.

     USAGE
      C = normxcorrn( T, A, [shape], [Tm] )

     INPUTS
      T           - template to correlate to each window in A
      A           - matrix to correlate T to
      shape       - ['full'] 'valid', 'full', or 'same', see convnFast help
      Tm          - [] figure/ground mask for the template

     OUTPUTS
      C           - correlation matrix

     EXAMPLE
      T=gaussSmooth(rand(20),2); A=repmat(T,[3 3]);  Tm=ones(size(T));
      C1=normxcorrn(T,A);  C2=normxcorr2(T,A);  C3=normxcorrn(T,A,[],Tm);
      figure(1); im(C1);  figure(2); im(C2);  figure(3); im(C3);
      figure(4); im(abs(C1-C2));  figure(5); im(abs(C2-C3));

     See also XEUCN, XCORRN, CONVNFAST

     Piotr's Image&Video Toolbox      Version 2.0
     Copyright 2008 Piotr Dollar.  [pdollar-at-caltech.edu]
     Please email me if you find bugs, or have suggestions or questions!
     Licensed under the Lesser GPL [see external/lgpl.txt]

## CROSS-REFERENCE INFORMATION

This function calls:

- convnFast Fast convolution, replacement for both conv2 and convn.
- localSum Fast routine for box filtering.

This function is called by: