compute normalization matrix for 2d points

Author: fredzzhang

getNormMat2d.m

@@ -0,0 +1,30 @@
+function Nmatrix = getNormMat2d(x)
+% Function: Compute the normalization matrix of 2d points in 
+%           homogeneous coordinate
+% Normalization criteria:
+%   1. Move the centroidto the origin
+%   2. Average distance of  points to the centroid is sqrt(2) 
+% 
+% Usage:
+% 
+%       Nmatrix = getNormMat(x)
+%   where:
+%       Nmatrix - the normalization matrix
+%       x - input data, dim: 3xN
+% 
+% Institute: Australian National University
+% Author: Zhen Zhang
+% Last modified: 11 Apr. 2018
+
+% Get the centroid
+centroid = mean(x, 2);
+% Compute the distance to the centroid
+dist = sqrt(sum((x - repmat(centroid, 1, size(x, 2))) .^ 2, 1));
+% Get the mean distance
+mean_dist = mean(dist);
+% Craft normalization matrix
+Nmatrix = [sqrt(2) / mean_dist, 0, -sqrt(2) / mean_dist * centroid(1);...
+           0, sqrt(2) / mean_dist, -sqrt(2) / mean_dist * centroid(2);...
+           0, 0, 1];
+
+end