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distancePoints.m
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distancePoints.m
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function dist = distancePoints(p1, p2, varargin)
%DISTANCEPOINTS Compute distance between two points.
%
% D = distancePoints(P1, P2)
% Return the Euclidean distance between points P1 and P2.
%
% If P1 and P2 are two arrays of points, result is a N1-by-N2 array
% containing distance between each point of P1 and each point of P2.
%
% D = distancePoints(P1, P2, NORM)
% Compute distance using the specified norm. NORM=2 corresponds to usual
% euclidean distance, NORM=1 corresponds to Manhattan distance, NORM=inf
% is assumed to correspond to maximum difference in coordinate. Other
% values (>0) can be specified.
%
% D = distancePoints(..., 'diag')
% compute only distances between P1(i,:) and P2(i,:).
%
% See also:
% points2d, minDistancePoints, nndist, hausdorffDistance
%
% ------
% Author: David Legland
% e-mail: [email protected]
% Copyright 2009 INRA - Cepia Software Platform.
% created the 24/02/2004.
%
% HISTORY :
% 25/05/2004: manage 2 array of points
% 07/04/2004: add option for computing only diagonal.
% 30/10/2006: generalize to any dimension, and manage different norms
% 03/01/2007: bug for arbitrary norm, and update doc
% 28/08/2007: fix bug for norms 2 and infinite, in diagonal case
%% Setup options
% default values
diag = false;
norm = 2;
% check first argument: norm or diag
if ~isempty(varargin)
var = varargin{1};
if isnumeric(var)
norm = var;
elseif strncmp('diag', var, 4)
diag = true;
end
varargin(1) = [];
end
% check last argument: diag
if ~isempty(varargin)
var = varargin{1};
if strncmp('diag', var, 4)
diag = true;
end
end
% number of points in each array and their dimension
n1 = size(p1, 1);
n2 = size(p2, 1);
d = size(p1, 2);
if diag
% compute distance only for apparied couples of pixels
dist = zeros(n1, 1);
if norm == 2
% Compute euclidian distance. this is the default case
% Compute difference of coordinate for each pair of point
% and for each dimension. -> dist is a [n1*n2] array.
for i = 1:d
dist = dist + (p2(:,i)-p1(:,i)).^2;
end
dist = sqrt(dist);
elseif norm == inf
% infinite norm corresponds to maximal difference of coordinate
for i = 1:d
dist = max(dist, abs(p2(:,i)-p1(:,i)));
end
else
% compute distance using the specified norm.
for i = 1:d
dist = dist + power((abs(p2(:,i)-p1(:,i))), norm);
end
dist = power(dist, 1/norm);
end
else
% compute distance for all couples of pixels
dist = zeros(n1, n2);
if norm == 2
% Compute euclidian distance. This is the default case.
% Compute difference of coordinate for each pair of point
% and for each dimension. -> dist is a [n1*n2] array.
for i = 1:d
% equivalent to:
% dist = dist + ...
% (repmat(p1(:,i), [1 n2])-repmat(p2(:,i)', [n1 1])).^2;
dist = dist + bsxfun (@minus, p1(:,i), p2(:, i)').^2;
end
dist = sqrt(dist);
elseif norm == inf
% infinite norm corresponds to maximal difference of coordinate
for i = 1:d
dist = max(dist, abs(bsxfun (@minus, p1(:,i), p2(:, i)')));
end
else
% compute distance using the specified norm.
for i = 1:d
% equivalent to:
% dist = dist + power((abs(repmat(p1(:,i), [1 n2]) - ...
% repmat(p2(:,i)', [n1 1]))), norm);
dist = dist + power(abs(bsxfun(@minus, p1(:,i), p2(:, i)')), norm);
end
dist = power(dist, 1/norm);
end
end