Euclidean distance returning strange results

Question

im writing a program to compare two images against each other based on color and im using the Euclidean distance algorithm however when i run it and pass in two images i get one distance and then when i pass in the same images but the other way round i get a completely different set of results.

is this normal or should the answers be the same?

The statement I'm using to compute the Euclidean distance is:

distance = (int) Math.sqrt(   (rgb1.getR()-rgb2.getR())^2
                            + (rgb1.getG()-rgb2.getG())^2
                            + (rgb1.getB()-rgb2.getB())^2
                          );

Euclidean distance (or, for that matter, any distance function), should be symmetric, so indeed your results seem strange. However you need to post more details for anybody to be able to help. What code are you using for the distance calculation? — Michał Kosmulski, Mar 10 '12 at 21:38
do you want the entire code or just the euclidean distance code? — Roy James Schumacher, Mar 10 '12 at 21:42
Let's start with the distance code - we'll see if it's enough to solve the issue. — Michał Kosmulski, Mar 10 '12 at 21:47
distance = (int) Math.sqrt( (rgb1.getR()-rgb2.getR())^2 + (rgb1.getG()-rgb2.getG())^2 + (rgb1.getB()-rgb2.getB())^2); — Roy James Schumacher, Mar 10 '12 at 21:54

score 7 · Accepted Answer · answered Mar 10 '12 at 22:00

Looking at the code you posted, it looks your RGB values are ints. However, the ^ operator is not the power operator, but XOR (exclusive-OR) - a bitwise operation. So in order to calculate the squares correctly, use regular multiplication - e.g., use a temporary variable int deltaR = rgb1.getR()-rgb2.getR(); and then in the formula write deltaR*deltaR instead of the ^ operator. Your RGB values will probably be in 0 to 255 range, so there shouldn't be overflow issues. Alternatively, you could use Math.pow(rgb1.getR()-rgb2.getR(),2) etc. in the formula.

thank you soo much this has solved the problem and it is working as expected now — Roy James Schumacher, Mar 10 '12 at 22:10

score 2 · Answer 2 · edited May 23 '17 at 10:34

For squaring a number in Java, use Math.pow(x, 2) or even simpler, x * x. The expression x ^ 2 does not square x, instead it XORs x with 2.

In your code:

int diffR = rgb1.getR() - rgb2.getR();
int diffG = rgb1.getG() - rgb2.getG();
int diffB = rgb1.getB() - rgb2.getB();

int distance = (int) Math.sqrt(diffR*diffR + diffG*diffG + diffB*diffB);

... Although I'm not quite sure of your algorithm, but that's a different issue.

score 0 · Answer 3 · answered Mar 10 '12 at 22:06

As people have said, you can use Math.pow(x, 2) for squaring. Just from personal experience, if you're going to call this function a lot it might be better to write out the multiplication yourself, i.e. Math.sqrt((deltaX * deltaX) + (deltaY * deltaY) + (deltaZ * deltaZ)); It may seem uglier but if you profile both forms of the code you'll see that the calls to Math.pow are much slower than the simple multiplications. Obviously there's nothing to do about the Math.sqrt call though.

Euclidean distance returning strange results

3 Answers3