Heurisitic Function

Euclidean Distance

Calculated using Pythagorean Theorem, where the Euclidean Distance is given by $H(x_n,y_n)=\sqrt{(x_n-x_g{)}^2+(y_n-y_g{)}^2}$

The squared Euclidean Distance is just getting rid of the square root, i.e. $H(x_n,y_n)=(x_n-x_g{)}^2+(y_n-y_g{)}^2$

Machine Learning

This notation is used for Computer Vision, we call it the L2 Distance / L2 Norm $d_1(I_1,I_2)=\sqrt{\sum _p(I_1^p-I_2^p{)}^2}$ Serendipity: This is also called the Root Mean Square, which I saw in ECE140.

Squared L2 Norm $d_1(I_1,I_2)=\sum _p(I_1^p-I_2^p{)}^2$ See Loss Function to see some discussions about why we would use L1 Distance vs L2 Distance.

Sum of Squared Differences (SSD)

This is the term that I saw from the Computer Vision world, learning from Cyrill Stachniss.

$\text{SSD}={\sum }_{i,j}(I(i,j)-T(i,j){)}^2$