ORB/BFMatcher - why norm_hamming distance?

Question

I'm using the OpenCV implementation of ORB along with the BFMatcher. The OpenCV states that NORM_HAMMING should be used with ORB.

Why is this? What advantages does norm_hamming offer over other methods such as euclidean distance, norm_l1, etc.

Answer 1

When comparing descriptors in computer vision, the Euclidian distance is usually understood as the square root of the sum of the squared differences between the two vectors' elements.

The ORB descriptors are vectors of binary values. If applying Euclidian distance to binary vectors, the squared result of a single comparison would always be 1 or 0, which is not informative when it comes to estimating the difference between the elements. The overall Euclidian distance would be the square root of the sum of those ones and zeroes, again not a good estimator of the difference between the vectors.

That's why the Hamming distance is used. Here the distance is the number of elements that are not the same. As noted by Catree, you can calculate it by a simple boolean operation on the vectors, as shown in the figure below. Here D1 is a single 4-bit descriptor that we are comparing with 4 descriptors shown in D2. Matrix H is the hamming distances for each row.