# BRIEF Descriptor

Binary robust independent elementary features. In In European Conference on Computer Vision, 2010.

https://www.cs.ubc.ca/~lowe/525/papers/calonder_eccv10.pdf Available locally: file:///Users/stevengong/My%20Drive/Books/calonder_eccv10.pdf

A modified version is used in ORB.

“Our experiments show that only 256 bits, or even 128 bits, often suffice to obtain very good matching results”.

BRIEF is a binary descriptor. Its description vector consists of many zeros and ones, which encode the size relationship between two random pixels near the keypoint (such as p and q): If $p$ is greater than $q$, then take $1$, otherwise take $0$.

We define test τ on patch p of size S × S as

$τ(p;x,y)={10 ifp(x)<p(y)otherwise $

- where p(x) is the pixel intensity in a smoothed version of p at x = (u, v) ⊤.
- Choosing a set of nd (x, y)-location pairs uniquely defines a set of binary tests. We take our BRIEF descriptor to be the nd-dimensional bitstring
- $f_{nd}(p)=∑_{1≤i≤n_{d}}2_{i−1}τ(p;xi,yi)$