# 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 $0$.

Random pattern, but not random across feature points!

In BRIEF, the randomness of the 128 pixel sampling is fixed after the initial random selection. The same pre-determined pattern of pixels is used for every feature point in an image.

- That makes sense, to ensure fair comparison

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 $n_{d}$ (x, y)-location pairs uniquely defines a set of binary tests. We take our BRIEF descriptor to be the $n_{d}$-dimensional bitstring
- $f_{nd}(p)=∑_{1≤i≤n_{d}}2_{i−1}τ(p;x_{i},y_{i})$