# Lbp

## 1-bit news

OK, it’s been a while again, but here are the reasons for being silent. 1-bit LBD reconstruction is out! Remember all those posts about LBDs, FREAKs, BRIEFs, and reconstructing images ? The latest version of tis work is out with a major feature: 1-bit quantized LBDs reconstruction. Yes, 1-bit ! To achieve this, we leverage some results from 1-bit Compressed Sensing thanks to my co-author Laurent Jacques. So, the pre-print is on arxiv and on infoscience, and you can get the code from github.

## Linearized model of LBPs

LBP model An LBP can be decomposed into two tiers: first, a real description vector, obtained by convolution-then-difference then the quantization (binarization) operation. Mathematically, the real i-th component of the descriptor is computed with the formula: $${\mathcal L}(p)i = \langle{\mathcal G}{x_i, \sigmai} , p \rangle - \langle G{x_i’, \sigmai’} , p\rangle,$$ where ${\mathcal G}{x_i, \sigmai}, {\mathcal G}{x’_i, \sigma’_i}$ are two Gaussians. The variety of the LBP family comes from the choice of these Gaussians : they can have a fixed size but random positions (a la BRIEF), fixed sizes and positions (a la BRISK)1… The choice in FREAK was :

## FREAK reconstruction as an inverse problem

In a previous post, I have briefly introduced our FREAK descriptor, which belongs to the more general family of the LBPs. In this post, I will state mathematically the problem of the reconstruction of an image patch given its descriptor, i.e. answering the question:

Can you guess which image part created this particular description vector ?

## FREAK makes it into OpenCV trunk

Integrating our lab’s FREAK in your vision workflow is getting easier and easier!

## Introducing FREAKs

OK, starting to mix posts in English and French since the English version of the blog is still buggy.