Question

Please explain to me, in few words, how the Viola-Jones face detection method works.

Answer 1

The Viola-Jones detector is a strong, binary classifier build of several weak
detectors

Each weak detector is an extremely simple binary classifier

During the learning stage, a cascade of weak detectors is trained so as to
gain the desired hit rate / miss rate (or precision / recall) using Adaboost
To detect objects, the original image is partitioned in several rectangular
patches, each of which is submitted to the cascade

If a rectangular image patch passes through all of the cascade stages, then
it is classified as “positive”
The process is repeated at different scales

Actually, at a low level, the
basic component of an object detector
is just something required to say if
a certain sub-region of the original
image contains an istance of the
object of interest or not. That is
what a binary classifier does.

The basic, weak classifier is based on a very simple visual feature (those
kind of features are often referred to as “Haar-like features”)

Haar-like features consist of a class of local
features that are calculated by subtracting the sum of a
subregion of the feature from the sum of the remaining
region of the feature.

These feature are characterised by the fact that they are easy to calculate and with the use of an integral image, very efficient to calculate.

Lienhart introduced an extended set of twisted Haar-like feature (see image)

These are the standard Haar-like feature that have been twisted by 45 degrees. Lienhart did not originally make use of the twisted checker board Haar-like feature (x2y2) since the diagonal elements that they represent can be simply represented using twisted
features, however it is clear that a twisted version of this feature can also be implemented and used.

These twisted Haar-like features can also be fast and efficiently calculated using an integral image that has been twisted 45 degrees. The only implementation issue is that
the twisted features must be rounded to integer values so that they are aligned with pixel boundaries. This process is similar to the rounding used when scaling a Haar-like
feature for larger or smaller windows, however one difference is that for a 45 degrees
twisted feature, the integer number of pixels used for the height and width of the
feature mean that the diagonal coordinates of the pixel will be always on the same diagonal set of pixels

This means that the number of different sized 45 degrees twisted features available is significantly reduced as compared to the standard vertically and horizontally
aligned features.

So we have something like:

About the formula, the Fast computation of Haar-like features using integral images looks like:

Finally, here is a c++ implementation which uses ViolaJones.h by Ivan Kusalic

to see the complete c++ project go here