ORB (Oriented FAST and Rotated BRIEF) {#tutorial_py_orb}
=====================================

Goal
----

In this chapter,
    -   We will see the basics of ORB

Theory
------

As an OpenCV enthusiast, the most important thing about the ORB is that it came from "OpenCV Labs".
This algorithm was brought up by Ethan Rublee, Vincent Rabaud, Kurt Konolige and Gary R. Bradski in
their paper **ORB: An efficient alternative to SIFT or SURF** in 2011. As the title says, it is a
good alternative to SIFT and SURF in computation cost, matching performance and mainly the patents.
Yes, SIFT and SURF are patented and you are supposed to pay them for its use. But ORB is not !!!

ORB is basically a fusion of FAST keypoint detector and BRIEF descriptor with many modifications to
enhance the performance. First it use FAST to find keypoints, then apply Harris corner measure to
find top N points among them. It also use pyramid to produce multiscale-features. But one problem is
that, FAST doesn't compute the orientation. So what about rotation invariance? Authors came up with
following modification.

It computes the intensity weighted centroid of the patch with located corner at center. The
direction of the vector from this corner point to centroid gives the orientation. To improve the
rotation invariance, moments are computed with x and y which should be in a circular region of
radius \f$r\f$, where \f$r\f$ is the size of the patch.

Now for descriptors, ORB use BRIEF descriptors. But we have already seen that BRIEF performs poorly
with rotation. So what ORB does is to "steer" BRIEF according to the orientation of keypoints. For
any feature set of \f$n\f$ binary tests at location \f$(x_i, y_i)\f$, define a \f$2 \times n\f$ matrix, \f$S\f$
which contains the coordinates of these pixels. Then using the orientation of patch, \f$\theta\f$, its
rotation matrix is found and rotates the \f$S\f$ to get steered(rotated) version \f$S_\theta\f$.

ORB discretize the angle to increments of \f$2 \pi /30\f$ (12 degrees), and construct a lookup table of
precomputed BRIEF patterns. As long as the keypoint orientation \f$\theta\f$ is consistent across views,
the correct set of points \f$S_\theta\f$ will be used to compute its descriptor.

BRIEF has an important property that each bit feature has a large variance and a mean near 0.5. But
once it is oriented along keypoint direction, it loses this property and become more distributed.
High variance makes a feature more discriminative, since it responds differentially to inputs.
Another desirable property is to have the tests uncorrelated, since then each test will contribute
to the result. To resolve all these, ORB runs a greedy search among all possible binary tests to
find the ones that have both high variance and means close to 0.5, as well as being uncorrelated.
The result is called **rBRIEF**.

For descriptor matching, multi-probe LSH which improves on the traditional LSH, is used. The paper
says ORB is much faster than SURF and SIFT and ORB descriptor works better than SURF. ORB is a good
choice in low-power devices for panorama stitching etc.

ORB in OpenCV
-------------

As usual, we have to create an ORB object with the function, **cv2.ORB()** or using feature2d common
interface. It has a number of optional parameters. Most useful ones are nFeatures which denotes
maximum number of features to be retained (by default 500), scoreType which denotes whether Harris
score or FAST score to rank the features (by default, Harris score) etc. Another parameter, WTA_K
decides number of points that produce each element of the oriented BRIEF descriptor. By default it
is two, ie selects two points at a time. In that case, for matching, NORM_HAMMING distance is used.
If WTA_K is 3 or 4, which takes 3 or 4 points to produce BRIEF descriptor, then matching distance
is defined by NORM_HAMMING2.

Below is a simple code which shows the use of ORB.
@code{.py}
import numpy as np
import cv2
from matplotlib import pyplot as plt

img = cv2.imread('simple.jpg',0)

# Initiate ORB detector
orb = cv2.ORB_create()

# find the keypoints with ORB
kp = orb.detect(img,None)

# compute the descriptors with ORB
kp, des = orb.compute(img, kp)

# draw only keypoints location,not size and orientation
img2 = cv2.drawKeypoints(img,kp,color=(0,255,0), flags=0)
plt.imshow(img2),plt.show()
@endcode
See the result below:

![image](images/orb_kp.jpg)

ORB feature matching, we will do in another chapter.

Additional Resources
--------------------

-#  Ethan Rublee, Vincent Rabaud, Kurt Konolige, Gary R. Bradski: ORB: An efficient alternative to
    SIFT or SURF. ICCV 2011: 2564-2571.

Exercises
---------
