Transfer of BRIEF,ORB,BRISK,FREAK, HOG (#205)

These demos are transferred from ImageFeatures' own documentation

Author: ashwanirathee

docs/examples/image_features/assets/boxes.jpg

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+# ---
+# cover: assets/brief.gif
+# title: BRIEF Descriptor
+# description: This demo shows BRIEF descriptor
+# author: Anchit Navelkar; Ashwani Rathee
+# date: 2021-07-12
+# ---
+
+# `BRIEF` (Binary Robust Independent Elementary Features) is an efficient feature point descriptor.
+# It is highly discriminative even when using relatively few bits and is computed using simple 
+# intensity difference tests. BRIEF does not have a sampling pattern thus pairs can be chosen 
+# at any point on the `SxS` patch.
+
+# To build a BRIEF descriptor of length `n`, we need to determine `n` pairs `(Xi,Yi)`. 
+# Denote by `X` and `Y` the vectors of point `Xi` and `Yi`, respectively.
+
+# In ImageFeatures.jl we have five methods to determine the vectors `X` and `Y` :
+
+# - `random_uniform` : `X` and `Y` are randomly uniformly sampled
+# - `gaussian` : `X` and `Y` are randomly sampled using a Gaussian distribution, meaning that locations that are closer to the center of the patch are preferred
+# - `gaussian_local` : `X` and `Y` are randomly sampled using a Gaussian distribution where first `X` is sampled with a standard deviation of `0.04*S^2` and then the `Yi’s` are sampled using a Gaussian distribution – Each `Yi` is sampled with mean `Xi` and standard deviation of `0.01 * S^2`
+# - `random_coarse` : `X` and `Y` are randomly sampled from discrete location of a coarse polar grid
+# - `center_sample` : For each `i`, `Xi` is `(0, 0)` and `Yi` takes all possible values on a coarse polar grid
+
+# As with all the binary descriptors, BRIEF’s distance measure is the number of 
+# different bits between two binary strings which can also be computed as the sum
+# of the XOR operation between the strings.
+
+# BRIEF is a very simple feature descriptor and does not provide scale or rotation 
+# invariance (only translation invariance). To achieve those, see ORB, BRISK,
+# FREAK examples
+
+# ## Example
+
+# Let us take a look at a simple example where the BRIEF descriptor is used to match 
+# two images where one has been translated by `(100, 200)` pixels. We will use the 
+# `lighthouse` image from the [TestImages](https://github.com/timholy/TestImages.jl) 
+# package for this example.
+
+
+# Now, let us create the two images we will match using BRIEF.
+
+using ImageFeatures, TestImages, Images, ImageDraw, CoordinateTransformations
+
+img = testimage("sudoku")
+img1 = Gray.(img)
+trans = Translation(-50, -50)
+img2 = warp(img1, trans, axes(img1))
+
+# To calculate the descriptors, we first need to get the keypoints. For this tutorial,
+# we will use the FAST corners to generate keypoints (see `fastcorners`).
+
+keypoints_1 = Keypoints(fastcorners(img1, 12, 0.4))
+keypoints_2 = Keypoints(fastcorners(img2, 12, 0.4))
+
+
+# To create the BRIEF descriptor, we first need to define the parameters by calling
+# the `BRIEF` constructor.
+
+brief_params = BRIEF(size = 256, window = 10, seed = 123)
+
+# Now pass the image with the keypoints and the parameters to the 
+# `create_descriptor` function.
+
+desc_1, ret_keypoints_1 = create_descriptor(img1, keypoints_1, brief_params)
+desc_2, ret_keypoints_2 = create_descriptor(img2, keypoints_2, brief_params)
+
+# The obtained descriptors can be used to find the matches between the two images 
+# using the `match_keypoints` function.
+
+matches = match_keypoints(ret_keypoints_1, ret_keypoints_2, desc_1, desc_2, 0.1)
+
+# We can use the [ImageDraw.jl](https://github.com/JuliaImages/ImageDraw.jl) package
+# to view the results.
+
+grid = hcat(img1, img2)
+offset = CartesianIndex(0, size(img1, 2))
+map(m -> draw!(grid, LineSegment(m[2] + offset,m[1] )), matches)
+grid
+
+
+# `grid` shows the results
+
+save("assets/brief.gif", cat(img1, img2, grid[1:512,1:512], grid[1:512,513:1024]; dims=3); fps=1) #src

docs/examples/image_features/assets/hog.gif

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+# ---
+# cover: assets/brisk.gif
+# title: BRISK Descriptor
+# description: This demo shows BRISK descriptor
+# author: Anchit Navelkar; Ashwani Rathee
+# date: 2021-07-12
+# ---
+
+# The *BRISK* (Binary Robust Invariant Scalable Keypoints) descriptor has a predefined 
+# sampling pattern as compared to `BRIEF` or `ORB`. 
+# Pixels are sampled over concentric rings. For each sampling point, a small patch 
+# is considered around it. Before starting the algorithm, the patch is smoothed 
+# using gaussian smoothing.
+
+# Two types of pairs are used for sampling, short and long pairs. 
+# Short pairs are those where the distance is below a set threshold distmax while the
+# long pairs have distance above distmin. Long pairs are used for orientation and 
+# short pairs are used for calculating the descriptor by comparing intensities.
+
+# BRISK achieves rotation invariance by trying the measure orientation of the keypoint
+# and rotating the sampling pattern by that orientation. This is done by first 
+# calculating the local gradient `g(pi,pj)` between sampling pair `(pi,pj)` where 
+# `I(pj, pj)` is the smoothed intensity after applying gaussian smoothing.
+
+# `g(pi, pj) = (pi - pj) . I(pj, j) -I(pj, j)pj - pi2`
+
+# All local gradients between long pairs and then summed and the `arctangent(gy/gx)`
+# between `y` and `x` components of the sum is taken as the angle of the keypoint. 
+# Now, we only need to rotate the short pairs by that angle to help the descriptor 
+# become more invariant to rotation.
+# The descriptor is built using intensity comparisons. For each short pair if the 
+# first point has greater intensity than the second, then 1 is written else 0 is 
+# written to the corresponding bit of the descriptor.
+
+# ## Example
+
+# Let us take a look at a simple example where the BRISK descriptor is used to 
+# match two images where one has been translated by `(50, 40)` pixels and then 
+# rotated by an angle of 75 degrees. We will use the `lighthouse` image from the
+#  [TestImages](https://github.com/timholy/TestImages.jl) package for this example.
+
+# First, let us create the two images we will match using BRISK.
+
+using ImageFeatures, TestImages, Images, ImageDraw, CoordinateTransformations, Rotations
+using MosaicViews
+
+img = testimage("lake_color")
+
+# Original Image 
+
+img1 = Gray.(img)
+rot = recenter(RotMatrix(5pi/6), [size(img1)...] .÷ 2)  # a rotation around the center
+tform = rot ∘ Translation(-50, -40)
+img2 = warp(img1, tform, axes(img1))
+mosaicview(img, img1, img2; nrow=1)
+
+# To calculate the descriptors, we first need to get the keypoints. For this 
+# tutorial, we will use the FAST corners to generate keypoints (see `fastcorners`).
+
+
+features_1 = Features(fastcorners(img1, 12, 0.35))
+features_2 = Features(fastcorners(img2, 12, 0.35))
+
+# To create the BRISK descriptor, we first need to define the parameters by 
+# calling the `BRISK` constructor.
+
+
+brisk_params = BRISK()
+
+
+# Now pass the image with the keypoints and the parameters to the 
+# `create_descriptor` function.
+
+desc_1, ret_features_1 = create_descriptor(img1, features_1, brisk_params)
+desc_2, ret_features_2 = create_descriptor(img2, features_2, brisk_params)
+
+# The obtained descriptors can be used to find the matches between the two 
+# images using the `match_keypoints` function.
+
+matches = match_keypoints(Keypoints(ret_features_1), Keypoints(ret_features_2), desc_1, desc_2, 0.1)
+
+# We can use the [ImageDraw.jl](https://github.com/JuliaImages/ImageDraw.jl) package to view the results.
+
+grid = hcat(img1, img2)
+offset = CartesianIndex(0, size(img1, 2))
+map(m -> draw!(grid, LineSegment(m[1], m[2] + offset)), matches)
+grid
+
+save("assets/brisk.gif", cat(img, img2, grid[1:512,1:512], grid[1:512,513:1024]; dims=3); fps=1) #src