06 image features

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2

Image Features
Image features are interesting locations in an image.
We want to be able to apply…
• Feature detection
Finding regions, when moved, that cause maximal variation
• Features description
Building a good context around a feature
We use this information about these interesting locations for a wide variety of uses.

Feature Detection
Background feature matches any background cell.
Foreground feature matches any foreground cell.
L-edge matches any vertical edge.
T-edge matches any horizontal edge.
But, CORNER only has one match!!!

Uses of Image Features: Matching

Classification (Object Recognition)
What is this object?
It is a Crayon

Tracking of Features in Motion
Image reference: https://commons.wikimedia.org/wiki/File:Madison_Square_Garden_food_court.jpg

Object Detection
Image from OpenCV documentation: https://docs.opencv.org/3.3.0/d7/d8b/tutorial_py_face_detection.html

Techniques for Image Features
Techniques that can be used for any of these use-cases:
• Corners
• HOG
• SIFT
• SURF
• FAST
• BRIEF
• However, these techniques are typically developed by a research group to solve
one use case.

Corners
An edge is indicated by a strong derivative.
• This is helpful to find an edge, but all features along that edge may look the same.
• We want a better way to identify an interesting feature.
Corners are edges in two orthogonal directions.
• Hopefully, a corner will have enough information to identify our feature over multiple
images, or frames.

Harris Corners
Harris
Corners
Corner on
Original
Image

Harris Corners
Used for sparse feature matching.
Use a Gaussian weighted window.
• Allows detection when there is in-plane rotation of an interesting feature
• Down-weights edge-like features
Compute a scalar interest measure.
Find local maxima.

Harris Corners
Harris corners are defined as second-order derivatives.
We create a second-derivative Hessian image.
A corner is identified when this matrix has two large eigenvalues.
Look at eigenvalues of the autocorrelation matrix.
• Eigenvectors tell us the orientation of a matrix.
• Eigenvalues tell us the scale in those directions.
• Either minimum eigenvalue, or something more complicated like:
𝜆0 𝜆1 − 0.06 𝜆0 𝜆1
2

Harris Corners and Shi-Tomasi
Shi-Tomasi modified the Harris corner.
In both cases we take the:
• Correlation between gradients in x and
y directions
Harris used:
Shi-Tomasi used:
• Invariant to rotation (because of eigenvalues)
𝜆0 𝜆1 − 0.06 𝜆0 𝜆1
2 < 𝑇ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑
𝜆0 < 𝑇ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑

Sub-Pixel Methods
Harris and Shi-Tomasi corners are good for feature recognition and used…
• When you are extracting geometric measurements
• When you need higher resolution feature recognition
If I am a…
Biologist trying to generate a 3D reconstruction of a blood vessel
Or a marine determining the location of a target in a satellite image
I need sub-pixel coordinates.

Sub-Pixel Methods
If we know an approximate (pixel level) location Capprox of a corner we can
find a better corner Cimproved by:
• Sampling a region of points P around Capprox.
• Setting up a series of equations that capture the directional similarities
between each p of P and Cimproved
Note, we don’t know Cimproved!
• Solve the equations. The result is Cimproved.
• Repeat this process.

Sub-Pixel Methods
Similarity measure has these important properties:
• Similarity(0,any) = Similarity(any,0) = 0
• Similarity(perpendicular directions) = 0
For us, our directions are:
1. The gradient at a region point p
2. The direction from C_approx to p

Sub-Pixel Methods
When the similarity between the direction of the gradient and the direction from
C_approx to p is 0
• The directions must be perpendicular.
In turn, this means that the direction lies along an edge
• Multiple edges meet at a corner!
The similarity measure is the dot product between the gradient at p and the direction
from Capprox to p.

Histogram of Oriented Gradients
Developed to detect pedestrians in a scene
Techniques focus on detection accuracy instead of computing speed and efficiency.
• Details about an object are determined as accurately as possible.
HOGs are a distribution of the directions of the gradients.
The histogram confers distribution
The oriented gradients confer direction of gradient

Histogram of Oriented Gradients
Features produced by HOG are the histograms from the cells.

Constants are Tuned for Recognizing Humans
HOG is described in terms of one ROI, but many steps can be precomputed
on the whole image.
Because HOG was originally developed for pedestrian recognition, many
HOG ROIs are humans.
Humans are basically tall rectangles.
Therefore, we will make patches around an ROI by using a…
Patch aspect of 2 (tall) to 1 (wide)
Cell size of 8 x 8 because it captures human features like eyes

You Can Use HOG on Other, Non-Human,
Features
Image
ROI
Frames for Normalization
Cells
Tree image from: https://commons.wikimedia.org/wiki/Christmas_tree#/media/File:Piazza_Portanova_Natale_2008.jpg

HOG: An Example
Step 1: Take the image and create a patch of the ROI with a fixed aspect ratio of 1:2.
 Essentially, you are cropping the image around the ROI.
Patch (or ROI)

HOG: An Example
Step 2: Calculate the horizontal and vertical gradients for each color in the patch.
– Convolve with [-1,0,1] kernels
– For instance, you can use Sobel for this step

HOG: An Example
Step 3: Consider the component-wise gradients in polar coordinates.
– Take x, y gradients and convert to Q
• x, y  r, Q [graphic]
• At every pixel, take max r over the three color channels
• r is magnitude
• Associated direction is the theta of that max r

HOG: An Example
Step 4: The patch is divided into 8 x 8
cells, from which we make a histogram
of gradients.
Each bucket, or bin, are angles (Q)
– Q = 0, 20, 40, ..., 160
• This gives us nine total bins
– We assign the magnitude (r) of a pixel to its
angle (th) bin.
– For angles between bins, we divide it
proportionally to distance from the bins.
Direction (Q) Magnitude (r)
0 20 40 60 80 100 120 140 160

HOG: An Example
Step 5: Create a mega-cell and associated mega-histogram with 36
total values.
• Use a sliding 16 x 16 window (of four histograms each time you slide the
window).
• Normalize this window with respect to L2 norm to create one block of
features.
• Slide the window over 8 pixels and repeat normalization.
• Some pixels will be repeated normalized, but with respect to different
neighborhoods extending differed directions.

Features per Patch: Some Simple Math
The result is 3,780 total features for one patch.
• On a 128 x 64 image we have 16 x 8 cells that are 8 x 8
• We have 15 x 7 mega-cells
• Which gives us 105 blocks of 36 features

Scale Invariant Feature Transform (SIFT)
Is a feature detection and description method that is
invariant to scale
• Particularly helpful when analyzing larger corners
Scale-space filtering is used to detect keypoints with
different scales.
• Uses difference of Gaussians (DoG) to approximate
Laplacian of Gaussians (LoG).
• Finds maxima with respect to space and scale.
Space is across an image
Scale is up and down a DoG pyramid

SIFT: Feature Detection
First, we need to find candidate keypoints (feature detection).
We do this by finding extrema versus neighbors in a Gaussian pyramid.
This is on the same scale but can be high or lower resolution.
Then, we find candidates by filtering out points with low contrast and on edges.

SIFT: Feature Description
Now that feature detection is complete, we need to describe the feature.
• The neighborhood is proportional to level of the extrema
• Estimate orientation in neighborhood around the keypoint
• Compute a histogram of gradients in this neighborhood
• Normalize histogram

SIFT: Matching
Lastly, we will use the feature description to match the feature.
• We will use the Euclidean distance between keypoint descriptors

Speeded Up Robust Features (SURF)
Similar to SIFT, but relies on several approximations and tricks to speed the processes.
Uses a box filter to approximate Gaussian smoothing.
• Integral images are easy to compute
Hessian matrix is used to find both extrema and scale.
• Matrix of mixed second-order derivatives

SURF: Feature Detection
Computed via its determinant
• Eigenvalues are like scale factors
• Determinant is like a volume
Multiply the eigenvalues together like dimensions of a cube
• The determinant of the matrix of partial second-order derivatives! (LOL)

SURF: Feature Description
Uses wavelet responses for orientation and description
• In turn, these calculations are sped-up by the use of the integral image.

Feature from Accelerated Segment Test
(FAST)
High-speed corner detector is even faster than SURF.
Imagine the corner of a building against a blue sky.
• From around 9 o'clock to 6 o'clock
The sky will be blue.
The center point will be building color (tan, brown, and so on).

FAST
Uses a trivial first test to rule out the big arc.
• Checks for 12 o’clock and 6 o’clock, then 3 o’clock and 9 o’clock, for sameness.
• Finds corners
But there is no real descriptor built in to FAST.
• FAST is not good with high-level noise.
Identifies points where much of an arc around it is all the same color (and different from
the center).

Binary Robust Independent Elementary
Features (BRIEF)
When we are looking at many features, feature description takes up too much memory
and time.
• The descriptors can be too verbose.
• They are often hard to learn from, hard to match, and have inefficient space use.
• There are various means to compress this data: PCA, hashing, and so on.
• Some methods will apply hashing after feature description.
This still requires too much memory
• BRIEF is designed to solve this problem.

BRIEF
BRIEF uses hashing to convert vectors to binary strings.
• The strings are then often compared with Hamming distance: the number of
characters that are different for two strings.
Fast and efficient process as it is binary (off/on)
BRIEF goes directly from pixels to binary numbers.
• Fixed set of pairs of points (pi, pj)
Selected once and permanently
Sampled from a random distribution
• The binary values
pi pj = 1
pi pj = 0
Example Hamming distances:
• 100→011: distance 3
• 010→111: distance 2
Source: Wikipedia
Image source: https://upload.wikimedia.org/wikipedia/commons/6/6e/Hamming_distance_3_bit_binary_example.svg

Oriented Fast and Rotated BRIEF (ORB)
Developed by OpenCV labs and is not patented like SIFT and SURF
Enhances FAST keypoint detectors
Adds orientation
Enhances BRIEF descriptors
Integrates orientation information into BRIEF

Oriented FAST and Rotated BRIEF (ORB)
Uses FAST to find keypoints.
Applies Harris corner measure to pick keypoints.
• Finds top N points among the keypoints
• Uses a pyramid to produce multiscale features
Builds BRIEF descriptors by incorporating keypoint orientation.

Feature Matching: Matching Strategy
We have seen many techniques for feature detection and description.
How do we match them?
First, we need to pick a matching strategy.
Brute force
 Compare all features against each other
 Quadratic time

Feature Matching: Matching Strategy
Use a maximal distance threshold with a Euclidean distance metric.
Simplest procedure
Thresholds can be difficult to set
Need to optimize against false positives/negatives
Use nearest neighbor in feature space.
Nearest neighbor distance ratio

Feature Matching: Indexing Structure
Efficient strategies need an indexing structure.
Multidimensional hashing
New features are hashed into buckets
Buckets are matched between images
Return buckets like me (family address, check members of family)
Locally sensitive hashing
Indexes features to unions of independently computed hashing functions

Feature Matching: Indexing Structure
Parameter-sensitive hashing
• More sensitive to distribution points
Mulitdimensional search trees
• kd-trees
Divides features into alternating
axis-aligned hyperplanes
Slicing
• Series of 1D binary searches
Metric tree Example KD tree in three dimensions
Source: Wikipedia
Image source: https://upload.wikimedia.org/wikipedia/commons/b/b6/3dtree.png

Evaluation of Algorithms: Accuracy
Determining the accuracy of our feature-matching algorithm:
Need to evaluate its accuracy
• Percentage of correct prediction of all predictions
• 95 percent accuracy is a good job
Example
• With 54 percent Democrats and 46 percent Republicans
Predict party using votes
How many times did I get it right?

Evaluation of Algorithms: Accuracy
Predicting low probability events
Example:
• 1 percent have leukemia, 99 percent are healthy
• Predict leukemia using health records and tests
• Imagine stupidest possible answer (Healthy = Always)
99 percent accuracy
You will be correct 99 percent of the time, but you will NOT catch sick
people
USELESS!

Evaluation Using a Confusion Matrix
Bastoncini
Box
(Predicted)
Not -
Bastoncini
Box
(Predicted)
Row-Wise
Accuracy
(Correctness)
Bastoncini
Box
(Actual)
27 6 81.81
Not -
Bastoncini
Box
(Actual)
10 57 85.07
Overall
Accuracy
83.44

Confusion Matrix
Positive Negative
Positive True positive
(TP)
False negative
(FN)
Negative False positive
(FP)
True negative
(TN)
Predicted
(our claim, diagnosis, our result)
Actual
(real-world,actual
sickness,relevance)

Sensitivity and Specificity
P N
P TP FN TP/
(TP+FN)
N FP TN TN/
(TN+FP)
Sensitivity
Specificity
Predicted
Actual

Precision and Recall
𝐹1 = 2 ∗
𝑃𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛 ∗ 𝑅𝑒𝑐𝑎𝑙𝑙
𝑃𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛 + 𝑅𝑒𝑐𝑎𝑙𝑙P N
P TP FN TP/
(TP+FN)
N FP TN
TP/
(TP+FP)
Predicted
Actual
Precision
Recall

Evaluation Using a Confusion Matrix
Bastoncini
Box
(Predicted)
Not -
Bastoncini
Box
(Predicted)
Accuracy
Bastoncini
Box
(Actual)
27 6 81.81
Not -
Bastoncini
Box
(Actual)
10 57 85.07
Overall
Accuracy
83.44
Precision = 27/37 = 73.0%
Recall= 27/33 = 81.8%

How to Tune Precision and Recall
Google.
Forget Recall. There are millions of relevant search results. Catching all of them is not
important: Most people only look at the first page of results.
Precision is way more important. If one of those ten links in the first page is not
relevant to the search, you’ll lose customers.

HIV Tests.
Recall is very, very important. We want to catch all sick people. Imagine an HIV+
person taking the test and being told they are HIV-. Worst outcome. Nope.
Precision is also important. Telling someone that they are HIV+ when they are not is
a devastating mistake. Not as bad as letting HIV+ slip through, but we still cannot turn
the knob all the way to recall without a care about this, either.

United States Legal System.
Higher Precision at the cost of Recall. Burden of proof. Reasonable doubt =
Acquittal. These mean that the threshold for classifying someone with the criminal label
is set very high.
High precision means making sure everyone sent to jail is indeed guilty.
High recall means making sure all criminals go to jail. The legal system is ready to pay
the cost of letting some criminals go to ensure no innocents go to jail.

Receiver Operating Characteristic

Tune Precision and Recall: Thresholds
Lower threshold: Ease criteria for calling it positive.
Can catch more positives by accepting edge cases.
higher recall, lower precision; higher true positive rate,
higher false positive rate.
Higher threshold: Only call it positive if absolutely sure.
To make most positive calls right, give up on
lower recall, higher precision; lower true positive rate, lower
false positive rate.

Area Under Curve
An evaluation of a classification algorithm
• including all possible thresholds

06 image features

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