02 image processing

2
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Processing Type
Applications of Image Processing
Example Applications
Enhancement
Example: Changing
saturation, contrast
to enhance look
• Marketing
• Photography
Understanding
Example: Object
detection, image
classification to
understand image
content
• Self-driving cars
• Security
Perturbation
Example: Blurring,
rotating images to
produce desired effect
• Censoring
• Animations

Image Processing Tools
Jupyter
Notebook*†
Matlab*
C++
IDEs
(Integrated Development
Environments)
Languages
Python*†
Libraries
NumPy† OpenCV†
Focus of this lesson
† = Taught in this course

If you do arithmetic with NumPy, overflow can occur:
Here, uint8 stores a max of 256: 300 is rounded down to 300 - 256 = 44.
To avoid this, we have to promote to a bigger type than our expected result, do arithmetic, then convert
back to smaller type:
Here, we promote uint8 to uint16, do arithmetic, convert back into uint8.
Computer Arithmetic with NumPy

Or
• Can use openCV arithmetic, which handles overflow (numbers being added to
quantities greater than 255), and clipping (automatically reducing numbers greater
than 255 down to 255) for us.
• With OpenCV, adding 100+200 with a max of 255 gets rounded down to 255, as
expected.
Computer Arithmetic with OpenCV

Resizing an image requires reassigning pixels from the original image to the new
image space.
Matplotlib* and OpenCV have the same interpolation methods.
The difference: Matplotlib applies interpolation at display time. OpenCV applies
interpolation prior to displaying the images.
Interpolation is used to address forward projection problems. These problems are
defined as:
1. Stretching the size of an image creates locations in the new image where pixels do
not have values.
2. Shrinking the size of an image creates float pixel values that need to be assigned to
an integer pixel value in the new image.
Interpolation

Nearest Neighbor (cv2.INTER.NN)

spline16 quadric laczos hermite kaiser
mitchell sinc hamming bessel hanning
guassian spline36 catron area
You can play with these, but we will not get into them.
Other Interpolation in OpenCV

Imshow arguments
o (m,n):
Rows, columns: NOT x,y coordinates
Can (m,n,3) and (m,n,4)
Values uint8 or float in [0,1]
(m,n,3) = RGB
(m,n,4) = RGBA
A  alpha
o “cmap”
Color map: can be RGB, grayscale, and so on
See upcoming slide for examples
o “vmin”, “vmax”
Used to change brightness
Display with matplotlib*: imshow

Display of 2D Arrays with matplotlib*: matshow

vmin (minimum brightness) defaults to min data
vmax (maximum brightness) defaults to max of data
Scalar, optional, default: None
Used to normalize
Tip: To prevent scaling (0,255) for a restricted range (say 100,200), pass in vmin=0,
vmax=255.
Display with matplotlib*: vmin and vmax

Interpolation = 'none' and interpolation = 'nearest'
• Are equivalent when converting a figure to an image file (that is, PNG)
Interpolation = 'none' and interpolation = 'nearest'
• Behave quite differently when converting a figure to a vector graphics file (that is,
PDF)
In our examples, interpolation = 'none' works well when a big image is scaled down.
While interpolation = 'nearest' works well when a small image is scaled up.
Display with matplotlib*: Interpolation

Display with matplotlib*: cmap

Color Spaces: Introduction
All images are represented by pixels with values in color spaces. Must represent an image
in a color space before applying any processing techniques.
Examples of color spaces:
Grayscale (black and white)
Color
RGB (red, green, blue)
HSV (hue, saturation, value)
CMYK (cyan, magenta, yellow, black)

Color Spaces: Grayscale
Grayscale to RGB conversion assumes all components of images are equal.
RGB to grayscale conversion uses
Y = (0.299)R + (0.587)G + (0.114)B

Color Spaces: RGB (Red, Green, Blue)
RGB (red, green, blue)
8-bit images 0-255
16-bit images 0-65,536
Floating point 0.0-1.0

Color Spaces: HSV (Hue, Saturation, Value)
Hue is normally 0-360
• Hue is walking around a color wheel
• OpenCV uses 0-179 to fit in 8 bit
Saturation (s) and value (v) are ranges
of light to dark (intensity)
• Trade off black/white
• OpenCV uses 0-255 for both s and v
In cone models
• s is white; distance from cone axis
• v is black; distance from cone point

Color Conversion in OpenCV
RGB is 8- or 16-bit colors.
Each pixel is represented by three values (one for each channel).
These values are pixel intensities
000 = black
111 = white

Color Conversion in OpenCV
When converted to grayscale, all RGB are equal.
When converted from RGB (or BGR) to grayscale:
𝑌 = 0.299 𝑅 + 0.587 𝐺 + 0.114 𝐵

Histograms are a way of showing the intensity of color across an image.
Abnormal histograms can be used to detect poor image exposure, saturation,
and contrast.
Example:
The image on the left has poor exposure, which can be detected via the
histogram.
Histograms: Introduction and Grayscale
Example

Histogram Equalization
Histogram equalization: Technique to adjust contrast to evenly spread
y-values from an original distribution to a new distribution.
Usually increases global contrast of an image.

Histogram Equalization: Probability Integral
Transform
Recall our original distribution:
• Bimodal peaks
• Want to flatten this effect to get a uniform
distribution
Probability integral transform allows us to convert
an arbitrary distribution to a uniform distribution

Transform
Covert an event from an arbitrary to a uniform distribution.
OriginalConverted

TransformOur original is a distribution of pixel intensities.
We will use percentiles from both the arbitrary distribution and the uniform distribution
to do this conversion.
We need to know, for our input intensity x, what percentile it falls in to.
We compute the cumulative (running total) of the probabilities of the values less than x.
Once we know that, we have an output value between [0,1] or U(0,1)
We can map U(0,1) to U(0,255) to get uniformly scaled pixel intensities.
Simple linear scaling for (0,1) to (0, 255)

Foreground/Background
Only part of the image has important data; we call these regions of interest (ROI).
In this case, we are interested in the foreground, but NOT the background of the logo
image.
foreground
background
foreground

In the case when the background has distinctively different color than the foreground,
we can use thresholding to separate them.
Example application:
Thresholding Application
Image source: https://upload.wikimedia.org/wikipedia/commons/2/23/Gfp-texas-big-bend-national-park-plants-on-the-desert-horizon.jpg

Thresholding: Foreground Versus Background
We need to build and interpret an image as foreground and background.
We need to make a final decision about points.
We will create a mask to denote regions of interest (foreground versus background).

Thresholding: Simple Methods
cv2.threshold( ) methods:
These methods are global / independent of neighbors.

Thresholding: Neighborhood Methods
cvAdaptiveThreshold( ) is used when there is uneven illumination.
To calculate threshold for neighborhood:
Calculate neighborhood means, using equal weights or weighted-averages based on
Gaussian windows/filters.
Subtract neighborhood mean from each point in the neighborhood.

Code to plot neighborhood thresholding:

Neighborhood methods illustration:

Thresholding: Otsu’s Method
In Otsu's method, we don't know the classes:
• We try every break point (for example, say 127, or an empirical mean or median)
and assume it is the separator.
• The data is in two classes and we can compute the ratio of the within class variance
and the between class variance.
• Only one break point maximizes the ratio of within class variance to between class
variance.
This is our desired threshold.
Generally, Otsu works well with a large region of interest (compared to background) and
a strong bimodal distribution.

Thresholding: Otsu’s Method
Optimal threshold unclear
(OpenCV finds 116)
Optimal threshold = 126

Geometric Transforms: Resizing
x,y  fx(x,y), fy(x,y)
Decreasing resolution (throwing out data) requires
decimation
Increasing resolution (creating data from nothing)
requires interpolation

Matrix Glossary
T Translation
R Rotation
A Affine (arbitrary)
S Scaling
H Homography (prospective, projective)

Translation
What you would see in trig class: OpenCV affine matrix:

Translation
The OpenCV affine matrix is applied to an augmented p
• p with a constant 1 tacked on to it.

Rigid (Rotation and Translation)
Again, in OpenCV, this is applied to an augmented point:

Rigid (Rotation and Translation)

Scale (Similarity Transform)
What you would see in trig class: OpenCV affine matrix:

Scale
When combining scaling with other transformation:
When xscale= yscale = 1
We get a rigid transformation
– Also called isometry or a Euclidean transformation
– Preserves scale (distance)
When xscale= yscale
We have a similarity transformation
– Also called a scaled-rotation

Perspective (Projective or Homography)
In a perspective transform, we have an arbitrary 3x3 matrix, P, applied to an augmented
point:
The first two columns represent the scale-rotation component.
The last column represents the shift component.

Perspective (Projective or Homography)

Geometric Transforms
Translation
Rigid
Similarity
Affine
Perspective
2
3
4
6
8
Orientation
Lengths
Angles
Parallelism
Straight lines
Transform Type Degrees of Freedom Attribute
preserved

02 image processing

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