Image Processing Intro2CS – week 6 1

Image Processing Many devices now have cameras on them Lots of image data recorded for computers to process. But how are images processed? How are they encoded? This week we explore some basic operations on images. Some tasks are incredibly complex (face recognition, navigation by video, etc.) 2

Grayscale images Images are divided into pixels Grayscale images have a brightness level associated with each pixel. (in this case from 1…256) 3

Color Images One way to represent color images is using 3 values for the brightness level of Red, Green, Blue colors. 4

Why RGB? The human eye has receptors of 3 different kinds. They each react to different colors. The colors R,G,B can be used to stimulate these receptors almost independently, allowing mixtures to “simulate“ other colors 5

Image Processing in Python We will be using the Pillow library in python. It can read images from files, show them (and do some processing – but we will do that ourselves). Find it here: I am using WinPython (for windows) that comes pre-packaged with Pillow (and many other useful packages) As usual, code show in this lecture, is available on the website. 6

Loading Images 7

Showing Images 8

Example Lena Söderberg, Playboy Centerfold, Nov Image became “standard” test photo for algorithms in image processing. 9

Example 10 data is a list of lists a 2-dimensional list data[row][column] is a tuple with 3 values: (R,G,B)

The Negative of an Image Subtract pixel RGB values from 255: 11

Inverting Rows 12

Inverting Columns What is the difference? 13

Changing Brightness 14 Factor: 2 Factor: 0.5

Bluring the Image We can blur the image by setting each pixel’s value to be the average of its neighbors 15

Bluring 16

Bluring 17 Original env: 3env: 6

Sharpen A trick to make images appear sharp: (In grayscale) Add to each pixel: its value minus average value of its 4 neighbors What happens to a pixel that is Brighter than its neighbors? Darker than its neighbors? The same brightness? 18 -1/4 1

Sharpen 19

Sharpen 20 Original Once Twice

General filters Both blur and sharpen can be seen as replacing each pixel with a linear sum of pixels in its area. Each with different weights: It is possible to generalize their action to a single function (Convolution) with a given filter (2D matrix of weights) 21 -1/4 2 1/9 Sharpen Blur

Laplacian During sharpen we looked at the difference between a pixel and its surroundings If we take the values (that can be negative as well), shift and scale. Notice that extreme values are near “edges” 22 -1/4 1

Histograms We can look at statistics of pixel values in an image. The histogram: for luminosity values , how many pixels have each value? Usually we’ll normalize: what is the percentage of pixels at each value ? 23

Examples 24

Computing the Histogram 25

Plotting the Bar Charts 26

Cumulative distribution For each of the brightness levels 0…255, what percentage of pixels have brightness that is darker or exactly the same? 27

Examples 28

“Balanced” Histograms An image that is properly exposed usually has pixels going all the way from dark to very bright. The “ideal”: an equal amount of pixels for each brightness level Can we shift the brightness levels so that this will happen? 29

Histogram Equalization Create “ideal” histogram Make full use of brightness levels (usually gives nice contrast in images) The idea: A pixel that has p pixels darker than it, is mapped to brightness level 255*p. (pixels of same brightness level are mapped to the same brightness) 30

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32 Original Equalized New Histogram Cumulative

33 OriginalEqualized New Histogram Cumulative

Extras 34

Clustering It is very useful to be able to “cluster” data: Take data given as vectors, and group parts of it together automatically, implying “similarity”. 35

Clustering An idea: define cluster through representative points. Items belong to cluster if that cluster’s representative is closest. 36

Clustering What is a good partition to clusters? – Find cluster centers such that sum of distances of points to their cluster is minimized. How do we solve this problem? 37

The k-means algorithm Start with k arbitrary cluster representatives. Repeat: – Assign points to clusters (using cluster reps) – Move cluster representative to center of mass of their cluster (average of all coordinates) Guaranteed to converge! 38

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Applying to images We’ll apply k-means to images. Find clusters of pixel colors Use them to segment the image into pixels that contain “similar things” (as we can judge by color). 40

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45 Original 2 Clusters 4 Clusters

46 2 Clusters3 Clusters 6 Clusters

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