Edge Detection
(with implementation on a GPU)
And
Text Recognition
(if time permits)
Jared Barnes
Chris Jackson

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◦ Wikipedia: Identifying points in a digital image at which the image has discontinuities.

http://4.bp.blogspot.com/-p_9w91wC_Rc/TbBgF7dQYhI/AAAAAAAAACM/DQTrM_a7Apg/s1600/edge-example-c.png

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John Canny
“A Computational Approach to Edge
Detection”
1986 http://ieeexplore.ieee.org.libproxy.mst.edu/stamp/stamp.jsp?tp=&arnumber=4767851

1.
Noise Removal
2.
Image Gradient Computation
3.
Non-Maximum Suppression
4.
Hysteresis Thresholding

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Gaussian Smoothing or Blurring
A pixel is changed based on a weighted average of itself and its neighbors
The number of neighbors (3x3, 5x5) and the relative weights can vary
3D Gaussian Distribution
Normalized 2D Gaussian
Approximation http://www.librow.com/content/common/im ages/articles/article-9/2d_distribution.gif
http://homepage.cs.uiowa.edu/~cwyman/classe s/spring08-22C251/homework/canny.pdf

Too much
Spotty
About right
Smooth http://media.tumblr.com/ccd6945141b46e5e2f5c36168f6a
8037/tumblr_inline_mhcv1l0EZB1qz4rgp.png
http://www.eversparkinteractive.com/wpcontent/uploads/2013/03/gaussian-blur-thumbnail.jpg


Calculus!

First derivative in the X and Y directions
(separately)
Sobel Operator (2 kernels)
G x
 Magnitude = 𝐷 2 𝑥 𝑥, 𝑦 + 𝐷 2 𝑦 𝑥, 𝑦
 Angle = arctan
𝐷 𝑦
(𝑥,𝑦)
𝐷 𝑥
(𝑥,𝑦)
Then round to:
0° =←→ 90°=↑↓
45°=↗↙ 135°=↘↖ http://homepage.cs.uiowa.edu/~cwyman/classes/spring08-22C251/homework/canny.pdf
G y

(Vertical Edges)
(Horizontal Edges) http://suraj.lums.edu.pk/~cs436a02/CannyImplementation.htm



Make edges exactly one pixel thick
Look at the gradient magnitude of your 2 neighbors in the direction of your angle
Example 1
Angle = 135°
↘↖
Keep it!
Example 2
Angle = 0°
←→
Kill it!

Thick Edges Thin Edges
(Gradient Magnitude) http://suraj.lums.edu.pk/~cs436a02/CannyImplementation.htm
(Gradient Magnitude)

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Two thresholds are better than one!
If a pixel’s value is above T edge.
high
, it’s an
If a pixel’s value is
, it’s not an below T edge.
low
If a pixel’s value is and T low
, between T it might be an edge
(provided it is connected to an actual edge)
T high
= 45 T low
= 35
0 50 50 50 50 50 0
0 50 0
0 50 0
0 36 0 255 0 40 0
39 0 0 50 0 0 39
0 38 0 255 0 43 0
0 50 0
0 40 40 50 40 40 0

1.
Smooth image to reduce noise
2.
Calculate X & Y derivatives to get edges
3.
Thin all edge widths to 1 pixel
4.
Remove weak, unconnected edges
(ta da!)


How do we parallelize the Canny Edge
Detector?


Convolution – Independent of order
5
Image
5 5
10 10 10
20 20 20
Element-wise
Multiplication
10 10 10
20 40 20
40 40 40
Kernel
2 2
4 2
2 2
Sum All Values
Divide by Kernel Sum
230


Convolve a Gaussian Kernel with the image

Each GPU core can convolve each pixel in the image individually with the Gaussian Kernel

One thread per pixel, each performing 9 multiplies, 9 adds, and 1 division

Embarrassingly Parallel with huge speedup

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Convolve two Sobel Kernels with the image

Wait, convolution again?

Same as previous step – we can even reuse the convolution function!

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Comparing 3 pixel gradient magnitudes and clearing the middle pixel or leaving it alone
Similar to convolution… but simpler!
Each GPU thread owns a pixel:
1.
Check gradient angle of pixel
2.
Compare this pixel’s magnitude with two neighbors in the direction of its angle
3.
If I’m greater than those neighbors, leave me alone; otherwise, mark me as “not an edge”
Less speedup than steps 1 and 2

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Mark pixels > T high
Mark pixels < T low as strong edges as not edges
Mark remaining pixels as weak edges if they connect to a strong edge
Typically implemented with recursion
Each thread with a weak-edge pixel looks at nearest 2 neighbors to find a strong-edge pixel
With identical algorithms on CPU and GPU, speedup is marginal (memory accesses, not much processing)

Wikipedia: The mechanical or electronic conversion of images of printed text into computer-readable text.
http://hackadaycom.files.wordpress.com/2010/09/helloworldconsole.png
http://www.flacom.com/content/uploads/2013/09/hello-world.jpg

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Label Connected
Components

Look For Letters

Adjust for disconnected letters
HELLO
WORLD
E
F
? ü j i
H E L L O
W O R L D

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
1.
2.
3.
Create a list of components in the image
A component is simply a set of connected edges
Label each edge pixel with a unique component ID
Examine each pixel’s 8 touching neighbors and set that pixel’s ID to the smallest neighbor ID
Repeat step 2 until no pixel IDs are changed

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Uhh… what’s a letter?
How do we know it’s a letter?
How does the computer know it’s a letter?


Letters are represented by a vector of numbers indicating the ratio of black pixels to white pixels in each division of the letter-image.
0
15
0
0
5
0 40 0 0
A
15 0 15 15

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Compute how closely each labelled component matches each letter in your alphabet
The component is then marked with whichever letter it most closely matches

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Letters like ‘i’ and ‘j’ have floating parts
Sometimes edge detection may accidentally break up a letter
A letter vector should then get an additional property indicating vertical discontinuity
L E T T E R V E C T O R … … … 0/1