Edge Detection

(with implementation on a GPU) And

Text Recognition

(if time permits) Jared Barnes Chris Jackson

 ◦

Edge Detection

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

   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

   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/wp content/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 𝑥 2 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)

    Two thresholds are better than one!

If a pixel’s value is above T high , it’s an edge.

If a pixel’s value is below T low , it’s not an edge.

If a pixel’s value is between T high and T low , it might be an edge (provided it is connected to an actual edge) T high = 45 T low = 35

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 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

 Convolve two Sobel Kernels with the image  Wait, convolution again?

 Same as previous step – we can even reuse the convolution function!

    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.

3.

Compare this pixel’s magnitude with two neighbors in the direction of its angle If I’m greater than those neighbors, leave me alone; otherwise, mark me as “not an edge” Less speedup than steps 1 and 2

      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

 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

  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

   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 0 0 5 0 40 0 A 0 15 15 0 15 15

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

   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