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.

 John Canny  “A Computational Approach to Edge Detection” 

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 ages/articles/article-9/2d_distribution.gif s/spring08-22C251/homework/canny.pdf

Too much About right /tumblr_inline_mhcv1l0EZB1qz4rgp.png content/uploads/2013/03/gaussian-blur-thumbnail.jpg SpottySmooth

GxGx GyGy Sobel Operator (2 kernels) Then round to: 0° =←→ 90°=↑↓ 45°=↗↙ 135°=↘↖

X Gradient (Horizontal Edges) Y Gradient (Vertical Edges)

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

Thick Edges (Gradient Magnitude) Thin Edges (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 = 45T low =

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 ImageKernel Element-wise Multiplication 230 Sum All Values 11 Divide by Kernel Sum 11

 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.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

 Mark pixels > T high as strong edges  Mark pixels < T low 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.

 Label Connected Components  Look For Letters  Adjust for disconnected letters HELLO WORLD HELLOWORLDHELLOWORLD E F ? ü j i

 Create a list of components in the image  A component is simply a set of connected edges 1. Label each edge pixel with a unique component ID 2. Examine each pixel’s 8 touching neighbors and set that pixel’s ID to the smallest neighbor ID 3. 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. A

 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 T E R V EL EO R………C T 0/1