CSE 160

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CSE 160 Lecture 10

• Programs 1 and 2

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Program 1

• Write a launcher program to specify exactly
  where programs are to be spawned, gather output,
  clean up on error
• Write a ring gather program
• Write a tree gather program

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Code Outline for Program 1

• Code outlines were given in lecture 5
• We will go over an example implementation for all
  three parts
• Looking carefully at each PVM function
• Using XPVM to control a virtual machine
• Space-time diagrams
• Trace masks
• Replaying traces
• This will interactive

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Program 2

• Implement the Sobel (Section 11.5 in WA) edge
  detection algorithm
• Input/output files in PGM format
• Master/worker configuration
• Bag of tasks load balancing
• Data decomposed by strips
• Assignment available on the web on Friday

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Edge Detection

• Basic problem Try to find edges (areas of local
  sharp contrast) in a greyscale image
• Think back to basic 1D calculus
• When df/dx is high, function is changing
  rapidly
• For 2D problems this is generalized to gradients.
  ?f(x,y) (?f/?x,?f/?y)
• The goal is to find areas in a picture where the
  ?f(x,y) is high.

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Approximating the Magnitude of the Gradient

• ?f(x,y) ?(? f/?x)2 (?f/?y)2
• For computational simplicity, this is
  approximated as ?f/?x ?f/?y
• Lets consider the following 3 x 3 matrix of
  values

x0 x1 x2
x3 x4 x5
x6 x7 x8
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Calculating the Gradient at X4

• X4 is the pixel of interest. Could try an
  approximation as
• ? f/?x x5 x3 (difference left and right)
• ? f/?y x7 x1 (difference top and bottom)
• One gets much better approximation of all
  surrounding pixels are used to approximate the
  gradient

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The Sobel Operator

• Look at calculating ? f/?y
• ? f/?y x6 x0 2(x7 x1) x9 x3
• This is only a weighted average of the gradient
  by using neighboring pixels.
• Extra weight is given to the pixels directly
  above and below the center pixel of interest
• ? f/?x x2 x0 2(x5 x3) x8 x6

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Cross Correlation

• Mask Pixels

x0 x1 x2
x3 x4 x5
x6 x7 x8
w0 w1 w2
w3 w4 w5
w6 w7 w8
?
Cross correlation is ?i?j xiwj Want to
calculate the cross-correlation at each point in
an image using two masks.
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Final Calculation

• Calculate a new x4 with the following Sobel
  formula
• x4 (1/9) (x6 x0 2(x7 x1) x9 x3
• x2 x0 2(x5 x3) x8 x6))
• Need to do this at every point in the picture.

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Master/Worker Model

• Master reads input/writes final output
• Give an input file, divide the image into K
  horizontal strips

K Strips
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Master Spawns P Workers

• Master will start P (? K) workers
• The first P strips are sent to the P slaves.
• Slaves compute the Sobel transform on their
  strip. Return transformed image to the master
• As the master gets data returned, it doles out
  more strips until the entire image is converted.

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Bag of tasks Load Balancing

• For this problem, a task is the Sobel transform
  of an image strip.
• Workers may compute at different speeds
• Faster workers get more work to do (Sounds like
  life ?)
• Slower workers get less work to do
• For few workers and may tasks, most workers are
  busy all of the time.

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What to do at the edge of regions to transform?

• Strip j needs 1 row of pixels from strip j1
  and strip j-1
• Have master send these 1 pixel rows as part of
  the jth strip.
• at edges, consider the image to have pixel value
  0 outside the pixel area.

j-1
j
j1
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Master Pseudo-code

• Read command line arguments
• Spawn P worker tasks
• Read complete image into an array, pad edges with
  zeros (N2)x(M2)
• Nrowsceil((N2)/K) // rows per block
• Pkidx0 //row index to pack
• stripsLeft K
• for (i 0 i lt P i)
• label strip i
• pack label of strip i
• pack the dimensions of strip i
• pack the data of strip i
• send ith strip to ith worker

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Master Pseudo Code continued

• stripsleft K P
• Stripsxformed 0
• While (stripsleft)
• receive transformed strip from any worker
• stripsxformed
• determine which strip has been sent Save data
• pack strip S K stripsleft
• send strip S to this worker
• stripsleft--

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Master Continued

• While (stripsxformed lt K)
• receive transformed strip from any worker
• stripsxformed
• determine strip that was sent save data
• stripsxformed
• Broadcast a done message to every worker
• Write out transformed data

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Worker Pseudo code

• done 0
• While (!done)
• receive message from parent (pvm_parent())
• determine message tag (pvm_bufinfo())
• if (Tag donemessage) break
• unpack strip id
• unpack strip dimension
• unpack strip data
• transform data
• pack strip id, dimension
• pack transformed data
• send back to parent