CSE 160 – Lecture 10

1. CSE 160 – Lecture 10 Programs 1 and 2

2. 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

3. 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

4. Program 2 • Implement the Sobel (Section 11.5 in W+A) 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

5. 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.

6. 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| • Let’s consider the following 3 x 3 matrix of values

7. 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

8. 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

9. Cross Correlation • Mask Pixels  Cross correlation is ij xiwj Want to calculate the cross-correlation at each point in an image using two masks.

10. 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.

11. Master/Worker Model • Master reads input/writes final output • Give an input file, divide the image into K horizontal strips K Strips

12. 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.

13. 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.

14. What to do at the edge of regions to transform? j-1 • Strip j needs 1 row of pixels from strip j+1 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 j+1

15. Master Pseudo-code Read command line arguments Spawn P worker tasks Read complete image into an array, pad edges with zeros (N+2)x(M+2) Nrows=ceil((N+2)/K) // rows per block Pkidx=0; //row index to pack stripsLeft = K; for (i = 0; i < 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; }

16. 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--; }

17. Master Continued While (stripsxformed < 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;

18. 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; }