Report

18.337: Image Median Filter Rafael Palacios Aeronautics and Astronautics department. Visiting professor (IIT-Institute for Research in Technology, University Pontificia Comillas, Madrid, Spain) 1 MEDIAN FILTER 2 Median Filter 3 Median filter algorithm • Median filter is a nonlinear operation for noise reduction (dust or spikes). • Eliminates noise while preserving edges. • Assigns to each point the median value of the neighborhood n*ns log(ns) • Matlab function: – C=medfilt2(cn); % 3x3 neighborhood – C=medfilt2(cn,[r c]); % rxc neighborhood 4 MATRIX PREPARATION 5 Size adjustment Original image 1024x1600x3 5 MB 2048x3200x3 20 MB 6 Noise added cn=imnoise(c,'salt & pepper'); 7 EXPERIMENTAL RESULTS 8 Sensitivity to Image size ~O(n) 9 Sensitivity to Neighborhood size Unexpected ! 10 Basic experiments • Original matrix size: 2048x3200x3=20M • Matrix sizes: n=[20M, 80M, 320M, 1280M] x4 steps • Neighborhood sizes: nn=[3 5 9 17 33 65]; 2^n + 1 neighborhood • Partitioning strategies: 11 Computer systems • Dell (Xeon 2.67 GHz 8M L3, 12 GB DDR3 1066MHz) – Matlab single core – Matlab parallel toolbox – Matlab with pMatlab • Cluster (beagle, beowulf) – MPI 12 SINGLE-CORE RESULTS 13 Matlab Single-Core 14 PARALLEL COMPUTING TOOLBOX 15 Matlab Multi-Core • Parallel computing toolbox using ‘spmd’ • Image size=80MB, neighborhood=65 Worker time matches prediction 16 Matlab Multi-Core • with spmd there is an overhead of 1.5s for the 80MB matrix (transfer rate 200 MB/s) • There are no memory conflict because each lab works on its own copy of the image • Parallelization by rows or columns are equivalent 17 Matlab Multi-Core • 8 core computer, slower memory • 2x Xeon Quad 2.26GHz, 8GB 667MHz More overhead 18 pMATLAB 19 pMatlab • Allows to run Matlab in parallel by launching several Matlab processes that communicate using MPI • Communications are transparent to the user, since pMatlab uses a distributed matrix approach How it works • Several Matlab processes are started • The leader process loads the image into a shared matrix • Each subprocess receives its corresponding section of the image in X • Each subprocess applies median filter and stores results in Y • The leader process aggregates results 21 Results • Computing time does not decrease significantly using double. • It scales well using uint8 less data to be moved double uint8 22 Testing remarks • Initially the pMatlab algorithm was implemented using 2D double matrices – Filtering was performed in three steps (R, G, B) – The conversion to double, involved multiplying by 8 the size of the matrices (affecting communications) • The final implementation involved 3D uint8 matrices 23 CONCLUSION 24 Conclusion • Performance may depend on the algorithm more that on parallelization. (5x5 neighborhood) • Matlab’s Parallel Computing Toolbox does not use shared memory. • Parallel toolbox uses a lot of memory and communication, because the whole matrix is propagated to all clients. – Algorithm implemented with spmd – It is possible to use distribute matrices to improve – It is possible to use sliced variables if parfor loops. • pMatlab uses memory efficiently. • MPI version was not developed. Conclusion • Speedup comparison Conclusion pMatlab using double pMatlab using uint8 pMatlab (3D uint8) 320MB This slide shows the effect of data transfer 320MB image matrix pMatlab Toolbox total time speedup total time speedup 1 core 138.8 1.0 132 1.0 2 core 71.6 1.9 72.1 1.8 4 core 40.5 3.4 46.1 2.9 •For larger sizes, the impact of latencies is reduced. (computing time and transmission time are linear with size) •Speedup is almost perfect in pMatlab, but worst in Toolbox. •The amount of memory needed to be sent increases asymptotically to 320MB in the case of pMatlab, however it increases linearly with the number of processors in the case of Parallel Computing Toolbox. 28 BACKUP SLIDES 29 Parallel computing toolbox: memory issues %Activate parallel computing %matlabpool(4) … tic %Create treads spmd c = myfilterP(a,labindex,numlabs); end toc %gather results from treads (inefficient memory allocation) result=[]; for ii=1:length( c ) result=[result,c{ii}]; end toc spmd(4) if labindex==1 c = myfilterP(a1); end if labindex==2 c = myfilterP(a2); end if labindex==3 c = myfilterP(a3); end if labindex==4 c = myfilterP(a4); end end %Close parallel computing %matlabpool close Same result 30 pMatlab: sending initial data to clients PARALLEL = 1; if (PARALLEL) … %Create map for XL. The leader process owns all data X(:,:)=XL; %only leader process has a non-empty X, mapL=map([1 1],{},0); % so only leader process writes something to X. %Writing to X involves sending data to subproceses, since % different chunks of X belong to different Pids. %Create map for distributed matrices X and Y. Each processor gets a set of columns mapM=map([1 Np],{},0:Np-1); else mapL=1; mapM=1; end %Create matrices XL, X and Y XL=zeros(n,m,mapL); %owned by Pid 0 X=zeros(n,m,mapM); %distributed input Y=zeros(n,m,mapM); %distributed output %Get local part in a standard double matrix. It is faster to work with local matrices. Xloc=local(X); %code %code Y=put_local(Y,res); %After obtaining the resulting matrix res, store it in distributed matrix Y if Pid==0 %only the main process makes the initialization load input_matrix XL(:,:)=a; %all data stored in Pid 0 end 31 pMatlab (double) computing % comm % total time speedup 1 core 34.7 93.8% 2.3 6.2% 37 1.0 2 core 18.2 75.8% 5.8 24.2% 24 1.5 4 core 8.4 52.5% 7.6 47.5% 16 2.3 •More data transfer occur with 4 cores (75% of the matrix) than 2 cores (50% of the matrix is copied back and forth). Results are consistent. •Conversions from uint8 to double is penalizing pMatlab tests. The 80MB image matrix is in fact 630MB in double format. 32 pMatlab (3D uint8) computing % comm % total time speedup 1 core 32.6 98.8% 0.4 1.2% 33 1.0 2 core 17 90.9% 1.7 9.1% 18.7 1.8 4 core 9 81.8% 2 18.2% 11 3.0 •Times are smaller •Speedup is better because communication delays don’t penalize as much 33