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18.337: Image Median Filter

Rafael PalaciosAeronautics and Astronautics department. Visiting professor

(IIT-Institute for Research in Technology, University Pontificia Comillas, Madrid, Spain)

MEDIAN FILTER

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Median Filter

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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

MATRIX PREPARATION

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Size adjustment

1024x1600x35 MB

2048x3200x320 MB

Original image

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Noise added

cn=imnoise(c,'salt & pepper');

EXPERIMENTAL RESULTS

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Sensitivity to Image size

~O(n)

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Sensitivity to Neighborhood size

Unexpected !

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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:

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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

SINGLE-CORE RESULTS

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Matlab Single-Core

PARALLEL COMPUTING TOOLBOX

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Matlab Multi-Core

• Parallel computing toolbox using ‘spmd’• Image size=80MB, neighborhood=65

Worker time matches prediction

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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

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Matlab Multi-Core

• 8 core computer, slower memory• 2x Xeon Quad 2.26GHz, 8GB 667MHz

More overhead

pMATLAB

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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

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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

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Results

• Computing time does not decrease significantly using double.• It scales well using uint8 less data to be moved

double uint8

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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

CONCLUSION

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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

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pMatlab (3D uint8) 320MB

•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.

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

This slide shows the effect of data transfer

BACKUP SLIDES

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Parallel computing toolbox: memory issues

%Activate parallel computing%matlabpool(4)

tic%Create treadsspmd c = myfilterP(a,labindex,numlabs);endtoc

%gather results from treads (inefficient memory allocation)result=[];for ii=1:length( c ) result=[result,c{ii}];endtoc

%Close parallel computing%matlabpool close

…

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); endend

Same result

All 4 matrices are

sent to all threads

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pMatlab: sending initial data to clients

PARALLEL = 1; if (PARALLEL) %Create map for XL. The leader process owns all data

mapL=map([1 1],{},0); %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 YXL=zeros(n,m,mapL); %owned by Pid 0X=zeros(n,m,mapM); %distributed inputY=zeros(n,m,mapM); %distributed output

if Pid==0 %only the main process makes the initialization

load input_matrix XL(:,:)=a; %all data stored in Pid 0end

…

X(:,:)=XL; %only leader process has a non-empty X, % 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.

%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

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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.

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pMatlab (3D uint8)

•Times are smaller•Speedup is better because communication delays don’t penalize as much

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