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Motion Detection using PCA

Motion Detection using PCA. Roland Miezianko rmiezian@temple.edu Video Analysis Project Spring 2004 Advisor: Prof. Dr. Longin Jan Latecki. Agenda. Motion Detection Input Video Algorithm Steps (2-D and 3-D blocks) Results Sample Videos and Results Video with 8x8 Detection Blocks

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Motion Detection using PCA

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  1. Motion Detectionusing PCA Roland Miezianko rmiezian@temple.edu Video Analysis Project Spring 2004 Advisor: Prof. Dr. Longin Jan Latecki

  2. Agenda • Motion Detection • Input Video • Algorithm Steps (2-D and 3-D blocks) • Results • Sample Videos and Results • Video with 8x8 Detection Blocks • Video with 32x32 Detection Blocks • Matlab Code • Source Code

  3. Input Video • MPEG video converted to 2688 JPEG image frames • Full RGB color

  4. Algorithm Steps • Reshape image to 8x8 blocks • Collect blocks from every frame, normalize and reshape array from 3-D 8x8 blocks • Compute PCA projection matrix per block • Compute PCA score by projecting blocks from each frame onto that block’s 3-PCA projection • Compute EV values with W=3 for each block • Generate global threshold based on all blocks and frames • Generate local dynamic threshold for each block/frame with W=3 • Generate motion matrix based on local and global dynamic threshold for all blocks-frames

  5. Step 1 - Details • Read the color image • Resize the image by scale factor of 0.5 • Convert the image to gray scale • Reshape the image into 8x8 distinct blocks • Transpose and save the data • Note: save per frame block data

  6. Step 1 - Reshape Image

  7. Step 1 - Code fileName = ...; imN = imread(fileName); imN = imresize(imN,0.5); imN = rgb2gray(imN); imCols = im2col(imN,[bH bW],'distinct'); imT = imCols';

  8. Step 1 - 8x8 Block Size Block size relative to image size Block 26x25 Image Size: 36x48 blocks

  9. Step 2 - Collect Blocks • Collect same block from all the frames • Create a single matrix for each block location • Reshape vector from 3-D 8x8 blocks • There are 1728 matrices holding pixel values • Each matrix is 2688 x 64 (frames x pixels/block)

  10. Step 2-Normalize Blocks • Normalize each block by its mean value • Each block has its mean subtracted from each of the 64 pixel values • Store the normalized block data to be used in Step 3 and Step 4

  11. Step 2 - Code fileName = ...;load(fileName, '-mat'); % matrix is BlockX % BlockN will be the normalized version of BlockX BlockN = BlockX; BlockXMean = (mean(BlockX'))'; for FrameIndex = FrameStart : FrameEnd BlockN(FrameIndex,:) = BlockX(FrameIndex,:) - BlockXMean(FrameIndex,1); End % store normalized block matrix as BlockN

  12. Step 2 - Block Matrix Each block X of 1728 total blocks has a matrix representation of size 2688x64 Each block is normalized by its mean value N = 2688

  13. Step 2 – 3-D 8x8 Blocks • Take 3 rows of Block matrix from previous slide 3x64 • Reshape into 1x192 vector • 3-D blocks are overlapping • New 3-D Block Matrix is used in computing PCA scores and projection matrices

  14. Step 3 - Compute PCA • Load normalized block matrix from Step 2 and compute the PCA projection matrix for this block sequence • Code: fileName = ...; load(fileName, '-mat'); % matrix is BlockN [pc,latent,explained] = pcacov(cov(BlockN));

  15. Step 3 - PCA Projection • The principal components projection matrix contains 64 rows representing each pixel location in the block and 64 columns representing 64 principal components • Only the first three components are used in projection (first 3 columns)

  16. Step 4 - Compute Score • Load normalized block matrix from Step 2 and project it onto the PCA projection matrix computed in Step 3 • Only the first 3 PCA projections are used

  17. Step 4 - Code fileName = ...; load(fileName, '-mat'); % matrix is BlockN fileName = ...; load(fileName, '-mat'); % matrix is pc Score = double(BlockN) * pc(:,1:3);

  18. Step 5 - Compute EV • For each block sequence, load the PCA score matrix computed in Step 4 • Compute a covariance matrix using a moving window of size 3 • Compute eigenvalues (EVs) • Sort to get the larges EV value • Store the data in one EV matrix, representing all blocks and all frames

  19. Step 5 - EV Matrix • EV matrix will contain a single EV value for a block-frame spatiotemporal location

  20. Step 5 - Code fileName = ...;load(fileName, '-mat'); % matrix is Score dd = Score;evx = zeros(FrameEnd,3);W = 3; for i=W+1:length(dd)-W; cc = dd(i-W:i+W,:); cm = cov(cc); evx(i,:)=sort(eig(cm)');end

  21. Step 6- Global Threshold • Load EV matrix from Step 5 • Compute mean and standard deviation • Find all entries in the EV matrix that are below mean+2*std • Update the EV matrix

  22. Step 6 - Code fileName ...;load(fileName, '-mat'); % matrix is ev gmean = mean(mean(ev'));gstd = std(mean(ev')); LessThanThr = find(ev < (gmean+2*gstd));ev(LessThanThr) = 20;

  23. Step 7 - Local Threshold • Use the updated EV matrix from Step 6 • Compute a local dynamic threshold using window • Generate a Motion matrix of same size as the EV matrix with a simple 0/1 values (1=motion)

  24. Step 7 - Assumptions • Assume that first 100 frames have no detectable motion • Compute mean and std of first 100 frames for each block • Compute local threshold for each block using a moving window (W=3) • Adjust local threshold, when no moving object is detected

  25. Step 7 - Code 1 for BlockIndex = 1 : NumBlocks W=3; current sample FrameStart = 100; % first frames = no motion meanl=mean(ev(BlockIndex,1:FrameStart)); stdl=std(ev(BlockIndex,1:FrameStart)); movingobject=0; for i = FrameStart+W : FrameEnd-W; ... (next slide) end % i end % BlockIndex

  26. Step 7 - Code 2 (…) lw=ev(BlockIndex,i-W:i); %left windowrw=ev(BlockIndex,i+1:i+W); %right window if mean(rw)-meanl>50*stdl mobin(i)=mean(rw)-meanl; %moving obj detected movingobject=1; Motion(BlockIndex,i) = 1;else if movingobject==0 meanl=0.9*meanl+0.1*mean(lw); stdl=0.9*stdl+0.1*std(lw); end end

  27. Step 8 - Motion Matrix • Motion matrix is of size 1728x2688, same size as the EV matrix • It contains values 0 or 1, where 1 = motion detected • Use the Motion matrix to create sample videos showing blocks where motion was detected

  28. Detected Motion No motion Detected Motion (red blocks)

  29. Conclusion • The method of motion detection using principal component analysis combined with dynamic thresholding yields very good results in detecting motion • Future projects will include processing images with variation in size of the blocks

  30. Questions & Answers • Sample Videos • 8x8 Blocks • 32x32 Blocks • Principal Component Analysis • Matlab Code

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