Motion vectors calculation - matlab

Question

I am working on the following code:
filename = 'C:\li_walk.avi';
hVidReader = vision.VideoFileReader(filename, 'ImageColorSpace', 'RGB','VideoOutputDataType', 'single');
hOpticalFlow = vision.OpticalFlow('OutputValue', 'Horizontal and vertical components in complex form', 'ReferenceFrameDelay', 3);
hMean1 = vision.Mean;
hMean2 = vision.Mean('RunningMean', true);
hMedianFilt = vision.MedianFilter;
hclose = vision.MorphologicalClose('Neighborhood', strel('line',5,45));
hblob = vision.BlobAnalysis('CentroidOutputPort', false, 'AreaOutputPort', true, 'BoundingBoxOutputPort', true, 'OutputDataType', 'double','MinimumBlobArea', 250, 'MaximumBlobArea', 3600, 'MaximumCount', 80);
herode = vision.MorphologicalErode('Neighborhood', strel('square',2));
hshapeins1 = vision.ShapeInserter('BorderColor', 'Custom', 'CustomBorderColor', [0 1 0]);
hshapeins2 = vision.ShapeInserter( 'Shape','Lines', 'BorderColor', 'Custom','CustomBorderColor', [255 255 0]);
htextins = vision.TextInserter('Text', '%4d', 'Location', [1 1],'Color', [1 1 1], 'FontSize', 12);
sz = get(0,'ScreenSize');
pos = [20 sz(4)-300 200 200];
hVideo1 = vision.VideoPlayer('Name','Original Video','Position',pos);
pos(1) = pos(1)+220; % move the next viewer to the right
hVideo2 = vision.VideoPlayer('Name','Motion Vector','Position',pos);
pos(1) = pos(1)+220;
hVideo3 = vision.VideoPlayer('Name','Thresholded Video','Position',pos);
pos(1) = pos(1)+220;
hVideo4 = vision.VideoPlayer('Name','Results','Position',pos);
% Initialize variables used in plotting motion vectors.
lineRow = 22;
firstTime = true;
motionVecGain = 20;
borderOffset = 5;
decimFactorRow = 5;
decimFactorCol = 5;
while ~isDone(hVidReader) % Stop when end of file is reached
frame = step(hVidReader); % Read input video frame
grayFrame = rgb2gray(frame);
ofVectors = step(hOpticalFlow, grayFrame); % Estimate optical flow
% The optical flow vectors are stored as complex numbers. Compute their
% magnitude squared which will later be used for thresholding.
y1 = ofVectors .* conj(ofVectors);
% Compute the velocity threshold from the matrix of complex velocities.
vel_th = 0.5 * step(hMean2, step(hMean1, y1));
% Threshold the image and then filter it to remove speckle noise.
segmentedObjects = step(hMedianFilt, y1 >= vel_th);
% Thin-out the parts of the road and fill holes in the blobs.
segmentedObjects = step(hclose, step(herode, segmentedObjects));
% Estimate the area and bounding box of the blobs.
[area, bbox] = step(hblob, segmentedObjects);
% Select boxes inside ROI (below white line).
Idx = bbox(:,1) > lineRow;
% Based on blob sizes, filter out objects which can not be cars.
% When the ratio between the area of the blob and the area of the
% bounding box is above 0.4 (40%), classify it as a car.
ratio = zeros(length(Idx), 1);
ratio(Idx) = single(area(Idx,1))./single(bbox(Idx,3).*bbox(Idx,4));
ratiob = ratio > 0.4;
count = int32(sum(ratiob)); % Number of cars
bbox(~ratiob, :) = int32(-1);
% Draw bounding boxes around the tracked cars.
y2 = step(hshapeins1, frame, bbox);
% Display the number of cars tracked and a white line showing the ROI.
y2(22:23,:,:) = 1; % The white line.
y2(1:15,1:30,:) = 0; % Background for displaying count
result = step(htextins, y2, count);
% Generate coordinates for plotting motion vectors.
if firstTime
[R C] = size(ofVectors); % Height and width in pixels
RV = borderOffset:decimFactorRow:(R-borderOffset);
CV = borderOffset:decimFactorCol:(C-borderOffset);
[Y X] = meshgrid(CV,RV);
firstTime = false;
sumu=0;
sumv=0;
end
grayFrame = rgb2gray(frame);
[ra ca na] = size(grayFrame);
ofVectors = step(hOpticalFlow, grayFrame); % Estimate optical flow
ua = real(ofVectors);
ia = ofVectors - ua;
va = ia/complex(0,1);
sumu=ua+sumu;
sumv=va+sumv;
[xa ya]=meshgrid(1:1:ca,ra:-1:1);
% Calculate and draw the motion vectors.
tmp = ofVectors(RV,CV) .* motionVecGain;
lines = [Y(:), X(:), Y(:) + real(tmp(:)), X(:) + imag(tmp(:))];
motionVectors = step(hshapeins2, frame, lines);
% Display the results
step(hVideo1, frame); % Original video
step(hVideo2, motionVectors); % Video with motion vectors
step(hVideo3, segmentedObjects); % Thresholded video
step(hVideo4, result); % Video with bounding boxes
quiver(xa,ya,sumu,sumv)
end
release(hVidReader);
Please help me to understand the following statements of the above code:
ua = real(ofVectors);
ia = ofVectors - ua;
va = ia/complex(0,1);
these are the horizontal (ua) and vertical (va) components of the motion vectors. what real part of the (Ofvectors) will be? please help me in understanding this code segment

Answer 1

When the object hOpticalFlow is constructed in the third line of the code, the OutputValue property is set to 'Horizontal and vertical components in complex form' which has the effect that when you apply the step command to hOpticalFlow and the image (frame), you will not get just the magnitudes of the flowVectors, but complex numbers that represent these planar flow vectors. It is just a compact way for the command to return the information. Once you have the complex numbers in ofVectors, which is the output of the step command, the command
ua = real(ofVectors);
stores the horizontal component of each vector in ua. After the command
ia = ofVectors - ua;
is executed, ia contains the imaginary (i.e., vertical components of the flow vectors) because the real parts in ua are subtracted from the complex numbers in ofVectors. However, you need to get rid of the imaginary units in ia, so you divide by 0+1i. This is what the command
va = ia/complex(0,1);
does.