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MATLAB代做-python代做-FPGA代做-仿射光流演示

时间:2019-4-8 20:42:52 点击:

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%% Affine Optic Flow Demonstration
%
% David Young
%
% Demonstration of estimation of an affine (first-order) optic flow field
% from a pair of images, using |affine_flow|.

%% Setting up test images
% We read in two test images. These should be in the current directory.
%
% The camera moved sideways between capturing these two images. The objects
% lie on a table top, so the features lie very roughly in a plane. As a
% result, the first-order flow provides an approximation to the true flow,
% though it does not capture its details or exact form.

% Convert to double for later processing. It's convenient to scale into the
% range 0 to 1 for imshow.
im1 = double(imread('maze1.png'))/256;
im2 = double(imread('maze2.png'))/256;

figure; imshow(im1);
figure; imshow(im2);

%% Measuring flow with conventional sampling
% We start by using the default rectilinear sampling.
%
% The motion between the test images is quite large, so to measure it we
% need to smooth quite heavily. We try a sigma of 25 pixels, and also
% sample every 25 pixels to cut down computation.

af = affine_flow('image1', im1, 'image2', im2, ...
    'sigmaXY', 25, 'sampleStep', 25);
af = af.findFlow;
flow = af.flowStruct;

%%
% We can inspect the numbers for the estimated flow.
%
% Printing the flow structure shows the magnitudes of the flow components.
% See the help information for |affine_flow| to find out what these
% components mean. Note that the large negative value for vx0 corresponds
% to the overall shift of the second image to the left, and the relatively
% large value for s2 is a result of the shear caused by the depth gradient
% in the image.

disp(flow);

%%
% And we can display the estimated flow graphically.
%
% A set of flow vectors illustrating the estimated flow field is displayed
% on the first image. This does not show the points at which the flow was
% computed; these are just representative vectors at arbitrary points to
% show the form of the first-order model.
%
% The flow vectors near the bottom of the image are larger than those
% higher up. This is because the surface is closer to the camera in this
% region; the flow vectors are like stereo disparities, larger (for
% parallel cameras) for closer objects.

affine_flowdisplay(flow, im1, 50);

%% 
% We check whether the estimated flow registers the images.
%
% We can see whether the flow that has been found maps the first image onto
% the second, by displaying edges. Here, the green edges are the original
% first image, the blue edges are the second image, and the red edges are
% the first image after warping by the flow.
%
% If the process has worked correctly, the red and blue edges should be
% close together. We do not expect exact overlap because the first-order
% flow can only be an approximate, smooth, model of the true flow. Even the
% overall form of the real flow is a perspective rather than an affine
% transformation, and there is a lot of depth variation which adds
% complexity. Nonetheless, the affine flow gives a respectable first
% approximation.

affine_flowedgedisplay(flow, im1, im2);

%% Assessing accuracy using synthetic flow
% One way to assess the accuracy of the flow estimation is to _synthesise_
% the second image by warping the first with a known flow field, then
% seeing if we can recover the parameters of the field.
%
% First, we set some parameters, look at the flow field they generate, and
% warp the first image according to this flow.

% The parameters for the test flow field
ftest.vx0 = 5;     % flow at centre of image (values changed later when
ftest.vy0 = 5;     % origin is moved)
ftest.d = 0.05;
ftest.r = -0.05;
ftest.s1 = 0.05;
ftest.s2 = -0.05;
% Shift origin to image origin
ftest = affine_flow.shift(ftest, -(size(im1,2)+1)/2, -(size(im1,1)+1)/2);

% Warp the first image
wtest = affine_flow.warp(ftest);    % convert to a warping matrix
ttest = maketform('affine', wtest); % make a transform structure
imtrans = imtransform_same(im1, ttest);   

% Display the transformed image
imshow(imtrans);

%%
% The flow is estimated as for the real image pair.
%
% In general, |sigmaXY| (the smoothing constant) needs to be set either
% using some prior knowledge of the likely maximum flow speed, or by
% experiment. The spatial scale of the smoothing needs to be comparable to
% the maximum optic flow speed.
%
% In this case it is easy to estimate the order of magnitude of the flow
% from the known parameters and the image size (use the equation in
% |affine_flow|'s help) and a value of 10 for the smoothing constant seems
% reasonable. It would be possible to refine this experimentally, given an
% error measure, a set of images, and a set of flow fields.
%
% Since we know the images will be smoothed on a scale of 10 pixels, we can
% cut down the computation by sampling the gradients every tenth row and
% column before solving the least-squares problem. This is done with the
% |sampleStep| parameter.
%
% We can see that the estimates are in the right region; whether they are
% adequate for any task depends, of course, on the application.

af.sigmaXY = 10;
af.sampleStep = 10;
af.image2 = imtrans;
af = af.findFlow;
ffound = af.flowStruct;

% Inspect the values
disp('The test flow parameters:'); disp(ftest);
disp('The recovered flow parameters:'); disp(ffound);

% Show the input flow field in blue and the recovered flow field in red,
% with slightly different positioning so that both sets of vectors can be
% seen.
clf;
affine_flowdisplay(ftest, size(im1), 50, 'b');
affine_flowdisplay(ffound, size(im1), 45, 'r');

%% Finding flow using log-polar sampling
% The rest of this demonstration deals with an alternative approach to the
% computation associated with ideas in foveal vision and active vision. It
% can be ignored if you only want standard Lucas-Kanade flow estimation.
%
% Log-polar image sampling can be an accurate and effective way to estimate
% first-order flow, because the sample spacing can vary with the flow speed
% across the image, provided that a point in the image is tracked. This is
% explained <http://www.bmva.org/bmvc/1994/bmvc-94-057.pdf here>. The
% |affine_flow| class will work in log-polar space as an option, using
% the method described in the paper.
%
% To see what this means, we can display a log-polar sampled image. This is
% done below, but note that this is for illustration only - |affine_flow|
% does its own resampling, and you always give it the original images to
% work on.
%
% The log-polar image appears distorted when displayed on the screen using
% |imshow|. The rings become vertical lines in the display and the wedges
% become horizontal lines. Dilation (the _D_ in the optic flow equations)
% becomes a horizontal shift in this picture, and rotation (_R_) becomes a
% vertical shift. Translation and shear have more complex effects on the
% log-polar image, but it is still easy to estimate them.
%
% If required, |affine_flow| resamples both images to log-polar
% coordinates, and takes advantage of the change in resolution to estimate
% first-order flow. To do this, it shifts the log-polar centre for the
% second image using its initial estimate of the flow, so as to track the
% motion. This produces low flow speeds at the high-resolution centre of
% the sampling pattern, with the flow speed increasing (for pure
% first-order flow) linearly with radius, matching the sample separation.

rmin = 3;                   % See help logsample for what these
rmax = min(size(im1))/2;    % parameters mean
xc = size(im1,2)/2;
yc = size(im1,1)/2;
nw = 300;
logim = logsample(im1, rmin, rmax, xc, yc, [], nw);
imshow(logim);

%% 
% First, we estimate the flow without tracking.
%
% As with the conventional approach, we need to set a smoothing constant.
% We will also set some other sampling parameters - see the help
% information for |logsample|.
%
% Smoothing is done on the resampled log-polar image, so the smoothing
% constant can be smaller than in the conventional case - if the
% translation is not too great, the expected norm of the first-order
% components divided by the angle between wedges is a reasonable order of
% magnitude. (The angle between wedges is |2*pi/logWedges|.) Here, we adopt
% 200 wedges and a smoothing constant of 4, but experimentation on a range
% of images and flow fields could be done.
%
% We set |logRmin| to 5 - it isn't critical, but small rings suffer badly
% from the mismatch between the original image resolution and the higher
% resolution that the foveal centre of the log-polar image ought to have,
% and there is little point in making |logRmin| too small.
%
% We set |logRmax| to 100 pixels. Setting it explicitly allows us to
% compare the results without and with tracking.
%
% With no tracking, the function makes a single estimate of the flow field,
% with both log-polar patterns centred at the centres of the images (the
% default).
%
% We see that the estimate is reasonable, but not as accurate as the
% conventional computation above. The |lastSpeed| field shows that the
% image was estimated to be moving past the centre of the sampling pattern
% at about 7 pixels/frame - enough to destroy any contribution from the
% high-resolution inner rings.

af.sampleMethod = 'logpolar';
af.logWedges = 200;
af.sigmaRW = 4;
af.logRmin = 5;
af.logRmax = 100;
af.maxIter = 1;        % No tracking

af = af.findFlow;
ffound = af.flowStruct;

% Compare true flow and result
disp('Test flow parameters:'); disp(ftest);
disp('Recovered flow, log-polar sampling, no tracking:'); disp(ffound);
% Display tracking parameters
disp('Tracking information:'); disp(af.trackInfo);

%%
% We now switch on tracking, keeping all the other parameters the same.
%
% The estimates, especially of vx0 and vy0, become more accurate. Three
% iterations were done and we can see from the |lastSpeed| field of the
% result that the estimated residual flow at the sampling centre on the
% final iteration was very close to zero. That is, accurate tracking was
% probably taking place.
%
% Displaying the edges shows almost exact registration - as we would
% expect, given that the synthetic flow is purely first-order.

af.maxIter = 5;  % allow up to 5 iterations
af.velTol = 0.5; % but stop if centre flow speed drops below 1 pixel/frame

af = af.findFlow;
ffound = af.flowStruct;

% Compare true flow and result
disp('Test flow parameters:'); disp(ftest);
disp('Recovered flow, log-polar sampling, tracking:'); disp(ffound);
disp('Tracking information:'); disp(af.trackInfo);

% and a visual check
affine_flowedgedisplay(ffound, im1, imtrans);

%%
% We now perform the same operation but using the real image pair. Only a
% qualitative comparison with the conventional approach is possible, but
% the log-polar method appears to perform somewhat better in this case.

af.image2 = im2;    % second real image

af = af.findFlow;
ffound = af.flowStruct;

disp('Recovered flow for real images:'); disp(ffound);
disp('Tracking information:'); disp(af.trackInfo);

% and a visual check
affine_flowedgedisplay(ffound, im1, im2);

%% Final note
% Some features of this class - notably the use of a region of interest
% mask - have not been explored in this demo.
%
% The class demonstrated here can be used in a variety of modes. It has
% been shown estimating the global flow field across the whole image, but
% it can be also be used to make local estimates of the flow field. This is
% done with the |rectRegion| or |regionOfInterest| options for conventional
% sampling, or by setting |logRmax| and |logCentre| for log-polar sampling.
% A good context for this is active vision systems associated with robot
% control.
%
% Copyright David Young 2010

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作者:仿射光流 来源:仿射光流
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