How to crop and rotate an image to bounding box? - matlab

I have a dataset of thousands of images containing hands
I also have .mat files which contain the coordinates of 4 corners of the bounding box
However, the edges of these bounding boxes are at an angle with the x & y axis. For example,
I want to crop out the hands using the bounding box coordinates & then rotate the hands such that they are aligned with the x or y axis.
EDIT:
The hand is represented as follows:
However, please keep in mind that the rectangle is NOT straight. So, I'll have to rotate it to straighten it out.

Good one!
First step:
Compute the size of the rectangle
width = sqrt( sum( (b-a).^2 ) );
height = sqrt( sum( (c-b).^2 ) );
Second step:
Compute an affine transformation from a...d to an upright image
Xin = [a(2) b(2) c(2) d(2)];
Yin = [a(1) b(1) c(1) d(1)];
Xout = [width 1 1 width];
Yout = [1 1 height height];
A = [Xin;Yin;ones(1,4)]';
B = [Xout; Yout]';
H = B \ A; % affine transformation
Note that despite the fact that we allow fo H to be affine, the choise of corners (depending on width and height) will acertain that H will not distort the cropped rectangle.
optionally use cp2tform:
H2 = cp2tform( [Xin;Yin]', [Xout;Yout]', 'nonreflectivesimilarity' );
Third step
Use the transformation to get the relevant image part
thumb = tformarray( img, maketform( 'affine', H' ), ... %//'
makeresampler( 'cubic', 'fill' ), ...
1:2, 1:2, ceil( [height width] ), [], 0 );
optionally use imtransform:
thumb = imtransform( img, H2, 'bicubic' );
A note regarding vectorization:
depends on how the coordinates of the corners are stored (a...d) the first two steps can be easily vectorize.

You can rotate images using the imrotate command.
You can crop images (once they are rotated properly) by using indexing. i.e.
subimg = img( c(1):b(1), c(2):d(2) )
(note, the above line is assuming, you've tracked the corners through the imrotate command, so that c(2) == b(2), c(1) == d(1) etc.)

Related

How do i create a rectangular mask at known angles?

I have created a synthetic image that consists of a circle at the centre of a box with the code below.
%# Create a logical image of a circle with image size specified as follows:
imageSizeY = 400;
imageSizeX = 300;
[ygv, xgv] = meshgrid(1:imageSizeY, 1:imageSizeX);
%# Next create a logical mask for the circle with specified radius and center
centerY = imageSizeY/2;
centerX = imageSizeX/2;
radius = 100;
Img = double( (ygv - centerY).^2 + (xgv - centerX).^2 <= radius.^2 );
%# change image labels from double to numeric
for ii = 1:numel(Img)
if Img(ii) == 0
Img(ii) = 2; %change label from 0 to 2
end
end
%# plot image
RI = imref2d(size(Img),[0 size(Img, 2)],[0 size(Img, 1)]);
figure, imshow(Img, RI, [], 'InitialMagnification','fit');
Now, i need to create a rectangular mask (with label == 3, and row/col dimensions: 1 by imageSizeX) across the image from top to bottom and at known angles with the edges of the circle (see attached figure). Also, how can i make the rectangle thicker than 1 by imageSizeX?. As another option, I would love to try having the rectangle stop at say column 350. Lastly, any ideas how I can improve on the resolution? I mean is it possible to keep the image size the same while increasing/decreasing the resolution.
I have no idea how to go about this. Please i need any help/advice/suggestions that i can get. Many thanks!.
You can use the cos function to find the x coordinate with the correct angle phi.
First notice that the angle between the radius that intersects the vertex of phi has angle with the x-axis given by:
and the x coordinate of that vertex is given by
so the mask simply needs to set that row to 3.
Example:
phi = 45; % Desired angle in degrees
width = 350; % Desired width in pixels
height = 50; % Desired height of bar in pixels
theta = pi-phi*pi/180; % The radius angle
x = centerX + round(radius*cos(theta)); % Find the nearest row
x0 = max(1, x-height); % Find where to start the bar
Img(x0:x,1:width)=3;
The resulting image looks like:
Note that the max function is used to deal with the case where the bar thickness would extend beyond the top of the image.
Regarding resolution, the image resolution is determined by the size of the matrix you create. In your example that is (400,300). If you want higher resolution simply increase those numbers. However, if you would like to link the resolution to a higher DPI (Dots per Inch) so there are more pixels in each physical inch you can use the "Export Setup" window in the figure File menu.
Shown here:

Drawing circles around points in a plot

I have two matrices
timeline = [0.0008 0.0012 0.0016 0.0020 0.0024 0.0028];
Origdata =
79.8400 69.9390 50.0410 55.5082 34.5200 37.4486 31.4237 27.3532 23.2860 19.3039
79.7600 69.8193 49.8822 55.3115 34.2800 37.1730 31.1044 26.9942 22.8876 18.9061
79.6800 69.6996 49.7233 55.1148 34.0400 36.8975 30.7850 26.6352 22.4891 18.5084
79.6000 69.5799 49.5645 54.9181 33.8000 36.6221 30.4657 26.2762 22.0907 18.1108
79.5200 69.4602 49.4057 54.7215 33.5600 36.3467 30.1464 25.9173 21.6924 17.7133
79.4400 69.3405 49.2469 54.5249 33.3200 36.0714 29.8271 25.5584 21.2941 17.3159
When I plot them, I get a graph like below.
plot(timeline, Origdata, '.');
How can I draw a circle of radius 0.3524 value around each point? This radius should be relative to the y-axis only.
You can do this easily using viscircles (which requires the Image Processing Toolbox) however I don't think that the output is actually what you're expecting.
radius = 0.3524;
dots = plot(timeline, Origdata, '.');
hold on
for k = 1:numel(dots)
plotdata = get(dots(k));
centers = [plotdata.XData(:), plotdata.YData(:)];
% Ensure the the colors match the original plot
color = get(dots(k), 'Color');
viscircles(centers, radius * ones(size(centers(:,1))), 'Color', color);
end
The reason that it looks like this is because your X data is very close together relative to your y data and for circles to appear as circles, I have forced the x and y scaling of the axes to be equal (axis equal)
Edit
If you only want the radius to be relative to the y axis (distance) then we actually need to draw ellipses with an x and y radius. We want to scale the "x-radius" to make it appear as a circle regardless of your true axes aspect ratio, something like this can actually do that.
The trick to the code below is setting the data and plot aspect ratios (pbaspect and daspect) to manual. This ensures that the aspect ratio of the axes doesn't change during zoom, resizing, etc and makes sure that our "circles" remain circular-looking.
dots = plot(timeline, Origdata, '.');
drawnow
% Force the aspect ratio to not change (keep the circles, as circles)
pbaspect('manual')
daspect('manual')
hold on
aspectRatio = daspect;
t = linspace(0, 2*pi, 100);
t(end+1) = NaN;
radius = 4.3524;
% Scale the radii for each axis
yradius = radius;
xradius = radius * aspectRatio(1)/aspectRatio(2);
% Create a circle "template" with a trailing NaN to disconnect consecutive circles
t = linspace(0, 2*pi, 100);
t(end+1) = NaN;
circle = [xradius*cos(t(:)), yradius*sin(t(:))];
for k = 1:numel(dots)
x = get(dots(k), 'XData');
y = get(dots(k), 'YData');
color = get(dots(k), 'Color');
% Center circle template at all points
circles = arrayfun(#(x,y)bsxfun(#plus, [x,y], circle), x, y, 'uni', 0);
circles = cat(1, circles{:});
plot(circles(:,1), circles(:,2), 'Color', color)
end
Just to demonstrate, if we increase the circle radius to 4.3524 we can see the circles better.
And this works with all resizing etc.
To draw circles in MATLAB, you obviously have to use the rectangle function ;)
As mentioned in my comment, the size of 0.3524 does not match your axis, so I chose different sizes to have the circles actually visible, These are rx and ry
timeline = [0.0008 0.0012 0.0016 0.0020 0.0024 0.0028];
Orgidata =[79.8400 69.9390 50.0410 55.5082 34.5200 37.4486 31.4237 27.3532 23.2860 19.3039
79.7600 69.8193 49.8822 55.3115 34.2800 37.1730 31.1044 26.9942 22.8876 18.9061
79.6800 69.6996 49.7233 55.1148 34.0400 36.8975 30.7850 26.6352 22.4891 18.5084
79.6000 69.5799 49.5645 54.9181 33.8000 36.6221 30.4657 26.2762 22.0907 18.1108
79.5200 69.4602 49.4057 54.7215 33.5600 36.3467 30.1464 25.9173 21.6924 17.7133
79.4400 69.3405 49.2469 54.5249 33.3200 36.0714 29.8271 25.5584 21.2941 17.3159];
ry=1;
rx=0.0001;
dots=plot(timeline, Orgidata , '.');
hold on
for ix=1:size(Orgidata ,1)
for jx=1:size(Orgidata ,2)
rectangle('Position',[timeline(ix)-(rx/2),Orgidata(ix,jx)-(ry/2),rx,ry],'Curvature',[1,1],'EdgeColor',get(dots(jx), 'Color'));
end
end

Plot depth image in matlab

I have an RGB-D image and am trying to get a 3D visualization in matlab. Currently I am doing:
depth = imread('img_031_depth.png');
depth = double(depth);
img = imread('img_031.png');
surf(depth, img, 'FaceColor', 'texturemap', 'EdgeColor', 'none' )
view(158, 38)
Which gives me an image like:
I have two questions:
1) how can I save the image without it blurring as above
2) As you can see some edges show lined going to zero (e.g. the top of the coffee cup) I would like to remove these.
What I'm trying to produce is a 3D looking pointcloud, as these are only 2.5D I must show them from the right angle.
Any help is appreciated
EDIT: added images (note depth image needs to be normalized for visualization)
If you are only interested in a point cloud, you might want to consider scatter3.
You can select which points to plot (discard those with depth == 0).
You need to have explicit x-y coordinates though.
[y x] = ndgrid( 1:size(img,1), 1:size(img,2) );
sel = depth > 0 ; % which points to plot
% "flatten" the matrices for scatter plot
x = x(:);
y = y(:);
img = reshape( img, [], 3 );
depth = depth(:);
scatter3( x(sel), y(sel), depth(sel), 20, img( sel, : ), 'filled' );
view(158, 38)
Edit: sampled version
[y x] = ndgrid( 1:2:size(img,1), 1:2:size(img,2) );
sel = depth( 1:2:end, 1:2:end ) > 0;
x = x(:);
y = y(:);
img = reshape( img( 1:2:end, 1:2:end, : ), [], 3 );
depth = depth( 1:2:end, 1:2:end );
scatter( x(sel), y(sel), depth(sel), 20, img( sel, : ), 'filled' );
view( 158, 38 );
Alternatively, you can directly manipulate sel mask.
i suggest you first restore x=zu/f and y=zv/f, to obtain x, y, z, where f is your camera focal length;
then apply whatever rotation, translation you want before displaying them [x’,y’,z’] = R[x, y, z] + t;
then project them back using col = xf/z+w/2, row = h/2-yf/z to get a simple image that you can display fast; you can add a depth buffer to the last operation to guarantee
proper occlusions by writing depth at each pixel there and checking that repetitive writing happens only if new z is smaller (that is a new pixel is close to the viewer). The resulting image will still have holes due to the nature of point clouds. You can interpolate in those holes but this means you have to trace rays from every pixels in the image to your point cloud and find a closest neighbor to the ray which probably takes forever in Matlab.
I am also doing some 3D image restoring and reconstructing. The first question is easy. Your photo is taken by a camera. So you need to transform the position to camera coordinate system. In other words, you need to know some intrinsic value of your camera! Or you can never recover it with a single image. Google 'kinect intrinsic value' you can get the focal length etc.
Also, change your view.
Try this! And if it's not working, ask again.

create cylinders in 3D volumetric data

I'm trying to create a dataset of raw volumetric data consisting of geometrical shapes. The point is to use volume ray casting to project them in 2D but first I want to create the volume manually.
The geometry is consisting of one cylinder that is in the middle of the volume, along the Z axis and 2 smaller cylinders that are around the first one, deriving from rotations around the axes.
Here is my function so far:
function cyl= createCylinders(a, b, c, rad1, h1, rad2, h2)
% a : data width
% b : data height
% c : data depth
% rad1: radius of the big center cylinder
% rad2: radius of the smaller cylinders
% h1: height of the big center cylinder
% h2: height of the smaller cylinders
[Y X Z] =meshgrid(1:a,1:b,1:c); %matlab saves in a different order so X must be Y
centerX = a/2;
centerY = b/2;
centerZ = c/2;
theta = 0; %around y
fi = pi/4; %around x
% First cylinder
cyl = zeros(a,b,c);
% create for infinite height
R = sqrt((X-centerX).^2 + (Y-centerY).^2);
startZ = ceil(c/2) - floor(h1/2);
endZ = startZ + h1 - 1;
% then trim it to height = h1
temp = zeros(a,b,h1);
temp( R(:,:,startZ:endZ)<rad1 ) = 255;
cyl(:,:,startZ:endZ) = temp;
% Second cylinder
cyl2 = zeros(a,b,c);
A = (X-centerX)*cos(theta) + (Y-centerY)*sin(theta)*sin(fi) + (Z-centerZ)*cos(fi)*sin(theta);
B = (Y-centerY)*cos(fi) - (Z-centerZ)*sin(fi);
% create again for infinite height
R2 = sqrt(A.^2+B.^2);
cyl2(R2<rad2) = 255;
%then use 2 planes to trim outside of the limits
N = [ cos(fi)*sin(theta) -sin(fi) cos(fi)*cos(theta) ];
P = (rad2).*N + [ centerX centerY centerZ];
T = (X-P(1))*N(1) + (Y-P(2))*N(2) + (Z-P(3))*N(3);
cyl2(T<0) = 0;
P = (rad2+h2).*N + [ centerX centerY centerZ];
T = (X-P(1))*N(1) + (Y-P(2))*N(2) + (Z-P(3))*N(3);
cyl2(T>0) = 0;
% Third cylinder
% ...
cyl = cyl + cyl2;
cyl = uint8(round(cyl));
% ...
The concept is that the first cylinder is created and then "cut" according to the z-axis value, to define its height. The other cylinder is created using the relation A2 + B 2 = R2 where A and B are rotated accordingly using the rotation matrices only around x and y axes, using Ry(θ)Rx(φ) as described here.
Until now everything seems to be working, because I have implemented code (tested that it works well) to display the projection and the cylinders seem to have correct rotation when they are not "trimmed" from infinite height.
I calculate N which is the vector [0 0 1] aka z-axis rotated in the same way as the cylinder. Then I find two points P of the same distances that I want the cylinder's edges to be and calculate the plane equations T according to that points and normal vector. Lastly, I trim according to that equality. Or at least that's what I think I'm doing, because after the trimming I usually don't get anything (every value is zero). Or, the best thing I could get when I was experimenting was cylinders trimmed, but the planes of the top and bottom where not oriented well.
I would appreciate any help or corrections at my code, because I've been looking at the geometry equations and I can't find where the mistake is.
Edit:
This is a quick screenshot of the object I'm trying to create. NOTE that the cylinders are opaque in the volume data, all the inside is considered as homogeneous material.
I think instead of:
T = (X-P(1))*N(1) + (Y-P(2))*N(2) + (Z-P(3))*N(3);
you should try the following at both places:
T = (X-P(1)) + (Y-P(2)) + (Z-P(3));
Multiplying by N is to account for the direction of the axis of the 2nd cylinder which you have already done just above that step.

How to measure the rotation of a image in MATLAB?

I have two images. One is the original, and the another is rotated.
Now, I need to discover the angle that the image was rotated. Until now, I thought about discovering the centroids of each color (as every image I will use has squares with colors in it) and use it to discover how much the image was rotated, but I failed.
I'm using this to discover the centroids and the color in the higher square in the image:
i = rgb2gray(img);
bw = im2bw(i,0.01);
s = regionprops(bw,'Centroid');
centroids = cat(1, s.Centroid);
colors = impixel(img,centroids(1),centroids(2));
top = max(centroids);
topcolor = impixel(img,top(1),top(2));
You can detect the corners of one of the colored rectangles in both the image and the rotated version, and use these as control points to infer the transformation between the two images (like in image registration) using the CP2TFORM function. We can then compute the angle of rotation from the affine transformation matrix:
Here is an example code:
%# read first image (indexed color image)
[I1 map1] = imread('http://i.stack.imgur.com/LwuW3.png');
%# constructed rotated image
deg = -15;
I2 = imrotate(I1, deg, 'bilinear', 'crop');
%# find blue rectangle
BW1 = (I1==2);
BW2 = imrotate(BW1, deg, 'bilinear', 'crop');
%# detect corners in both
p1 = corner(BW1, 'QualityLevel',0.5);
p2 = corner(BW2, 'QualityLevel',0.5);
%# sort corners coordinates in a consistent way (counter-clockwise)
p1 = sortrows(p1,[2 1]);
p2 = sortrows(p2,[2 1]);
idx = convhull(p1(:,1), p1(:,2)); p1 = p1(idx(1:end-1),:);
idx = convhull(p2(:,1), p2(:,2)); p2 = p2(idx(1:end-1),:);
%# make sure we have the same number of corner points
sz = min(size(p1,1),size(p2,1));
p1 = p1(1:sz,:); p2 = p2(1:sz,:);
%# infer transformation from corner points
t = cp2tform(p2,p1,'nonreflective similarity'); %# 'affine'
%# rotate image to match the other
II2 = imtransform(I2, t, 'XData',[1 size(I1,2)], 'YData',[1 size(I1,1)]);
%# recover affine transformation params (translation, rotation, scale)
ss = t.tdata.Tinv(2,1);
sc = t.tdata.Tinv(1,1);
tx = t.tdata.Tinv(3,1);
ty = t.tdata.Tinv(3,2);
translation = [tx ty];
scale = sqrt(ss*ss + sc*sc);
rotation = atan2(ss,sc)*180/pi;
%# plot the results
subplot(311), imshow(I1,map1), title('I1')
hold on, plot(p1(:,1),p1(:,2),'go')
subplot(312), imshow(I2,map1), title('I2')
hold on, plot(p2(:,1),p2(:,2),'go')
subplot(313), imshow(II2,map1)
title(sprintf('recovered angle = %g',rotation))
If you can identify a color corresponding to only one component it is easier to:
Calculate the centroids for each image
Calculate the mean of the centroids (in x and y) for each image. This is the "center" of each image
Get the red component color centroid (in your example) for each image
Subtract the mean of the centroids for each image from the red component color centroid for each image
Calculate the ArcTan2 for each of the vectors calculated in 4), and subtract the angles. That is your result.
If you have more than one figure of each color, you need to calculate all possible combinations for the rotation and then select the one that is compatible with the other possible rotations.
I could post the code in Mathematica, if you think it is useful.
I would take a variant to the above mentioned approach:
% Crude binarization method to knock out background and retain foreground
% features. Note one looses the cube in the middle
im = im > 1
Then I would get the 2D autocorrelation:
acf = normxcorr2(im, im);
From this result, one can easily detect the peaks, and as rotation carries into the autocorrelation function (ACF) domain, one can ascertain the rotation by matching the peaks between the original ACF and the ACF from the rotated image, for example using the so-called Hungarian algorithm.