Erasing previous data/plots in Julia (Plots.jl, GR backend) - animation

I have solved an ODE in Julia describing the motion of a particle, and I have saved the coordinates and respective time in an array. I would like to create an animated gif image of a plot with the particle along the solved trajectory, but to do that (the only way that I have come up) is to plot the position of the particle using scatter, and erase the previous position of the particle every moment. However I only know about scatter! which will add more particles to the plot rather than showing the change of particle position. So how can I erase the previous plot every iteration, or are there more clever ways to do this? And what about if I want to mark down the trajectory of the particle in earlier moments using plots?

Erasing previous data is not possible with Plots.jl. The previous plot can be erased by using plot or scatter commands instead of plot! and scatter!. Here are some examples how animations can be created using the #gif macro (http://docs.juliaplots.org/latest/animations/)
Create some dummy data:
using Plots
t = range(0, 4π, length = 100)
r = range(1, 0, length = 100)
x = cos.(t) .* r
y = sin.(t) .* r
Plot only the last current point in each step:
#gif for i in eachindex(x)
scatter((x[i], y[i]), lims = (-1, 1), label = "")
end
Plot all previous steps with a marker at the current position:
#gif for i in eachindex(x)
plot(x[1:i], y[1:i], lims = (-1, 1), label = "")
scatter!((x[i], y[i]), color = 1, label = "")
end
The same as above with decreasing alpha for older steps (only showing the newest 10 steps):
#gif for i in eachindex(x)
plot(x[1:i], y[1:i], alpha = max.((1:i) .+ 10 .- i, 0) / 10, lims = (-1, 1), label = "")
scatter!((x[i], y[i]), color = 1, label = "")
end

Related

cv2 pose estimation using homography matrix

I am trying to calculate the pose of image Y, given image X. Image Y is the same as image X rotated 90º degrees.
1 -So, for starters i find the matches between both images.
2 -Then i store all the good matches.
3 -The homography between the the matches from both images is calculated using cv2.RANSAC.
4 -Then for the X image, i transform the 2d matching points into 3d, adding 0 as the Z axis.
5 -Object points contain all points from matches of original image, while image points contain matches from the training image. Both array of points are filtered using the mask returned by homography.
6 -After that, i use cv2.calibrateCamera with these object points and image points.
7 -Finnaly i use cv2.projectPoints to get the projections of the axis
I know with that until step 5, the results are correct because i use cv2.drawMatches to see the matches. However this may not be the way to get what i want to achieve.
matches = flann.knnMatch(query_image.descriptors, descriptors, k=2)
good = []
for m, n in matches:
if m.distance < 0.70 * n.distance:
good.append(m)
current_good = good
src_pts = np.float32([selected_image.keypoints[m.queryIdx].pt for m in current_good]).reshape(-1, 1, 2)
dst_pts = np.float32([keypoints[m.trainIdx].pt for m in current_good]).reshape(-1, 1, 2)
homography, mask = cv2.findHomography(src_pts, dst_pts, cv2.RANSAC, 5.0)
test = np.zeros(((mask.ravel() > 0).sum(), 3),np.float32) #obj points
test1 = np.zeros(((mask.ravel() > 0).sum(), 2), np.float32) #img points
i=0
counter=0
for m in current_good:
if mask.ravel()[i] == 1:
test[counter][0] = selected_image.keypoints[m.queryIdx].pt[0]
test[counter][1] = selected_image.keypoints[m.queryIdx].pt[1]
test1[counter][0] = selected_image.keypoints[m.trainIdx].pt[0]
test1[counter][1] = selected_image.keypoints[m.trainIdx].pt[1]
counter+=1
i+=1
gray = cv2.cvtColor(self.train_image, cv2.COLOR_BGR2GRAY)
gray = np.float32(gray)
#here start my doubts about what i want to do and if it is possible to do it this way
ret, mtx, dist, rvecs, tvecs = cv2.calibrateCamera([test], [test1], gray.shape[::-1], None, None)
axis = np.float32([[3, 0, 0], [0, 3, 0], [0, 0, -3]]).reshape(-1, 3)
rvecs = np.array(rvecs, np.float32)
tvecs = np.array(tvecs, np.float32)
imgpts, jac = cv2.projectPoints(axis, rvecs, tvecs, mtx, dist)
However after all this, imgpts returned by cv2.projectPoints give results that don't make much sense to me, like :
[[[857.3185 109.317406]]
[[857.2196 108.360954]]
[[857.2846 107.579605]]]
I would like to have a normal to my image like it is shown here https://docs.opencv.org/trunk/d7/d53/tutorial_py_pose.html and i successfully got it to work using the chessboard image. But trying to adapt to a general image is giving me strange results.

Merging 2 images by showing one next to the other separated by a diagonal line

I have 2 images ("before" and "after"). I would like to show a final image where the left half is taken from the before image and the right half is taken from the after image.
The images should be separated by a white diagonal line of predefined width (2 or 3 pixels), where the diagonal is specified either by a certain angle or by 2 start and end coordinates. The diagonal should overwrite a part of the final image such that the size is the same as the sources'.
Example:
I know it can be done by looping over all pixels to recombine and create the final image, but is there an efficient way, or better yet, a built-in function that can do this?
Unfortunately I don't believe there is a built-in solution to your problem, but I've developed some code to help you do this but it will unfortunately require the image processing toolbox to play nicely with the code. As mentioned in your comments, you have this already so we should be fine.
The logic behind this is relatively simple. We will assume that your before and after pictures are the same size and also share the same number of channels. The first part is to declare a blank image and we draw a straight line down the middle of a certain thickness. The intricacy behind this is to declare an image that is slightly bigger than the original size of the image. The reason why is because I'm going to draw a line down the middle, then rotate this blank image by a certain angle to achieve the first part of what you desire. I'll be using imrotate to rotate an image by any angle you desire. The first instinct is to declare an image that's the same size as either the originals, draw a line down the middle and rotate it. However, if you do this you'll end up with the line being disconnected and not draw from the top to the bottom of the image. That makes sense because the line being drawn on an angle covers more pixels than if you were to draw this vertically.
Using Pythagorean's theorem, we know that the longest line that can ever be drawn on your image is the diagonal. Therefore we declare an image that is sqrt(rows*rows + cols*cols) in both the rows and columns where rows and cols are the rows and columns of the original image. After, we'll take the ceiling to make sure we've covered as much as possible and we add a bit of extra room to accommodate for the width of the line. We draw a line on this image, rotate it then we'll crop the image after so that it's the same size as the input images. This ensures that the line drawn at whatever angle you wish is fully drawn from top to bottom.
That logic is the hardest part. Once you do that, you declare two logical masks where you use imfill to fill the left side of the mask as one mask and we'll invert the mask to find the other mask. You will also need to use the line image that we created earlier with imrotate to index into the masks and set the values to false so that we ignore these pixels that are on the line.
Finally, you take each mask, index into your image and copy over each portion of the image you desire. You finally use the line image to index into the output and set the values to white.
Without further ado, here's the code:
% Load some example data
load mandrill;
% im is the image before
% im2 is the image after
% Before image is a colour image
im = im2uint8(ind2rgb(X, map));
% After image is a grayscale image
im2 = rgb2gray(im);
im2 = cat(3, im2, im2, im2);
% Declare line image
rows = size(im, 1); cols = size(im, 2);
width = 5;
m = ceil(sqrt(rows*rows + cols*cols + width*width));
ln = false([m m]);
mhalf = floor(m / 2); % Find halfway point width wise and draw the line
ln(:,mhalf - floor(width/2) : mhalf + floor(width/2)) = true;
% Rotate the line image
ang = 20; % 20 degrees
lnrotate = imrotate(ln, ang, 'crop');
% Crop the image so that it's the same dimensions as the originals
mrowstart = mhalf - floor(rows/2);
mcolstart = mhalf - floor(cols/2);
lnfinal = lnrotate(mrowstart : mrowstart + rows - 1, mcolstart : mcolstart + cols - 1);
% Make the masks
mask1 = imfill(lnfinal, [1 1]);
mask2 = ~mask1;
mask1(lnfinal) = false;
mask2(lnfinal) = false;
% Make sure the masks have as many channels as the original
mask1 = repmat(mask1, [1 1 size(im,3)]);
mask2 = repmat(mask2, [1 1 size(im,3)]);
% Do the same for the line
lnfinal = repmat(lnfinal, [1 1 size(im, 3)]);
% Specify output image
out = zeros(size(im), class(im));
out(mask1) = im(mask1);
out(mask2) = im2(mask2);
out(lnfinal) = 255;
% Show the image
figure;
imshow(out);
We get:
If you want the line to go in the other direction, simply make the angle ang negative. In the example script above, I've made the angle 20 degrees counter-clockwise (i.e. positive). To reproduce the example you gave, specify -20 degrees instead. I now get this image:
Here's a solution using polygons:
function q44310306
% Load some image:
I = imread('peppers.png');
B = rgb2gray(I);
lt = I; rt = B;
% Specify the boundaries of the white line:
width = 2; % [px]
offset = 13; % [px]
sz = size(I);
wlb = [floor(sz(2)/2)-offset+[0,width]; ceil(sz(2)/2)+offset-[width,0]];
% [top-left, top-right; bottom-left, bottom-right]
% Configure two polygons:
leftPoly = struct('x',[1 wlb(1,2) wlb(2,2) 1], 'y',[1 1 sz(1) sz(1)]);
rightPoly = struct('x',[sz(2) wlb(1,1) wlb(2,1) sz(2)],'y',[1 1 sz(1) sz(1)]);
% Define a helper grid:
[XX,YY] = meshgrid(1:sz(2),1:sz(1));
rt(inpolygon(XX,YY,leftPoly.x,leftPoly.y)) = intmin('uint8');
lt(repmat(inpolygon(XX,YY,rightPoly.x,rightPoly.y),1,1,3)) = intmin('uint8');
rt(inpolygon(XX,YY,leftPoly.x,leftPoly.y) & ...
inpolygon(XX,YY,rightPoly.x,rightPoly.y)) = intmax('uint8');
final = bsxfun(#plus,lt,rt);
% Plot:
figure(); imshow(final);
The result:
One solution:
im1 = imread('peppers.png');
im2 = repmat(rgb2gray(im1),1,1,3);
imgsplitter(im1,im2,80) %imgsplitter(image1,image2,angle [0-100])
function imgsplitter(im1,im2,p)
s1 = size(im1,1); s2 = size(im1,2);
pix = floor(p*size(im1,2)/100);
val = abs(pix -(s2-pix));
dia = imresize(tril(ones(s1)),[s1 val]);
len = min(abs([0-pix,s2-pix]));
if p>50
ind = [ones(s1,len) fliplr(~dia) zeros(s1,len)];
else
ind = [ones(s1,len) dia zeros(s1,len)];
end
ind = uint8(ind);
imshow(ind.*im1+uint8(~ind).*im2)
hold on
plot([pix,s2-pix],[0,s1],'w','LineWidth',1)
end
OUTPUT:

Matlab transparent overlay matrix

I want to load an image and then create a Matrix with the size of the image.
The Matrix should be transparent with only some spare values (points).
I then want to show the image in a figure and put the Matrix on top.
The code so far:
world = imread('map1.jpg'); % import image of location
[x_world,y_world] = size(world); % get the size of the image
A = zeros(x_world,y_world); % create matrix with dimension of image
imshow(world); % display image
axis image; % label the axis
My Matrix contains some points:
A(200,300) = 1;
A(500,500) = 5;
A(580,200) = 3;
if I now iterate through each value in the Matrix like that:
for i = 1:x_world
for j = 1:y_world
if(A(i,j) == 1)
plot(i,j,'r.','MarkerSize',20); % plot a single point
elseif(A(i,j) == 2)
plot(i,j,'y.','MarkerSize',20); % plot a single point
elseif(A(i,j) == 3)
plot(i,j,'m.','MarkerSize',20); % plot a single point
elseif(A(i,j) == 4)
plot(i,j,'g.','MarkerSize',20); % plot a single point
elseif(A(i,j) == 5)
plot(i,j,'b.','MarkerSize',20); % plot a single point
elseif(A(i,j) == 6)
plot(i,j,'w.','MarkerSize',20); % plot a single point
end
end
end
it would be really slow.
So what I want to do is create a transparent Matrix and then set some points, so that I just can print the Matrix over the original image.
Is that possible? How do I do that? Is there maybe another better way to do that?
As a start, you could avoid looping over all of theese rows and columns by actually looping over your 6 groups. The code blow should give the same result:
markers = {'r.', 'y.', 'm.', 'g.', 'b.', 'w.'}; % // define some markers
figure
hold on
for group = 1:6
[i, j] = ind2sub(size(A), find(A==group)); % // find indices of current group
plot(i, j, markers{group}, 'markersize', 20) % // plot them with their marker
end
If speed is an issue, you maybe can have a look at gscatter() and or sparse().

converting rgb image to double and keeping the values in matlab

I have an image and I want to import this image to matlab. I am using the following code. The problem that I have is that when I convert the image to grayscale, everything will be changed and the converted image is not similar to original one. In another words, I want to keep the values (or let say the image) as it is in the original image. Is there any way for doing this?
I = imread('myimage.png');
figure, imagesc(I), axis equal tight xy
I2 = rgb2gray(I);
figure, imagesc(I2), axis equal tight xy
Your original image is already using a jet colormap. The problem is, when you convert it to grayscale, you lose some crucial information. See the image below.
In the original image you have a heatmap. Blue areas generally indicate "low value", whereas red areas indicate "high values". But when converted to grayscale, both areas indicate low value, as they aproach dark pixels (see the arrows).
A possible solution is this:
You take every pixel of your image, find the nearest (closest)
color value in the jet colormap and use its index as a gray value.
I will show you first the final code and the results. The explanation goes below:
I = im2double(imread('myimage.png'));
map = jet(256);
Irgb = reshape(I, size(I, 1) * size(I, 2), 3);
Igray = zeros(size(I, 1), size(I, 2), 'uint8');
for ii = 1:size(Irgb, 1)
[~, idx] = min(sum((bsxfun(#minus, Irgb(ii, :), map)) .^ 2, 2));
Igray(ii) = idx - 1;
end
clear Irgb;
subplot(2,1,1), imagesc(I), axis equal tight xy
subplot(2,1,2), imagesc(Igray), axis equal tight xy
Result:
>> whos I Igray
Name Size Bytes Class Attributes
I 110x339x3 894960 double
Igray 110x339 37290 uint8
Explanation:
First, you get the jet colormap, like this:
map = jet(256);
It will return a 256x3 colormap with the possible colors on the jet palette, where each row is a RGB pixel. map(1,:) would be kind of a dark blue, and map(256,:) would be kind of a dark red, as expected.
Then, you do this:
Irgb = reshape(I, size(I, 1) * size(I, 2), 3);
... to turn your 110x339x3 image into a 37290x3 matrix, where each row is a RGB pixel.
Now, for each pixel, you take the Euclidean distance of that pixel to the map pixels. You take the index of the nearest one and use it as a gray value. The minus one (-1) is because the index is in the range 1..256, but a gray value is in the range 0..255.
Note: the Euclidean distance takes a square root at the end, but since we are just trying to find the closest value, there is no need to do so.
EDIT:
Here is a 10x faster version of the code:
I = im2double(imread('myimage.png'));
map = jet(256);
[C, ~, IC] = unique(reshape(I, size(I, 1) * size(I, 2), 3), 'rows');
equiv = zeros(size(C, 1), 1, 'uint8');
for ii = 1:numel(equiv)
[~, idx] = min(sum((bsxfun(#minus, C(ii, :), map)) .^ 2, 2));
equiv(ii) = idx - 1;
end
Irgb = reshape(equiv(IC), size(I, 1), size(I, 2));
Irgb = Irgb(end:-1:1,:);
clear equiv C IC;
It runs faster because it exploits the fact that the colors on your image are restricted to the colors in the jet palette. Then, it counts the unique colors and only match them to the palette values. With fewer pixels to match, the algorithm runs much faster. Here are the times:
Before:
Elapsed time is 0.619049 seconds.
After:
Elapsed time is 0.061778 seconds.
In the second image, you're using the default colormap, i.e. jet. If you want grayscale, then try using colormap(gray).

How can I draw a circle on an image in MATLAB?

I have an image in MATLAB:
im = rgb2gray(imread('some_image.jpg');
% normalize the image to be between 0 and 1
im = im/max(max(im));
And I've done some processing that resulted in a number of points that I want to highlight:
points = some_processing(im);
Where points is a matrix the same size as im with ones in the interesting points.
Now I want to draw a circle on the image in all the places where points is 1.
Is there any function in MATLAB that does this? The best I can come up with is:
[x_p, y_p] = find (points);
[x, y] = meshgrid(1:size(im,1), 1:size(im,2))
r = 5;
circles = zeros(size(im));
for k = 1:length(x_p)
circles = circles + (floor((x - x_p(k)).^2 + (y - y_p(k)).^2) == r);
end
% normalize circles
circles = circles/max(max(circles));
output = im + circles;
imshow(output)
This seems more than somewhat inelegant. Is there a way to draw circles similar to the line function?
You could use the normal PLOT command with a circular marker point:
[x_p,y_p] = find(points);
imshow(im); %# Display your image
hold on; %# Add subsequent plots to the image
plot(y_p,x_p,'o'); %# NOTE: x_p and y_p are switched (see note below)!
hold off; %# Any subsequent plotting will overwrite the image!
You can also adjust these other properties of the plot marker: MarkerEdgeColor, MarkerFaceColor, MarkerSize.
If you then want to save the new image with the markers plotted on it, you can look at this answer I gave to a question about maintaining image dimensions when saving images from figures.
NOTE: When plotting image data with IMSHOW (or IMAGE, etc.), the normal interpretation of rows and columns essentially becomes flipped. Normally the first dimension of data (i.e. rows) is thought of as the data that would lie on the x-axis, and is probably why you use x_p as the first set of values returned by the FIND function. However, IMSHOW displays the first dimension of the image data along the y-axis, so the first value returned by FIND ends up being the y-coordinate value in this case.
This file by Zhenhai Wang from Matlab Central's File Exchange does the trick.
%----------------------------------------------------------------
% H=CIRCLE(CENTER,RADIUS,NOP,STYLE)
% This routine draws a circle with center defined as
% a vector CENTER, radius as a scaler RADIS. NOP is
% the number of points on the circle. As to STYLE,
% use it the same way as you use the rountine PLOT.
% Since the handle of the object is returned, you
% use routine SET to get the best result.
%
% Usage Examples,
%
% circle([1,3],3,1000,':');
% circle([2,4],2,1000,'--');
%
% Zhenhai Wang <zhenhai#ieee.org>
% Version 1.00
% December, 2002
%----------------------------------------------------------------
Funny! There are 6 answers here, none give the obvious solution: the rectangle function.
From the documentation:
Draw a circle by setting the Curvature property to [1 1]. Draw the circle so that it fills the rectangular area between the points (2,4) and (4,6). The Position property defines the smallest rectangle that contains the circle.
pos = [2 4 2 2];
rectangle('Position',pos,'Curvature',[1 1])
axis equal
So in your case:
imshow(im)
hold on
[y, x] = find(points);
for ii=1:length(x)
pos = [x(ii),y(ii)];
pos = [pos-0.5,1,1];
rectangle('position',pos,'curvature',[1 1])
end
As opposed to the accepted answer, these circles will scale with the image, you can zoom in an they will always mark the whole pixel.
Hmm I had to re-switch them in this call:
k = convhull(x,y);
figure;
imshow(image); %# Display your image
hold on; %# Add subsequent plots to the image
plot(x,y,'o'); %# NOTE: x_p and y_p are switched (see note below)!
hold off; %# Any subsequent plotting will overwrite the image!
In reply to the comments:
x and y are created using the following code:
temp_hull = stats_single_object(k).ConvexHull;
for k2 = 1:length(temp_hull)
i = i+1;
[x(i,1)] = temp_hull(k2,1);
[y(i,1)] = temp_hull(k2,2);
end;
it might be that the ConvexHull is the other way around and therefore the plot is different. Or that I made a mistake and it should be
[x(i,1)] = temp_hull(k2,2);
[y(i,1)] = temp_hull(k2,1);
However the documentation is not clear about which colum = x OR y:
Quote: "Each row of the matrix contains the x- and y-coordinates of one vertex of the polygon. "
I read this as x is the first column and y is the second colum.
In newer versions of MATLAB (I have 2013b) the Computer Vision System Toolbox contains the vision.ShapeInserter System object which can be used to draw shapes on images. Here is an example of drawing yellow circles from the documentation:
yellow = uint8([255 255 0]); %// [R G B]; class of yellow must match class of I
shapeInserter = vision.ShapeInserter('Shape','Circles','BorderColor','Custom','CustomBorderColor',yellow);
I = imread('cameraman.tif');
circles = int32([30 30 20; 80 80 25]); %// [x1 y1 radius1;x2 y2 radius2]
RGB = repmat(I,[1,1,3]); %// convert I to an RGB image
J = step(shapeInserter, RGB, circles);
imshow(J);
With MATLAB and Image Processing Toolbox R2012a or newer, you can use the viscircles function to easily overlay circles over an image. Here is an example:
% Plot 5 circles at random locations
X = rand(5,1);
Y = rand(5,1);
% Keep the radius 0.1 for all of them
R = 0.1*ones(5,1);
% Make them blue
viscircles([X,Y],R,'EdgeColor','b');
Also, check out the imfindcircles function which implements the Hough circular transform. The online documentation for both functions (links above) have examples that show how to find circles in an image and how to display the detected circles over the image.
For example:
% Read the image into the workspace and display it.
A = imread('coins.png');
imshow(A)
% Find all the circles with radius r such that 15 ≤ r ≤ 30.
[centers, radii, metric] = imfindcircles(A,[15 30]);
% Retain the five strongest circles according to the metric values.
centersStrong5 = centers(1:5,:);
radiiStrong5 = radii(1:5);
metricStrong5 = metric(1:5);
% Draw the five strongest circle perimeters.
viscircles(centersStrong5, radiiStrong5,'EdgeColor','b');
Here's the method I think you need:
[x_p, y_p] = find (points);
% convert the subscripts to indicies, but transposed into a row vector
a = sub2ind(size(im), x_p, y_p)';
% assign all the values in the image that correspond to the points to a value of zero
im([a]) = 0;
% show the new image
imshow(im)

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