Binning 2D set of coordinates

I'm pretty new to MATLAB, so sorry if this seems easy. I've got a single long trajectory for a particle below. I have about 100,000 X and Y coordinates from which I've assembled the graph. I'm trying to create a density plot of the coordinates to show where the trajectory is most concentrated. I'm trying to create a density plot of the coordinates to show where the trajectory is most concentrated. I've got the second plot using the following code:

bins = 200;
binsizeX = 3/bins;
binsizeY = 1.2/bins;
xbins = -1.5:binsizeX:1.5;
ybins = -0.6:binsizeY:0.6;

[nx,idxx] = histc(X,xbins);
[ny,idxy] = histc(Y,ybins);

out = accumarray([idxx,idxy], 1);
figure(2);
hold on;
h=imagesc(xbins,ybins,out);hold on;
colorbar; hold on;
axis([-1.5 1.5 -0.6 0.6]); hold on;

But it seems that the density is shifted up and to the right for some reason? Any help is appreciated! Thanks!

Answer 1

[alessandro]

Old post, but will try to answer anyway, in case anybody else end up with same issue.

The easiest way to do what you are willing to do is to use hist3 function, with which binning resolution is user dependent and density matrix can be stored easily.

https://www.mathworks.com/help/stats/hist3.html

Answer 2

[Katalin]

imagesc flips the image I think. This is from the help: imagesc(x,y,C) displays C as an image and specifies the bounds of the x- and y-axis with vectors x and y. If x(1) > x(2) or y(1) > y(2), the image is flipped left-right or up-down, respectively.

[Akhil Ghanta]

If that's true why are the axes still going in the proper direction on the plot? Also, for my vectors x(1)<x(2) and y(1)<y(2)

Answer 3

[Image Analyst]

With images, since they are arrays, line 1 (row 1) is at the top, and the line numbers get bigger as you go down the screen. This is the standard custom with images.

With a plot, since it's like regular Cartesian coordinates, where the "y" value increases as it goes up the screen.

The right/left are not flipped, just the up/down. You could use flipud(out) to flip the image vertically before displaying it if you want the plot and image to look similar.

imagesc(xbins, ybins, flipud(out));

[Akhil Ghanta]

Well now, the density is just flipped. The slope of the ellipse is now negative. The big thing is that the density isn't centered like the original trajectory is in the original post.

[Image Analyst]

Is the centroid supposed to be at (0,0)? Please attach your data file with the paper clip icon, along with code to read it in.

Answer 4

[Walter Roberson]

out = accumarray([idxx,idxy], 1);

should be

out = accumarray([idxy,idxx], 1);

Height (y) is expressed as row number so the y index needs to be first.

[Akhil Ghanta]

This did seem to fix the slope of the density ellipse, but it's still not centered on the origin like I'd expect it to be.

[Walter Roberson]

Could you attach the data as a file?