I have an unknown scalar fonction defined into a partial space (a pyramid portion), for this function, I have several measurements points into the coordonates mesurePoints, where the mesure mesure is known :
size(mesurePoints) = [n 3]
size(mesure) = n
I also have my space discretized into a clood of equidistant points wich I'll call interpolPoints,
I would like to obtain interpolated values interp_mesure on the points interpolPoints based on my measurements mesure on the points mesurePoints.
I tried to use interp3,
interp_mesure = interp3(...
mesurePoints(:,1),mesurePoints(:,2),mesurePoints(:,2),...
mesure,...
interpolPoints(:,1),interpolPoints(:,2),interpolPoints(:,3));
but I get the error that V (mesure) should be a 3D array, but I am confuse, my data isn't 3D, it is 3D dependant, but it's a scalar data, how can I proceed? Is interpol3 not adapted to my problem?
Edit 1 : Here is a similar problem to illustrate mine : how do you interpolate temperature in a volume if you have some temperature measurements in this volume?
Edit 2 : as no matlab solution have come to mind yet, I use a hand-made interpolation weighted by inverse distance with a power factor, the result is good close to points but as my points are quite scattered, the result is not good in empty areas.
I'm having trouble understanding exactly what is your data, but I get the impression that maybe interp1 or interp2 would be better suited to your needs, as your data isn't organized as a 3-D array
Related
I have a huge set of data of a timelapse of 2D laser scans of waves running up and down stairs (see fig.1fig.2fig.3).
There is a lot of noise in the scans, since the water splashes a lot.
Now I want to smoothen the scans.
I have 2 questions:
How do I apply a moving median filter (as recommended by another study dealing with a similar problem)? I can only find instructions for single e.g. (x,y) or (t,y) plots but not for x and y values that vary over time. Maybe an average filter would do it as well, but I do not have a clue on that either.
The scanner is at a fixed point (222m) so all the data spikes point towards that point at the ceiling. Is it possible or necessary to include this into the smoothing process?
This is the part of the code (I hope it's enough to get it):
% Plot data as real time profile
x1=data.x;y1=data.y;
t=data.t;
% add moving median filter here?
h1=plot(x1(1,:),y1(1,:));
axis([210 235 3 9])
ht=title('Scanner data');
for i=1:1:length(t);
set(h1,'XData',x1(i,:),'YData',y1(i,:));set(ht,'String',sprintf('t = %5.2f
s',data.t(i)));pause(.01);end
The data.x values are stored in a (mxn) matrix in which the change in time is arranged vertically and the x values i.e. "laser points" of the scanner are horizontally arranged. The data.y is stored in the same way. The data.t values are stored in a (mx1) matrix.
I hope I explained everything clearly and that somebody can help me. I am already pretty desperate about it... If there is anything missing or confusing, please let me know.
If you're trying to apply a median filter in the x-y plane, then consider using medfilt2 from the Image Processing Toolbox. Note that this function only accepts 2-D inputs, so you'll have to loop over the third dimension.
Also note that medfilt2 assumes that the x and y data are uniformly spaced, so if your x and y data don't fall onto a uniformly spaced grid you may have to manually loop over indices, extract the corresponding patches, and compute the median.
If you can/want to apply an averaging filter instead of a median filter, and if you have uniformly spaced data, then you can use convn to compute a k x k moving average by doing:
y = convn(x, ones(k,k)/(k*k), 'same');
Note that you'll get some bias on the boundaries because you're technically trying to compute an average of k^2 pixels when you have less than that number of values available.
Alternatively, you can use nested calls to movmean since the averaging operation is separable:
y = movmean(movmean(x, k, 2), k, 1);
If your grid is separable, but not uniform, you can still use movmean, just use the SamplePoints name-value pair:
y = movmean(movmean(x, k, 2, 'SamplePoints', yv), k, 1, 'SamplePoints', xv);
You can also control the endpoint handling in movmean with the Endpoints name-value pair.
I am kind of new to analyzing circular data and I have a quite complex problem.
I'm trying to correlate 2 multidimensional vectors (N observations x 2 dimensions) where one dimension is circular (i.e. angles in radians).
I have found the corr2 function for 2D correlations which seems to work fine (http://www.mathworks.com/help/images/ref/corr2.html), I am however uncertain if I can use it on circular data (there isn't much information on it in the Matlab Documentation).
I found documentation on the Origin software which states that the correlations can be circular (http://www.originlab.com/doc/Origin-Help/2D-Correlation) but I have no idea if it this generalizes to Malab.
I tried two approaches:
1- I input the linear and circular data as is:
r = corr2([Theta_X Amplitude_X], [Theta_Y Amplitude_Y]);
which yields very good results but I am unsure if they are valid.
2- I "linearized" the data by converting the polar coordinates into Cartesian (pol2cart):
r = corr2([x_X y_X], [x_Y y_Y]);
which yields noisier results.
My question is thus: can I use the corr2 function on circular data? If not, can anyone point me in the right direction?
I have a list of scattered 3D points similar to the one below:
Using MATLAB, I want to interpolate further points from the surface that those original points correspond to, in order to obtain a more complete scatter. Note that there are no particular slices defined on this scattered data. That is, the z values of the point cloud are not discrete, so it's not possible to interpolate slice by slice.
I think that the ideal way to achieve this would be to somehow obtain the smooth closed surface which best matches the scattered data, and then sample it. But I have found no straightforward way to achieve this.
The scatterinterpolant class could be a simple option.
Use scatteredInterpolant to perform interpolation on a 2-D or 3-D
Scattered Data set. For example, you can pass a set of (x,y) points
and values, v, to scatteredInterpolant, and it returns a surface of
the form v = F(x, y). This surface always passes through the sample
values at the point locations. You can evaluate this surface at any
query point, (xq,yq), to produce an interpolated value, vq.
http://au.mathworks.com/help/matlab/math/interpolating-scattered-data.html
Scattered data consists of a set of points X and corresponding values
V, where the points have no structure or order between their relative
locations. There are various approaches to interpolating scattered
data. One widely used approach uses a Delaunay triangulation of the
points.
As i've explained in a previous question: I have a dataset consisting of a large semi-random collection of points in three dimensional euclidian space. In this collection of points, i am trying to find the point that is closest to the area with the highest density of points.
As high performance mark answered;
the most straightforward thing to do would be to divide your subset of
Euclidean space into lots of little unit volumes (voxels) and count
how many points there are in each one. The voxel with the most points
is where the density of points is at its highest. Perhaps initially
dividing your space into 2 x 2 x 2 voxels, then choosing the voxel
with most points and sub-dividing that in turn until your criteria are
satisfied.
Mark suggested i use triplequad for this, but this is not a function i am familiar with, or understand very well. Does anyone have any pointers on how i could go about using this function in Matlab for what i am trying to do?
For example, say i have a random normally distributed matrix A = randn([300,300,300]), how could i use triplequad to find the point i am looking for? Because as i understand currently, i also have to provide triplequad with a function fun when using it. Which function should that be for this problem?
Here's an answer which doesn't use triplequad.
For the purposes of exposition I define an array of data like this:
A = rand([30,3])*10;
which gives me 30 points uniformly distributed in the box (0:10,0:10,0:10). Note that in this explanation a point in 3D space is represented by each row in A. Now define a 3D array for the counts of points in each voxel:
counts = zeros(10,10,10)
Here I've chosen to have a 10x10x10 array of voxels, but this is just for convenience, it would be only a little more difficult to have chosen some other number of voxels in each dimension, and there don't have to be the same number of voxels along each axis. Then the code
for ix = 1:size(A,1)
counts(ceil(A(ix,1)),ceil(A(ix,2)),ceil(A(ix,3))) = counts(ceil(A(ix,1)),ceil(A(ix,2)),ceil(A(ix,3)))+1
end
will count up the number of points in each of the voxels in counts.
EDIT
Unfortunately I have to do some work this afternoon and won't be able to get back to wrestling with the triplequad solution until later. Hope this is OK in the meantime.
I have a time series of temperature profiles that I want to interpolate, I want to ask how to do this if my data is irregularly spaced.
Here are the specifics of the matrix:
The temperature is 30x365
The time is 1x365
Depth is 30x1
Both time and depth are irregularly spaced. I want to ask how I can interpolate them into a regular grid?
I have looked at interp2 and TriScatteredInterp in Matlab, however the problem are the following:
interp2 works only if data is in a regular grid.
TriscatteredInterp works only if the vectors are column vectors. Although time and depth are both column vectors, temperature is not.
Thanks.
Function Interp2 does not require for a regularly spaced measurement grid at all, it only requires a monotonic one. That is, sampling positions stored in vectors depths and times must increase (or decrease) and that's all.
Assuming this is indeed is the situation* and that you want to interpolate at regular positions** stored in vectors rdepths and rtimes, you can do:
[JT, JD] = meshgrid(times, depths); %% The irregular measurement grid
[RT, RD] = meshgrid(rtimes, rdepths); %% The regular interpolation grid
TemperaturesOnRegularGrid = interp2(JT, JD, TemperaturesOnIrregularGrid, RT, RD);
* : If not, you can sort on rows and columns to come back to a monotonic grid.
**: In fact Interp2 has no restriction for output grid (it can be irregular or even non-monotonic).
I would use your data to fit to a spline or polynomial and then re-sample at regular intervals. I would highly recommend the polyfitn function. Actually, anything by this John D'Errico guy is incredible. Aside from that, I have used this function in the past when I had data on a irregularly spaced 3D problem and it worked reasonably well. If your data set has good support, which I suspect it does, this will be a piece of cake. Enjoy! Hope this helps!
Try the GridFit tool on MATLAB central by John D'Errico. To use it, pass in your 2 independent data vectors (time & temperature), the dependent data matrix (depth) along with the regularly spaced X & Y data points to use. By default the tool also does smoothing for overlapping (or nearly) data points. If this is not desired, you can override this (and other options) through a wide range of configuration options. Example code:
%Establish regularly spaced points
num_points = 20;
time_pts = linspace(min(time),max(time),num_points);
depth_pts = linspace(min(depth),max(depth),num_points);
%Run interpolation (with smoothing)
Pest = gridfit(depth, time, temp, time_pts, depth_pts);