Does MATLAB have a built-in function to find general properties like center of mass & moments of inertia for a polygon defined as a list of (non-integer valued) points?
regionprops performs this task for integer valued points, on the assumption that these represent indices of pixels in an image. But the only functions I can find that treat non integral point lists are polyarea and inpolygon.
My kludge for now is to create a bwconncomp structure with all the points multiplied by some large value (like 10,000), then feeding it in to regionprops, but wondered if there is a more elegant solution.
You should check out the submission POLYGEOM by H.J. Sommer on the MathWorks File Exchange. It looks like it has all the property measurements you want, and nice documentation describing the formulae used in the code.
I don't know of a function in MATLAB that would do this for you.
However, poly2mask might be of use for you to create the pixel masks to feed into regionprops. I also suggest that, should you decide to go this route, you carefully test how much the discretization affects the results, so that you don't create crazy large arrays (and waste time) for no real gain in accuracy.
One possibility is to farm out the calculations to the Java Topology Suite. I don't know about "moments of inertia", but it does at least have a centroid method.
Related
I am trying to implement the algorithm for estimating the fundamental matrix between two images using RANSAC. So far I have found the interest points using Harris corner detection. I am stuck at computing the putative correspondences using these interest points. I don't want to use matlab toolbox for that , I like to know a way to learn about corresponding point extraction from two images and it's implementation. I have read about block matching but have not completely understood the concept of it. Any samples and guidelines would help me to understand this problem better.
Thanks in advance.
There are many ways to search for corresponding interest points, but they're usually based on describing each of these interest points using the characteristics of the image around them, and, for each point in one image, comparing its surrounding's characteristics to the characteristics of the surroundings of other interest points in the other image.
Now assume you've decided to consider only a squared region (a block) around each point of interest that contains the intensity values of the image around the point. Now you can compare these blocks, and match those that are close to each other. The problem is now how to define "close" or, in other words, how to define the distance metric you'll use to compare these blocks.
There are many approaches, for example, you could use the sum-of-absolute-differences between two blocks, which means you could subtract two blocks, take the absolute value of the resulting block, and then sum all values in this resulting block, obtaining a scalar value which represents how close these blocks are. If this distance is less than a given threshold, you can consider the two blocks a match. This is basically what block matching does.
Similarly, you could define other types of regions to describe your points of interes, for example by changing their shapes, sizes, orientations etc, and create more complex descriptors for these points of interest, which might capture more distinguishable characteristics (which is highly desired if you have the purpose of matching them later).
If you want to learn more about the topic, I think this presentation can get you started:
http://courses.cs.washington.edu/courses/cse455/09wi/Lects/lect6.pdf
In my project i deal with big data surfaces.
In a certain point, i have a line across the data, and I need the values of the points of the line.
The grid is non,homogeneous, it doesnt go from n:m with fixed steps nor nothing.
Lets ilustrate!
In the figure the 2D proyection of my data can be seen. Each of the points has also other 3 data information. I defined a arbitrary red line with the form y=ax+b. a and b are known.
How can I define i.e. 50 points in the line that has not only the x and y coords (wich is straigforward) but also the interpolation of the 3 data information of each of the points around it.
I know is not an easy question but I can't seem to step forward even a bit.
PD: realize I DONT want code written for me, but the idea of how to achieve my objective.
You could use a tool like triScatteredInterp, which will triangulate the 2-d domain, then interpolate a list of points along your line. Griddata is also an option.
I have a toolbox for problems like this (of course.) It allows me to build a triangulation of the non-convex domain in the (x,y) plane. Then it can form a completely general slice through that surface, interpolating in z also as it does so. The result will be a 1-manifold, in this case a piecewise linear function along that path in (x,y,z). While those tools are not posted on the file exchange, they are available for the person willing to invest the time to learn to use them.
If the surface you describe is a completely general one in 3-d, that might be fairly complex, then you might need a CRUST based tool to define that surface triangulation. These can be found online too. Once a triangulation is available, my tools can then be used to slice them. (Sorry, I never did finish that piece.)
What I did was to define several points in the crack line and then cheack for each one of them in wich quadrilateral it is with inpoligon matlab function (no tthe fastest way but less than 2 secs).
Then I created a triangular plane in the used quadrilaterals using x,y and Z or the othre data , achieving a linear interpolation between the data.
finally i take out all the points that are 0 o Nan.
I have about 100 data points which mostly satisfying a certain function (but some points are off). I would like to plot all those points in a smooth curve but the problem is the points are not uniformly distributed. So is that anyway to get the smooth curve? I am thinking to interpolate some points in between, but the only way that comes up to my mind is to linearly insert some artificial points between two data points. But that will show a pretty weird shape (like some sharp corner). So any better idea? Thanks.
If you know more or less what the actual curve should be, you can try to fit that curve to your points (e.g. using polyfit). Depending on how many points are off and how far, you can get by with least squares regression (which is fairly easy to get working). If you have too many outliers (or they are much too large/small), you can also try robust regression (e.g. least absolute deviation fitting) using the robustfit function.
If you can manually determine the outliers, you can also fit a curve through the other points to get better results or even use interpolation methods (e.g. interp1 in MATLAB) on those points to get a smoother curve.
If you know which function describes your data, robust fitting (using, e.g. ROBUSTFIT, or the new convenient functions LINEARMODEL and NONLINEARMODEL with the robust option) is a good way to go if there are outliers in your data.
If you don't know the function that describes your data, but want a smooth trendline that is little affected by outliers, SMOOTHN from the File Exchange does an excellent job in my experience.
Have you looked at the use of smoothing splines? Like interpolating splines, but with the knot points and coefficients chosen to minimise a least-squares error function. There is an excellent implementation available from Matlab central which I have used successfully.
I need to construct an interpolating function from a 2D array of data. The reason I need something that returns an actual function is, that I need to be able to evaluate the function as part of an expression that I need to numerically integrate.
For that reason, "interp2" doesn't cut it: it does not return a function.
I could use "TriScatteredInterp", but that's heavy-weight: my grid is equally spaced (and big); so I don't need the delaunay triangularisation.
Are there any alternatives?
(Apologies for the 'late' answer, but I have some suggestions that might help others if the existing answer doesn't help them)
It's not clear from your question how accurate the resulting function needs to be (or how big, 'big' is), but one approach that you could adopt is to regress the data points that you have using a least-squares or Kalman filter-based method. You'd need to do this with a number of candidate function forms and then choose the one that is 'best', for example by using an measure such as MAE or MSE.
Of course this requires some idea of what the form underlying function could be, but your question isn't clear as to whether you have this kind of information.
Another approach that could work (and requires no knowledge of what the underlying function might be) is the use of the fuzzy transform (F-transform) to generate line segments that provide local approximations to the surface.
The method for this would be:
Define a 2D universe that includes the x and y domains of your input data
Create a 2D fuzzy partition of this universe - chosing partition sizes that give the accuracy you require
Apply the discrete F-transform using your input data to generate fuzzy data points in a 3D fuzzy space
Pass the inverse F-transform as a function handle (along with the fuzzy data points) to your integration function
If you're not familiar with the F-transform then I posted a blog a while ago about how the F-transform can be used as a universal approximator in a 1D case: http://iainism-blogism.blogspot.co.uk/2012/01/fuzzy-wuzzy-was.html
To see the mathematics behind the method and extend it to a multidimensional case then the University of Ostravia has published a PhD thesis that explains its application to various engineering problems and also provides an example of how it is constructed for the case of a 2D universe: http://irafm.osu.cz/f/PhD_theses/Stepnicka.pdf
If you want a function handle, why not define f=#(xi,yi)interp2(X,Y,Z,xi,yi) ?
It might be a little slow, but I think it should work.
If I understand you correctly, you want to perform a surface/line integral of 2-D data. There are ways to do it but maybe not the way you want it. I had the exact same problem and it's annoying! The only way I solved it was using the Surface Fitting Tool (sftool) to create a surface then integrating it.
After you create your fit using the tool (it has a GUI as well), it will generate an sftool object which you can then integrate in (2-D) using quad2d
I also tried your method of using interp2 and got the results (which were similar to the sfobject) but I had no idea how to do a numerical integration (line/surface) with the data. Creating thesfobject and then integrating it was much faster.
It was the first time I do something like this so I confirmed it using a numerically evaluated line integral. According to Stoke's theorem, the surface integral and the line integral should be the same and it did turn out to be the same.
I asked this question in the mathematics stackexchange, wanted to do a line integral of 2-d data, ended up doing a surface integral and then confirming the answer using a line integral!
I am looking for numerical integration with matlab. I know that there is a trapz function in matlab but the precision is not good enough. By searching it online, I found there is a quad function there it seems only accept symbolic expression as input. My data is all discrete and one-dimensional. Is that any way to use quad on my data? Thanks.
An answer to your question would be no. The only way to perform numerical integration for data with no expression in Matlab is by using the trapz function. If it's not accurate enough for you, try writing your own quad function as Li-aung said, it's very simple, this may help.
Another method you may try is to use the powerful Curve Fitting Tool cftool to make a fit then use the integrate function which can operate on cfit objects (it has a weird convention, the upper limit is the first argument!). I don't think you will get much accurate answers than trapz, it depends on the fit.
Use the spline function in MATLAB to interpolate your data, then integrate this data. This is the standard method for integrating data in discrete form.
You can use quadl() to integrate your data if you first create a function in which you interpolate them.
function f = int_fun(x,xdata,ydata)
f = interp1(xdata,ydata,x);
And then feed it to the quadl() function:
integral = quadl(#int_fun,A,B,[],[],x,y) % syntax to pass extra arguments
% to the function
Integration of a function of one variable is the computation of the area under the curve of the graph of the function. For this answer I'll leave aside the nasty functions and the corner cases and all the twists and turns that trip up writers of numerical integration routines, most of which are probably not relevant here.
Simpson's rule is an approach to the numerical integration of a function for which you have a code to evaluate the function at points within its domain. That's irrelevant here.
Let's suppose that your data represents a time series of values collected at regular intervals. Then you can plot your data as a histogram with bars of equal width. The integrand you seek is the sum of the areas of the bars in the histogram between the limits you are interested in.
You should be able to apply this approach to data sets where the x-axis (ie the width of the bars in the histogram) does not show time, to the situation where the bars are not of equal width, to the situation where the data crosses the x-axis, and most reasonable data sets, quite easily.
The discretisation of your data establishes a limit to the accuracy of the result you can get. If, for example, your time series is sampled at 1sec intervals you can't integrate over an interval which is not a whole number of seconds by this approach. But then, you don't really have the data on which to compute a figure with any more accuracy by any approach. Sure, you can use Matlab (or anything else) to generate extra digits of precision but they don't carry any meaning.