I would like to find a better way of fitting my data. Right now, that it the best I can do, see Figure.
It's done using Gnuplot and smooth when plotting. However, as you might see in the Figure, 'csplines' seems to be the most acuarate technique, but it is not enough. It is fine in the first half of the graph, but not good at all in the second half.
The real data, just 4 points in 'x=[1,2,4,8]', is marked in 'Line 1'. Is there a better way of doing it using Gnuplot?
What about Matlab (or even other tools)? How can I easily create a smooth curve connecting a few points?
Why not have a look at the scipy interpolation documentation:
http://docs.scipy.org/doc/scipy/reference/tutorial/interpolate.html
There are plenty of schemes there which will help you plot your smoothed data using matplotib.
HTH
Related
I would like to follow a curve (with matlab or opencv) and to find the other end of it when it is cut by an empty space like this example, which is simplified to illustrate the problem:
Link to image of cut curve
Real images are more like this one: Link to real image to analyse
To follow the curve, I can use a skeleton and look at the neighbourhood. The problem is that I don't know how to find the other end efficiently.
I don't think that closing or opening operations could help because as shown on the previous image, there are other curves and the two parts of the curve are quite far from each other so it could lead to boundaries between the different curves instead of the two parts.
I was thinking about polynomial evaluation which could be a solution for simple curves but I am not sure about the precision I could get. If I use a skeleton, I have to find exactly the right pixel or to search in a reasonable neighbourhood which would take some time and once again, as there are other curves in the images, I have to be sure that I will find the good one.
That's why I am searching for an existing function which could estimate precisely the trajectory of the curve and give an usefull output to go further and find the second part of the curve.
If that kind of function doesn't exist, I'm open to any other way of analysing the problem if it can help.
I will start to explain with the first image you provided, you can implement common OpenCV function useful for detecting contour(black region in your case as you have binary image) known as cv2.findContours(), which returns the coordinates of the edges of the surface detected then you can plot each detected contour separately in a blank image to get the edge of your desired line.
Now coming to your 2nd image you have to be slightly careful while performing above analysis as there are many tiny lines. get back to me for further help
I got this data curve.
Because it's real data it's kind of shaky.
I want to differentiate the curve... this looks pretty ugly because of the shakyness.
So I went on and used ployfit and polyval to smooth the curve. As this doesn't resemble a ploynomal curve, I needed to split this curve in three and smooth them all separately and later fit them together again.
But polyval tend to overdo the edges... (the smooth one in red, the original in blue)
so when I add them together I get non smooth junctions like this one here: (I know this is extreme, but it accurs always)
when I later differentiate the curve, I get huge errors at the junctions:
any ideas to solve my problem?
I do need a clean curve for calculations and so on...
Edit
I implemented the comments:
here the results
spline isn't smooth enough for differentiation,
Savitzky-Golay Filter also not perfect
I have 8 plots which I want to implement in my Matlab code. These plots originate from several research papers, hence, I need to digitize them first in order to be able to use them.
An example of a plot is shown below:
This is basically a surface plot with three different variables. I know how to digitize a regular plot with just X and Y coordinates. However, how would one digitize a graph like this? I am quite unsure, hence, the question.
Also, If I would be able to obtain the data from this plot. How would you be able to utilize it in your code? Maybe with some interpolation and extrapolation between the given data points?
Any tips regarding this topic are welcome.
Thanks in advance
Here is what I would suggest:
Read the image in Matlab using imread.
Manually find the pixel position of the left bottom corner and the upper right corner
Using these pixels values and the real numerical value, it is simple to determine the x and y value of every pixel. I suggest you use meshgrid.
Knowing that the curves are in black, then remove every non-black pixel from the image, which leaves you only with the curves and the numbers.
Then use the function bwareaopen to remove the small objects (the numbers). Don't forget to invert the image to remove the black instead of the white.
Finally, by using point #3 and the result of point #6, you can manually extract the data of the graph. It won't be easy, but it will be feasible.
You will need the data for the three variables in order to create a plot in Matlab, which you can get either from the previous research or by estimating and interpolating values from the plot. Once you get the data though, there are two functions that you can use to make surface plots, surface and surf, surf is pretty much the same as surface but includes shading.
For interpolation and extrapolation it sounds like you might want to check out 2D interpolation, interp2. The interp2 function can also do extrapolation as well.
You should read the documentation for these functions and then post back with specific problems if you have any.
I am trying to detect corners (x/y coordinates) in 2D scatter vectors of data.
The data is from a laser rangefinder and our current platform uses Matlab (though standalone programs/libs are an option, but the Nav/Control code is on Matlab so it must have an interface).
Corner detection is part of a SLAM algorithm and the corners will serve as the landmarks.
I am also looking to achieve something close to 100Hz in terms of speed if possible (I know its Matlab, but my data set is pretty small.)
Sample Data:
[Blue is the raw data, red is what I need to detect. (This view is effectively top down.)]
[Actual vector data from above shots]
Thus far I've tried many different approaches, some more successful than others.
I've never formally studied machine vision of any kind.
My first approach was a homebrew least squares line fitter, that would split lines in half resurivly until they met some r^2 value and then try to merge ones with similar slope/intercepts. It would then calculate the intersections of these lines. It wasn't very good, but did work around 70% of the time with decent accuracy, though it had some bad issues with missing certain features completely.
My current approach uses the clusterdata function to segment my data based on mahalanobis distance, and then does basically the same thing (least squares line fitting / merging). It works ok, but I'm assuming there are better methods.
[Source Code to Current Method] [cnrs, dat, ~, ~] = CornerDetect(data, 4, 1) using the above data will produce the locations I am getting.
I do not need to write this from scratch, it just seemed like most of the higher-class methods are meant for 2D images or 3D point clouds, not 2D scatter data. I've read a lot about Hough transforms and all sorts of data clustering methods (k-Means etc). I also tried a few canned line detectors without much success. I tried to play around with Line Segment Detector but it needs a greyscale image as an input and I figured it would be prohibitivly slow to convert my vector into a full 2D image to feed it into something like LSD.
Any help is greatly appreciated!
I'd approach it as a problem of finding extrema of curvature that are stable at multiple scales - and the split-and-merge method you have tried with lines hints at that.
You could use harris corner detector for detecting corners.
I have a list of 200 points I garnered from a graph digitization software I would like to transform into a smooth curve and then into Solidworks.
My points form an ellipse (airfoil shape to be more precise), so the commands I've tried in Matlab didn't have a circular curve.
My issues are:
* Obtaining a smooth curve that doesn't necessarily pass through all points, smooth being motus operandi.
* Being able to have a elliptical curve
* Somehow being able to export this curve into Solidwords
If anyone knows the right software, command line or anything that could get me started, I would be extremely thankful.
imacube
I've used Solid Works before. It's a very powerful tool. There should be some way to draw a curved spline through these points, such as a cubic spline.
If you are using a standard(ish) airfoil, then you can use a variety of tools to plot the points without having to use a graph digitization software.
Javafoil, for instance, is one of those. Even if you know the characteristics of your airfoil, you can use this to give you a smooth set of points.
Again, if your airfoil is a naca 4-series, then these are governed by a set of equations.
But I take it that the airfoil you want a more complicated one. Let me know if I can help anymore.