My task at hand is finding specific contours in a cloud of points. They need to be determined as accurately as possible. Therefore higher order polynomial interpolation must be used. I have data consisting of points in a grid, each point having its own height.
I had great success finding contours with matplotlib.contours function. Then I directly used matplotlib.cntr (C++ algorithm) to determine specific contours. But because the file uses marching squares algorithm (linear interpolation) the precision of found contours is not good enough.
I am looking for alternative ways to solve this problem. A suggested solution was to
Use bicubic interpolation to find analytical function around a specific point.
Followed by calculation of the function derivative.
Derived function is then used to determine direction in which derivative stays at 0 (using point as a point of view). By moving a small distance in that direction height should remain constant.
Using this algorithm a contour should be found. Would this algorithm work, can I take any shortcuts when implementing it (by using already implemented functions)?
Implementing this algorithm would take quite the effort on my part, and besides it may only work in theory. I am guessing that the numerical error should still be present (the derivative may not be exactly 0) and may in the end even surpass the current one (using marching squares). I want to consider other, easier and faster methods to solve this problem.
What other algorithm could be used to solve it?
Did anyone ever face a similar problem? How did you solve it?
Related
First of all, sorry if this is rather basic but it is certainly not my field of expertise.
So, I'm working with protein surface and I have this cavity:
Protein cavity
It is part of a larger, watertight, triangular mesh (.ply format) that represents a protein surface.
What I want to do, is find whether this particular "sub-mesh" is found in other proteins. However, I'm not looking for a perfect fit, rather similar "sub-meshes" since the only place I will find this exact shape is in the original protein.
I've been reading the docs for the Python modules trimesh and open3d. Trimesh does have a comparison module, but it doesn't seem to have the functionality I'm looking for. Also, open3d has a "compute point cloud distance" function that is recommended to compare the difference between two point cloud or meshes.
However, since what I'm actually trying to find is similarity, I would need a way to fit my cavity's "sub-mesh" onto the surface of the protein I'm analyzing, and then "score" how different or deformed the fitted submesh is. Another way would be to rotate and translate my sub-mesh to match the most vertices and faces on the protein surface and score that I guess.
Just a heads-up, I'm a biotechnologist, self-taught in Python and with extremely limited experience in anything 3D. At this point, anything helps, be it a paper, Python module or whatever knowledge you have that you think might be useful.
Thank you very much for any help you can provide with this!
I have a problem: I have an expensive to compute 1D function (float->float). I want to approximate it with splines for efficiency.
I know I can define a set of knot points with a uniform grid on the function's domain, evaluate the function on that grid and calculate a spline over that set. But the functions are special - they have huge dull regions and some special places with complex behavior. I want an algorithm that adaptively finds some optimal set of the knot points, sapling them more densely where the function has a difficult shape, and less so when the spline makes a good job in approximating it.
How can I find a library (preferably Python, but at this point I will take anything open source) that does it with an automatic knot selection? I tried many Google searches and still found nothing
I have finally found one, that seems to be working. It's splipy. It's method fit produces a B-Spline interpolation of the function object, with a relatively precise way to control the accuracy of the interpolation.
The source is on GitHub.
I would like to represent a bunch of particles (~100k grains), for which I have the position (including rotation) and a discretized level set function (i.e. the signed distance of every voxel from surface). Due to the large sample, I'm searching for eficient solutions to visualize it.
I first went for vtk, using its python interface, but I'm not really sure if it's the best (and simplest) way to do it since, as far as I know, there is no direct implementation for getting an isosurface from a 3D data set. In the beginning I was thinking usind marching cubes, but then I still would have to use a threshold or to interpolate in order to get the voxels that are on the surface and label them in order to be used by the marching cubes.
Now I found mayavi which has a python function
mlab.pipeline.iso_surface()
I however did not find much documentation on it and was wondering how it behaves in terms of performance.
Does someone have experience with this kind of tools? Which would be the best solution (in terms of efficiency and, secondly, in terms of simplicity - I do not know the vtk library, but if there is a huge difference in performance I can dig into it, also without python interface).
I am working on some code that needs to recognize some fairly basic geometry based on a cloud of nodes. I would be interested in detecting:
plates (simple bounded planes)
cylinders (two node loops)
half cylinders (arc+line+arc+line)
domes (n*loop+top node)
I tried searching for "geometry from node cloud", "get geometry from nodes", but I cant find a nice reference. There is probably a whole field on this, can someone point me the way? i already started coding something, but I feel like re-inventing the wheel...
A good start is to just get the convex hull (the tightest fitting polygon that can surround your node cloud) of the nodes, use either Grahams algorithm or QuickHull. Note that QuickHull is easier to code and probably faster, unless you are really unlucky. There is a pure python implementation of QuickHull here. But I'm sure a quick Google search will show many other results.
Usually the convex hull is the starting point for most other shape recognition algorithms, if your cloud can be described as a sequence of strokes, there are many algorithms and approaches:
Recognizing multistroke geometric shapes: an experimental evaluation
This may be even better, once you have the convex hull, break down the polygon to pairs of vertices and run this algorithm to match based on similarity to training data:
Hierarchical shape recognition using polygon approximation and dynamic alignment
Both of these papers are fairly old, so you can use google scholar to see who cites these papers and there you have a nice literature trail of attempts to solve this problem.
There are a multitude of different methods and approaches, this has been well studied in the literature, what method you take really depends on the level of accuracy you hope to achieve, and the amount of shapes you want to recognize, as well as your input data set.
Either way, using a convex hull algorithm to produce polygons out of point clouds is the very first step and usually input to the more sophisticated algorithmms.
EDIT:
I did not consider the 3D case, for that their is a lot of really interesting work in computer graphics that has focused on this, for instance this paper Efficient RANSAC for Point-Cloud Shape Detection
Selections from from Abstract:
We present an automatic algorithm to detect basic shapes in unorganized point clouds. The algorithm decomposes the point cloud into a concise, hybrid structure of inherent shapes and a set of remaining points. Each detected shape serves as a proxy for a set of corresponding points. Our method is based on random sampling and detects planes, spheres, cylinders, cones and tori...We demonstrate that the algorithm is robust even in the presence of many outliers and a high degree of noise...Moreover the algorithm is conceptually simple and easy to implement...
To complement Josiah's answer -- since you didn't say whether there is a single such object to be detected in your point cloud -- a good solution can be to use a (generalized) Hough transform.
The idea is that each point will vote for a set of candidates in the parameter space of the shape you are considering. For instance, if you think the current object is a cylinder, you have a 7D parameter space consisting of the cylinder center (3D), direction (2D), height (1D) and radius (1D), and each point in your point cloud will vote for all parameters that agree with the observation of that point. Doing so allows to find the parameters of the actual cylinder by taking the set of parameters who have the highest number of votes.
Doing the same thing for planes, spheres etc.., will give you the best matching shape.
A strength of this method is that it allows for multiple objects in the same point cloud.
I need to crossmatch a list of astronomical coordinates with different catalogues, and I want to decide a maximum radius for the crossmatch. This will avoid mismatches between my list and the catalogues.
To do this, I compute the separation between the best match with the catalogue for each object in my list. My initial list is supossed to be the position of a known object, but it could happend that it is not detected in the catalog, and my coordinates may suffer from small offsets.
They way I am computing the maximum radius is by fitting the gaussian kernel density of the separation with a gaussian, and use the center + 3sigmas value. The method works nicely for most of the cases, but when a small subsample of my list has an offset, I have two gaussians instead. In these cases, I will specify the max radius in a different way.
My problem is that when this happens, curve_fit can't normally do the fit with one gaussian. For a scientific publication, I will need to justify the "no fit" in curve_fit, and in which cases the "different way" is used. Could someone give me a hand on what this means in mathematical terms?
There are varying lengths to which you can go justifying this or that fitting ansatz --- which strongly depends on the details of your specific case (eg: why do you expect a gaussian to work in a first place? to what depth you need/want to delve into why exactly a certain fitting procedure fails and what exactly is a fail etc).
If the question is really about the curve_fit and its failure to converge, then show us some code and some input data which demonstrate the problem.
If the question is about how to evaluate the goodness-of-fit, you're best off going back to the library and picking a good book on statistics.
If all you look for is way of justifying why in a certain case a gaussian is not a good fitting ansatz, one way would be to calculate the moments: for a gaussian distribution 1st, 2nd, 3rd and higher moments are related to each other in a very precise way. If you can demonstrate that for your underlying data the relation between moments is very different, it sounds reasonable that these data can't be fit by a gaussian.