I am trying to obtain a radius and diameter distribution from some AFM (Atomic force microscopy) measurements. So far I am trying out Gwyddion, ImageJ and different workflows in Matlab.
At the moment the best results I have found is to use Gwyddion and to take the Phase image, high pass filter it and then try an edge detection with 'Laplacian of Gaussian'. The result is shown in figure 3. However this image is still too noisy and doesnt really capture the edges of all the particles. (some are merged together others do not have a clear perimeter).
In the end I need an image which segments each of the spherical particles which I can use for blob detection/analysis to obtain size/radius information.
Can anyone recommend a different method?
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I would definitely try a Granulometry, it was designed for something really similar. There is a good explanation of granulometry here starting page 158.
The granulometry will perform consecutive / increasing openings that will erase the different patterns according to their dimensions. The bigger the pattern, the latter it will be erased. It will give you a curve that represent the pattern dimension distributions in your image, so exactly what you want.
However, it will not give you any information about the position inside the image. If you want to have a rough modeling of the blobs present in your image, you can take a look to the Ultimate Opening.
Maybe you can use Avizo, it's a powerful software for dealing with image issues, especially for three D data (CT)
I have a grid on pictures (they are from camera). After binarization they look like this (red is 255, blue is 0):
What is the best way to detect grid nodes (crosses) on these pictures?
Note: grid is distorted from cell to cell non-uniformly.
Update:
Some examples of different grids and thier distortions before binarization:
In cases like this I first try to find the best starting point.
So, first I thresholded your image (however I could also skeletonize it and just then threshold. But this way some data is lost irrecoverably):
Then, I tried loads of tools to get the most prominent features emphasized in bulk. Finally, playing with Gimp's G'MIC plugin I found this:
Based on the above I prepared a universal pattern that looks like this:
Then I just got a part of this image:
To help determine angle I made local Fourier freq graph - this way you can obtain your pattern local angle:
Then you can make a simple thick that works fast on modern GPUs - get difference like this (missed case):
When there is hit the difference is minimal; what I had in mind talking about local maximums refers more or less to how the resulting difference should be treated. It wouldn't be wise to weight outside of the pattern circle difference the same as inside due to scale factor sensitivity. Thus, inside with cross should be weighted more in used algorithm. Nevertheless differenced pattern with image looks like this:
As you can see it's possible to differentiate between hit and miss. What is crucial is to set proper tolerance and use Fourier frequencies to obtain angle (with thresholded images Fourier usually follows overall orientation of image analyzed).
The above way can be later complemented by Harris detection, or Harris detection can be modified using above patterns to distinguish two to four closely placed corners.
Unfortunately, all techniques are scale dependent in such case and should be adjusted to it properly.
There are also other approaches to your problem, for instance by watershedding it first, then getting regions, then disregarding foreground, then simplifying curves, then checking if their corners form a consecutive equidistant pattern. But to my nose it would not produce correct results.
One more thing - libgmic is G'MIC library from where you can directly or through bindings use transformations shown above. Or get algorithms and rewrite them in your app.
I suppose that this can be a potential answer (actually mentioned in comments): http://opencv.itseez.com/2.4/modules/imgproc/doc/feature_detection.html?highlight=hough#houghlinesp
There can also be other ways using skimage tools for feature detection.
But actually I think that instead of Hough transformation that could contribute to huge bloat and and lack of precision (straight lines), I would suggest trying Harris corner detection - http://docs.opencv.org/2.4/doc/tutorials/features2d/trackingmotion/harris_detector/harris_detector.html .
This can be further adjusted (cross corners, so local maximum should depend on crossy' distribution) to your specific issue. Then some curves approximation can be done based on points got.
Maybe you cloud calculate Hough Lines and determine the intersections. An OpenCV documentation can be found here
I get a pointcloud from my lidar which is basically an numpy array of points in 2D cartesian coordinates. Is there any efficient way to detect corners formed by such 2D points?
What I tried until now was to detect clusters, then apply RANSAC on each cluster to detect two lines and then estimate the intersection point of those two lines. This method works well when I know how many clusters I have (in this case I put 3 boxes in front of my robot) and when the surrounding of the robot is free and no other objects are detected.
What I would like to do is run a general corner detection, then take the points surrounding each corner and check if lines are orthogonal. If it is the case then I can consider this corner as feature. This would make my algorithm more flexible when it comes to the surrounding environment.
Here is a visualization of the data I get:
There are many many ways to do this. First thing I'd try in your case would be to chain with a reasonable distance threshold for discontinuities, using the natural lidar scan ordering of the points. Then it become a problem of either estimating local curature or, as you have done, grow and merge linear segments.
I would like to implement a Maya plugin (this question is independent from Maya) to create 3D Voronoi patterns, Something like
I just know that I have to start from point sampling (I implemented the adaptive poisson sampling algorithm described in this paper).
I thought that, from those points, I should create the 3D wire of the mesh applying Voronoi but the result was something different from what I expected.
Here are a few example of what I get handling the result i get from scipy.spatial.Voronoi like this (as suggested here):
vor = Voronoi(points)
for vpair in vor.ridge_vertices:
for i in range(len(vpair) - 1):
if all(x >= 0 for x in vpair):
v0 = vor.vertices[vpair[i]]
v1 = vor.vertices[vpair[i+1]]
create_line(v0.tolist(), v1.tolist())
The grey vertices are the sampled points (the original shape was a simple sphere):
Here is a more complex shape (an arm)
I am missing something? Can anyone suggest the proper pipeline and algorithms I have to implement to create such patterns?
I saw your question since you posted it but didn’t have a real answer for you, however as I see you still didn’t get any response I’ll at least write down some ideas from me. Unfortunately it’s still not a full solution for your problem.
For me it seems you’re mixing few separate problems in this question so it would help to break it down to few pieces:
Voronoi diagram:
The diagram is by definition infinite, so when you draw it directly you should expect a similar mess you’ve got on your second image, so this seems fine. I don’t know how the SciPy does that, but the implementation I’ve used flagged some edge ends as ‘infinite’ and provided me the edges direction, so I could clip it at some distance by myself. You’ll need to check the exact data you get from SciPy.
In the 3D world you’ll almost always want to remove such infinite areas to get any meaningful rendering, or at least remove the area that contains your camera.
Points generation:
The Poisson disc is fine as some sample data or for early R&D but it’s also the most boring one :). You’ll need more ways to generate input points.
I tried to imagine the input needed for your ball-like example and I came up with something like this:
Create two spheres of points, with the same center but different radius.
When you create a Voronoi diagram out of it and remove infinite areas you should end up with something like a football ball.
If you created both spheres randomly you’ll get very irregular boundaries of the ‘ball’, but if you scale the points of one sphere, to use for the 2nd one you should get a regular mesh, similar to ball. You can also use similar points, but add some random offset to control the level of surface irregularity.
Get your computed diagram and for each edge create few points along this edge - this will give you small areas building up the edges of bigger areas. Play with random offsets again. Try to ignore edges, that doesn't touch any infinite region to get result similar to your image.
Get the points from both stages and compute the diagram once more.
Mesh generation:
Up to now it didn’t look like your target images. In fact it may be really hard to do it with production quality (for a Maya plugin) but I see some tricks that may help.
What I would try first would be to get all my edges and extrude some circle along them. You may modulate circle size to make it slightly bigger at the ends. Then do Boolean ‘OR’ between all those meshes and some Mesh Smooth at the end.
This way may give you similar results but you’ll need to be careful at mesh intersections, they can get ugly and need some special treatment.
I got two images showing exaktly the same content: 2D-gaussian-shaped spots. I call these two 16-bit png-files "left.png" and "right.png". But as they are obtained thru an slightly different optical setup, the corresponding spots (physically the same) appear at slightly different positions. Meaning the right is slightly stretched, distorted, or so, in a non-linear way. Therefore I would like to get the transformation from left to right.
So for every pixel on the left side with its x- and y-coordinate I want a function giving me the components of the displacement-vector that points to the corresponding pixel on the right side.
In a former approach I tried to get the positions of the corresponding spots to obtain the relative distances deltaX and deltaY. These distances then I fitted to the taylor-expansion up to second order of T(x,y) giving me the x- and y-component of the displacement vector for every pixel (x,y) on the left, pointing to corresponding pixel (x',y') on the right.
To get a more general result I would like to use normalized cross-correlation. For this I multiply every pixelvalue from left with a corresponding pixelvalue from right and sum over these products. The transformation I am looking for should connect the pixels that will maximize the sum. So when the sum is maximzied, I know that I multiplied the corresponding pixels.
I really tried a lot with this, but didn't manage. My question is if somebody of you has an idea or has ever done something similar.
import numpy as np
import Image
left = np.array(Image.open('left.png'))
right = np.array(Image.open('right.png'))
# for normalization (http://en.wikipedia.org/wiki/Cross-correlation#Normalized_cross-correlation)
left = (left - left.mean()) / left.std()
right = (right - right.mean()) / right.std()
Please let me know if I can make this question more clear. I still have to check out how to post questions using latex.
Thank you very much for input.
[left.png] http://i.stack.imgur.com/oSTER.png
[right.png] http://i.stack.imgur.com/Njahj.png
I'm afraid, in most cases 16-bit images appear just black (at least on systems I use) :( but of course there is data in there.
UPDATE 1
I try to clearify my question. I am looking for a vector-field with displacement-vectors that point from every pixel in left.png to the corresponding pixel in right.png. My problem is, that I am not sure about the constraints I have.
where vector r (components x and y) points to a pixel in left.png and vector r-prime (components x-prime and y-prime) points to the corresponding pixel in right.png. for every r there is a displacement-vector.
What I did earlier was, that I found manually components of vector-field d and fitted them to a polynom second degree:
So I fitted:
and
Does this make sense to you? Is it possible to get all the delta-x(x,y) and delta-y(x,y) with cross-correlation? The cross-correlation should be maximized if the corresponding pixels are linked together thru the displacement-vectors, right?
UPDATE 2
So the algorithm I was thinking of is as follows:
Deform right.png
Get the value of cross-correlation
Deform right.png further
Get the value of cross-correlation and compare to value before
If it's greater, good deformation, if not, redo deformation and do something else
After maximzied the cross-correlation value, know what deformation there is :)
About deformation: could one do first a shift along x- and y-direction to maximize cross-correlation, then in a second step stretch or compress x- and y-dependant and in a third step deform quadratic x- and y-dependent and repeat this procedure iterativ?? I really have a problem to do this with integer-coordinates. Do you think I would have to interpolate the picture to obtain a continuous distribution?? I have to think about this again :( Thanks to everybody for taking part :)
OpenCV (and with it the python Opencv binding) has a StarDetector class which implements this algorithm.
As an alternative you might have a look at the OpenCV SIFT class, which stands for Scale Invariant Feature Transform.
Update
Regarding your comment, I understand that the "right" transformation will maximize the cross-correlation between the images, but I don't understand how you choose the set of transformations over which to maximize. Maybe if you know the coordinates of three matching points (either by some heuristics or by choosing them by hand), and if you expect affinity, you could use something like cv2.getAffineTransform to have a good initial transformation for your maximization process. From there you could use small additional transformations to have a set over which to maximize. But this approach seems to me like re-inventing something which SIFT could take care of.
To actually transform your test image you can use cv2.warpAffine, which also can take care of border values (e.g. pad with 0). To calculate the cross-correlation you could use scipy.signal.correlate2d.
Update
Your latest update did indeed clarify some points for me. But I think that a vector field of displacements is not the most natural thing to look for, and this is also where the misunderstanding came from. I was thinking more along the lines of a global transformation T, which applied to any point (x,y) of the left image gives (x',y')=T(x,y) on the right side, but T has the same analytical form for every pixel. For example, this could be a combination of a displacement, rotation, scaling, maybe some perspective transformation. I cannot say whether it is realistic or not to hope to find such a transformation, this depends on your setup, but if the scene is physically the same on both sides I would say it is reasonable to expect some affine transformation. This is why I suggested cv2.getAffineTransform. It is of course trivial to calculate your displacement Vector field from such a T, as this is just T(x,y)-(x,y).
The big advantage would be that you have only very few degrees of freedom for your transformation, instead of, I would argue, 2N degrees of freedom in the displacement vector field, where N is the number of bright spots.
If it is indeed an affine transformation, I would suggest some algorithm like this:
identify three bright and well isolated spots on the left
for each of these three spots, define a bounding box so that you can hope to identify the corresponding spot within it in the right image
find the coordinates of the corresponding spots, e.g. with some correlation method as implemented in cv2.matchTemplate or by also just finding the brightest spot within the bounding box.
once you have three matching pairs of coordinates, calculate the affine transformation which transforms one set into the other with cv2.getAffineTransform.
apply this affine transformation to the left image, as a check if you found the right one you could calculate if the overall normalized cross-correlation is above some threshold or drops significantly if you displace one image with respect to the other.
if you wish and still need it, calculate the displacement vector field trivially from your transformation T.
Update
It seems cv2.getAffineTransform expects an awkward input data type 'float32'. Let's assume the source coordinates are (sxi,syi) and destination (dxi,dyi) with i=0,1,2, then what you need is
src = np.array( ((sx0,sy0),(sx1,sy1),(sx2,sy2)), dtype='float32' )
dst = np.array( ((dx0,dy0),(dx1,dy1),(dx2,dy2)), dtype='float32' )
result = cv2.getAffineTransform(src,dst)
I don't think a cross correlation is going to help here, as it only gives you a single best shift for the whole image. There are three alternatives I would consider:
Do a cross correlation on sub-clusters of dots. Take, for example, the three dots in the top right and find the optimal x-y shift through cross-correlation. This gives you the rough transform for the top left. Repeat for as many clusters as you can to obtain a reasonable map of your transformations. Fit this with your Taylor expansion and you might get reasonably close. However, to have your cross-correlation work in any way, the difference in displacement between spots must be less than the extend of the spot, else you can never get all spots in a cluster to overlap simultaneously with a single displacement. Under these conditions, option 2 might be more suitable.
If the displacements are relatively small (which I think is a condition for option 1), then we might assume that for a given spot in the left image, the closest spot in the right image is the corresponding spot. Thus, for every spot in the left image, we find the nearest spot in the right image and use that as the displacement in that location. From the 40-something well distributed displacement vectors we can obtain a reasonable approximation of the actual displacement by fitting your Taylor expansion.
This is probably the slowest method, but might be the most robust if you have large displacements (and option 2 thus doesn't work): use something like an evolutionary algorithm to find the displacement. Apply a random transformation, compute the remaining error (you might need to define this as sum of the smallest distance between spots in your original and transformed image), and improve your transformation with those results. If your displacements are rather large you might need a very broad search as you'll probably get lots of local minima in your landscape.
I would try option 2 as it seems your displacements might be small enough to easily associate a spot in the left image with a spot in the right image.
Update
I assume your optics induce non linear distortions and having two separate beampaths (different filters in each?) will make the relationship between the two images even more non-linear. The affine transformation PiQuer suggests might give a reasonable approach but can probably never completely cover the actual distortions.
I think your approach of fitting to a low order Taylor polynomial is fine. This works for all my applications with similar conditions. Highest orders probably should be something like xy^2 and x^2y; anything higher than that you won't notice.
Alternatively, you might be able to calibrate the distortions for each image first, and then do your experiments. This way you are not dependent on the distribution of you dots, but can use a high resolution reference image to get the best description of your transformation.
Option 2 above still stands as my suggestion for getting the two images to overlap. This can be fully automated and I'm not sure what you mean when you want a more general result.
Update 2
You comment that you have trouble matching dots in the two images. If this is the case, I think your iterative cross-correlation approach may not be very robust either. You have very small dots, so overlap between them will only occur if the difference between the two images is small.
In principle there is nothing wrong with your proposed solution, but whether it works or not strongly depends on the size of your deformations and the robustness of your optimization algorithm. If you start off with very little overlap, then it may be hard to find a good starting point for your optimization. Yet if you have sufficient overlap to begin with, then you should have been able to find the deformation per dot first, but in a comment you indicate that this doesn't work.
Perhaps you can go for a mixed solution: find the cross correlation of clusters of dots to get a starting point for your optimization, and then tweak the deformation using something like the procedure you describe in your update. Thus:
For a NxN pixel segment find the shift between the left and right images
Repeat for, say, 16 of those segments
Compute an approximation of the deformation using those 16 points
Use this as the starting point of your optimization approach
You might want to have a look at bunwarpj which already does what you're trying to do. It's not python but I use it in exactly this context. You can export a plain text spline transformation and use it if you wish to do so.