How do I implement the Medial Axis Transform algorithm to transform the first image into the second?
(source: algorith at www.cs.sunysb.edu)
(source: algorith at www.cs.sunysb.edu)
What library in C++/C# have support for Medial Axis Transform?
There are many implementations of the medial axis transform on the Internet (personally I don't use OpenCV library but I'm sure it has a decent implementation). However, you could easily implement it yourself.
In order to perform medial axis transform, we need to define only one term: simple point.
A point (P) is simple point iff removing P doesn't effect the number of connected components of either the foreground or the background. So, you have to decide the connectivity (4 or 8) for the background and for the foreground - in order to work pick different one for both (if you are interested why, look up Jordan property on google).
Medial transform axis could be implemented by sequentally deleting simple points. You get the final skeleton if there are no more simple points. You get the curved skeleton (I don't know the english name for it which is rare - please correct me) if you only have endpoints OR non-simple points. You provided examples of the latter in your question.
Finding simple points could be easily implemented with morphological operators or a look-up table. Hint: a point is simple point iff the number of connected components in the background is 1 and the number of connected components in the foreground is 1 in a 3x3 local window.
There is a medial axis transform available in this C Library:http://www.pinkhq.com/
There are lot other related functionalities.
Check out this Function:http://www.pinkhq.com/medialaxis_8c.html
Related
I have an image processing problem. I have pictures of yarn:
The individual strands are partly (but not completely) aligned. I would like to find the predominant direction in which they are aligned. In the center of the example image, this direction is around 30-34 degrees from horizontal. The result could be the average/median direction for the whole image, or just the average in each local neighborhood (producing a vector map of local directions).
What I've tried: I rotated the image in small steps (1 degree) and calculated statistics in the vertical vs horizontal direction of the rotated image (for example: standard deviation of summed rows or summed columns). I reasoned that when the strands are oriented exactly vertically or exactly horizontally the difference in statistics would be greatest, and so that angle of rotation is the correct direction in the original image. However, for at least several kinds of statistical properties I tried, this did not work.
I further thought that perhaps this wasn't working because there were too many different directions at the same time in the whole image, so I tired it in a small neighborhood. In this case, there is always a very clear preferred direction (different for each neighborhood), but it is not the direction that the fibers really go... I can post my sample code but it is basically useless.
I keep thinking there has to be some kind of simple linear algebra/statistical property of the whole image, or some value derived from the 2D FFT that would give the correct direction in one step... but how?
What probably won't work: detecting individual fibers. They are not necessarily the same color, and the image can shade from light to dark so edge detectors don't work well, and the image may not even be in focus sometimes. Because of that, it is not always even possible to see individual fibers for a human (see top-right in the example), they kinda have to be detected as preferred direction in a statistical sense.
You might try doing this in the frequency domain. The output of a Fourier Transform is orientation dependent so, if you have some kind of oriented pattern, you can apply a 2D FFT and you will see a clustering around a specific orientation.
For example, making a greyscale out of your image and performing FFT (with ImageJ) gives this:
You can see a distinct cluster that is oriented orthogonally with respect to the orientation of your yarn. With some pre-processing on your source image, to remove noise and maybe enhance the oriented features, you can probably achieve a much stronger signal in the FFT. Once you have a cluster, you can use something like PCA to determine the vector for the major axis.
For info, this is a technique that is often used to enhance oriented features, such as fingerprints, by applying a selective filter in the FFT and then taking the inverse to obtain a clearer image.
An alternative approach is to try a series of Gabor filters see here pre-built with a selection of orientations and frequencies and use the resulting features as a metric for identifying the most likely orientation. There is a scikit article that gives some examples here.
UPDATE
Just playing with ImageJ to give an idea of some possible approaches to this - I started with the FFT shown above, then - in the following image, I performed these operations (clockwise from top left) - Threshold => Close => Holefill => Erode x 3:
Finally, rather than using PCA, I calculated the spatial moments of the lower left blob using this ImageJ Plugin which handily calculates the orientation of the longest axis based on the 2nd order moment. The result gives an orientation of approximately -38 degrees (with respect to the X axis):
Depending on your frame of reference you can calculate the approximate average orientation of your yarn from this rather than from PCA.
I tried to use Gabor filters to enhance the orientations of your yarns. The parameters I used are:
phi = x*pi/16; % x = 1, 3, 5, 7
theta = 3;
sigma = 0.65*theta;
filterSize = 3;
And the imag part of the convoluted image are shown below:
As you mentioned, the most orientations lies between 30-34 degrees, thus the filter with phi = 5*pi/16 in left bottom yields the best contrast among the four.
I would consider using a Hough Transform for this type of problem, there is a nice write-up here.
I am trying to implement a gesture recognition system which interprets the geometric gestures user makes and draws it on screen,
I have some idea of how circle can be recognized, however I have no clue how to get started with triangle recognition.
The data I have is X and Y coordinates of all points the gesture passed through. I get this data by tracking right hand.
I found something online called Hough Transform, which is used for detecting lines but I am not sure whether it will work for discrete collections of points.
Any ideas folks?
If you already have an x,y pair for the hand, the simplest thing that comes to mind is try the $1 Unistroke Recognizer.
A handy thing to look at is Dynamic Time Warping(DTW).
I've seen a fun Processing/SimpleOpenNI project that makes
use of that technique and the full skeleton called KineticSpace.
Since it's open-source might be worth having a peak.
I'd recommend trying the $1 Unistroke Recognizer first. You probably
need to work out a system to mimic press/release (perhaps using
the sign of the hand's velocity on z (positive to negative transitions/
negative to positive transitions) ?).
HTH
You can look for a space filling curve. It reduces the 2 dimension and reorder the points. It also add some spatial information. Maybe you can train or compare the new reordered 1d index with some simulated annealing or ant colony optimization?! A space filling curve is used in map tiling programs.
I have set of binary images, on which i need to find the cross (examples attached). I use findcontours to extract borders from the binary image. But i can't understand how can i determine is this shape (border) cross or not? Maybe opencv has some built-in methods, which could help to solve this problem. I thought to solve this problem using Machine learning, but i think there is a simpler way to do this. Thanks!
Viola-Jones object detection could be a good start. Though the main usage of the algorithm (AFAIK) is face detection, it was actually designed for any object detection, such as your cross.
The algorithm is Machine-Learning based algorithm (so, you will need a set of classified "crosses" and a set of classified "not crosses"), and you will need to identify the significant "features" (patterns) that will help the algorithm recognize crosses.
The algorithm is implemented in OpenCV as cvHaarDetectObjects()
From the original image, lets say you've extracted sets of polygons that could potentially be your cross. Assuming that all of the cross is visible, to the extent that all edges can be distinguished as having a length, you could try the following.
Reject all polygons that did not have exactly 12 vertices required to
form your polygon.
Re-order the vertices such that the shortest edge length is first.
Create a best fit perspective transformation that maps your vertices onto a cross of uniform size
Examine the residuals generated by using this transformation to project your cross back onto the uniform cross, where the residual for any given point is the distance between the projected point and the corresponding uniform point.
If all the residuals are within your defined tolerance, you've found a cross.
Note that this works primarily due to the simplicity of the geometric shape you're searching for. Your contours will also need to have noise removed for this to work, e.g. each line within the cross needs to be converted to a single simple line.
Depending on your requirements, you could try some local feature detector like SIFT or SURF. Check OpenSURF which is an interesting implementation of the latter.
after some days of struggle, i came to a conclusion that the only robust way here is to use SVM + HOG. That's all.
You could erode each blob and analyze their number of pixels is going down. No mater the rotation scaling of the crosses they should always go down with the same ratio, excepted when you're closing down on the remaining center. Again, when the blob is small enough you should expect it to be in the center of the original blob. You won't need any machine learning algorithm or training data to resolve this.
I'd like to implement a Filter that allows resampling of an image by moving a number of control points that mark edges and tangent directions. The goal is to be able to freely transform an image as seen in Photoshop when you use "Free Transform" and chose Warpmode "Custom". The image is fitted into a some kind of Spline-Patch (if that is a valid name) that can be manipulated.
I understand how simple splines (paths) work but how do you connect them to form a patch?
And how can you sample such a patch to render the morphed image? For each pixel in the target I'd need to know what pixel in the source image corresponds. I don't even know where to start searching...
Any helpful info (keywords, links, papers, reference implementations) are greatly appreciated!
This document will get you a good insight into warping: http://www.gson.org/thesis/warping-thesis.pdf
However, this will include filtering out high frequencies, which will make the implementation a lot more complicated but will give a better result.
An easy way to accomplish what you want to do would be to loop through every pixel in your final image, plug the coordinates into your splines and retrieve the pixel in your original image. This pixel might have coordinates 0.4/1.2 so you could bilinearly interpolate between 0/1, 1/1, 0/2 and 1/2.
As for splines: there are many resources and solutions online for the 1D case. As for 2D it gets a bit trickier to find helpful resources.
A simple example for the 1D case: http://www-users.cselabs.umn.edu/classes/Spring-2009/csci2031/quad_spline.pdf
Here's a great guide for the 2D case: http://en.wikipedia.org/wiki/Bicubic_interpolation
Based upon this you could derive an own scheme for splines for the 2D case. Define a bivariate (with x and y) polynomial and set your constraints to solve for the coefficients of the polynomial.
Just keep in mind that the borders of the spline patches have to be consistent (both in value and derivative) to avoid ugly jumps.
Good luck!
I'm searching for an certain object in my photograph:
Object: Outline of a rectangle with an X in the middle. It looks like a rectangular checkbox. That's all. So, no fill, just lines. The rectangle will have the same ratios of length to width but it could be any size or any rotation in the photograph.
I've looked a whole bunch of image recognition approaches. But I'm trying to determine the best for this specific task. Most importantly, the object is made of lines and is not a filled shape. Also, there is no perspective distortion, so the rectangular object will always have right angles in the photograph.
Any ideas? I'm hoping for something that I can implement fairly easily.
Thanks all.
You could try using a corner detector (e.g. Harris) to find the corners of the box, the ends and the intersection of the X. That simplifies the problem to finding points in the right configuration.
Edit (response to comment):
I'm assuming you can find the corner points in your image, the 4 corners of the rectangle, the 4 line endings of the X and the center of the X, plus a few other corners in the image due to noise or objects in the background. That simplifies the problem to finding a set of 9 points in the right configuration, out of a given set of points.
My first try would be to look at each corner point A. Then I'd iterate over the points B close to A. Now if I assume that (e.g.) A is the upper left corner of the rectangle and B is the lower right corner, I can easily calculate, where I would expect the other corner points to be in the image. I'd use some nearest-neighbor search (or a library like FLANN) to see if there are corners where I'd expect them. If I can find a set of points that matches these expected positions, I know where the symbol would be, if it is present in the image.
You have to try if that is good enough for your application. If you have too many false positives (sets of corners of other objects that accidentially form a rectangle + X), you could check if there are lines (i.e. high contrast in the right direction) where you would expect them. And you could check if there is low contrast where there are no lines in the pattern. This should be relatively straightforward once you know the points in the image that correspond to the corners/line endings in the object you're looking for.
I'd suggest the Generalized Hough Transform. It seems you have a fairly simple, fixed shape. The generalized Hough transform should be able to detect that shape at any rotation or scale in the image. You many need to threshold the original image, or pre-process it in some way for this method to be useful though.
You can use local features to identify the object in image. Feature detection wiki
For example, you can calculate features on some referent image which contains only the object you're looking for and save the results, let's say, to a plain text file. After that you can search for the object just by comparing newly calculated features (on images with some complex scenes containing the object) with the referent ones.
Here's some good resource on local features:
Local Invariant Feature Detectors: A Survey