What's the best approach for the following.
Suppose I measure a circular part at various points along the outer shell.
Lets assume that these measurements taken are very repeatable, but not 100% accurate.
Lets assume as I take the points they gradually get a little worse but the change is somewhat linear
Suppose I measure a calibrated part of a certain diameter and I know this diameter.
How do I calculate a calibration formula / curve to correct the raw data into what should be close to the ideal. Basically I want to correct / transform the points with this formula so that I get an accurate sets of points. The output of this would be a very accurate diameter when I fit a circle to the 'calibrated' points
Hope this makes sense
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I am currently working on program which could help at my work. I'm trying to use Machine Learning for the classification purpose. The problem is that I don't have enough samples for training the model and augmentation is something I'm trying to avoid because hardware problems (not enough RAM) either on my company laptop and on the Google Collab. So I decided to try to somehow normalize the position of the elements so the differences would be visible for the machine even with no big amount of different samples. Unfortunately now I'm struggling how to normalize those pictures.
Element 1a:
Element 1b:
Element 2a:
Element 2b:
Elements 1a and 1b are the same type and 2a - 2b are the same type. Is there a way to somehow normalize position for those pictures (something like position 0) which would help the algorithm to see differences between them? I've tried using cv2.minAreaSquare to get the square position, rotating them and cropping don't needed area but unfortunately those elements can have different width so after scaling them down the contours are deformed unevenly. Then I was trying to get symmetry axis and using this to do a proper cropping after rotation but still the results didn't meet my expectations. I was thinking to add more normalization points like this:
Normalization Points:
And using this points normalize position of the rest of my elements but Perspective Transform takes only 4 points and with 4 points its also not very good methodology. Maybe you guys know a way how to move those elements to have them in the same positions.
Seeing the images, I believe that the transformation between two pictures is either an isometry (translation + rotation) or a similarity (translation + rotation + scaling). These can be determined with just two points. (Perspective takes four points but I think that this is overkill.)
But for good accuracy, you must make sure that the points are found reliably and precisely. In the first place, you need to guess which features of the shapes are repeatable from one sample to the next.
For example, you might estimate that the straight edges are always in the same relative position. In such a case, I would recommend finding two points on some edges, drawing a line between them and find intersections between the lines.
In the illustration, you find edge points along the red profiles, and from them you draw the green lines. They intersect in the yellow points.
For increased accuracy, you can use a least-squares approach to find a best fit on more than two points.
I have a problem at hand where I need to detect/predict the coordinates of the hinge point or axis of rotation point using image processing. The image is as shown below:
I've used a method where I started with tracking the circular movement (in an arc) of a few feature points in an RoI around the default hinge coordinates (entered manually) in a configuration file. This circular motion of these tracked points happens around the vertical axis which passes through the hinge point. Now, I tracked these points from their initial position until the connecting bar made a particular angle (15°/20°) with the y-axis, I drew secants between these different positions (start and end positions) of the same point and drew its perpendicular bisector, which will ideally pass through the centre of the (concentric) circles, which is the ideal hinge point.
Eg:
y_intercepts calculated for each point
H0 (322, 42)
H1 (322, 64) (within tolerance, closest to GT)
H2 (322, 48)
H_avg (322,52)
H_groundtruth (x,y): (322, 61)
We need an accuracy or tolerance of +/- 3 pixels.
Now, the issues we faced in this ideal scenario to practical working of it is:
Different tracked points give different potential hinge points (different dots on the vertical yellow line), (few of which are very close the ground truth(yellow circle)), but their weighted/average (big green circle) goes off the mark. Quite frankly, this is a problem of too many in which we do get the closest potentially to ground truth, but we’re not sure, which of these points is the closest as we’re not to use the default hitch coordinates (entered manually) from config file.
One solution could be to use frameworks already implemented for image registration such as elastix. If you configure it for a rigid registration, you can get the transformation matrix and therefore the center of the rotation.
The problem here is that only one part of your image is moving. Before doing the registration, I would simply mask the region of interest by calculating a mask from the subtraction of the two images, to keep only the part where something actually moved.
Such approach could get a subpixel accuracy. You could also repeat it for multiple angles and average the result. Alternatively to the averaging, you could use the RANSAC algorithm to know which hinge points are off (outliers) and exclude them.
Here is an example how to do a simple rigid transformation with elastix.
I hope this helps!
I intended this as only a comment, but it ended up significantly over the character limit:
The problem from an accuracy perspective (sorry, couldn't resist) seems to be that you're trying to use a planar euclidean geometry technique to solve a projective geometry problem.
Those feature tracks are only circular arcs in 3D world space. They're actually (noisy) elliptical arcs in 2D image pixel space due to the projection.
Your hinge rotation axis isn't a single pixel either, unless your camera's optical axis is directly aligned with the hinge axis. If that's not the case (as the perspective in the photo you added suggests), then your hinge axis is actually a line in pixel space, not a point, and different heights for the different tracks in model space will be 'centered' around different pixels on that line. So asking for +/- 3 pixel hinge 'point' accuracy is unclear, and so is measuring angles in pixel space in general in a way that doesn't account for perspective.
I only mention these details because you seem focused on measuring accurately. Often, those kinds of 2D approximations are fine for many applications, but high accuracy and precision from a single camera (if that's really what you need) requires better 3D scene understanding. (Or you could train a deep network with a bunch of labeled ground truth images and let it figure out the mappings.)
Now maybe you don't need such high accuracy for your application after all. In that case, simple affine geometry techniques like that mentioned in the other answer might work well enough.
I am trying to calculate the real world distance of an arbitrary line drawn along the field of view from a one point perspective, single camera setup.
I will have a known distance running parallel. How can I find the compensation factor I need to apply to the pixel length of the measuring line?
Do I have to take into account the distance from the vanishing point, as the length per pixel increases the nearer you get to the vanishing point? Do I need to use the gradient of the known line to give me a rate of change?
A good study on this and similar problems can be found in Antonio Criminisi's papers and Ph.D. thesis on single-view metrology. This is a good link to start, and the whole paperdump is here
I'm looking for an efficient way of selecting a relatively large portion of points (2D Euclidian graph) that are the furthest away from the center. This resembles the convex hull, but would include (many) more points. Further criteria:
The number of points in the selection / set ("K") must be within a specified range. Most likely it won't be very narrow, but it most work for different ranges (eg. 0.01*N < K < 0.05*N as well as 0.1*N < K < 0.2*N).
The algorithm must be able to balance distance from the center and "local density". If there are dense areas near the upper part of the graph range, but sparse areas near the lower part, then the algorithm must make sure to select some points from the lower part even if they are closer to the center than the points in the upper region. (See example below)
Bonus: rather than simple distance from center, taking into account distance to a specific point (or both a point and the center) would be perfect.
My attempts so far have focused on using "pigeon holing" (divide graph into CxR boxes, assign points to boxes based on coordinates) and selecting "outer" boxes until we have sufficient points in the set. However, I haven't been successful at balancing the selection (dense regions over-selected because of fixed box size) nor at using a selected point as reference instead of (only) the center.
I've (poorly) drawn an Example: The red dots are the points, the green shape is an example of what I want (outside the green = selected). For sparse regions, the bounding shape comes closer to the center to find suitable points (but doesn't necessarily find any, if they're too close to the center). The yellow box is an example of what my Pigeon Holing based algorithms does. Even when trying to adjust for sparser regions, it doesn't manage well.
Any and all ideas are welcome!
I don't think there are any standard algorithms that will give you what you want. You're going to have to get creative. Assuming your points are embedded in 2D Euclidean space here are some ideas:
Iteratively compute several convex hulls. For example, compute the convex hull, keep the points that are part of the convex hull, then compute another convex hull ignoring the points from the original convex hull. Continue to do this until you have a sufficient number of points, essentially plucking off points on the perimeter for each iteration. The only problem with this approach is that it will not work well for concavities in your data set (e.g., the one on the bottom of your sample you posted).
Fit a Gaussian to your data and keep everything > N standard
deviations away from the mean (where N is a value that you'd have to
choose). This should work pretty well if your data is Gaussian. If
it isn't, you could always model it with several Gaussians (instead
of one), and keep points with a joint probability less than some threshold. Using multiple Gaussians will probably handle concavities decently. References:
http://en.wikipedia.org/wiki/Gaussian_function
How to fit a gaussian to data in matlab/octave?\
Use Kernel Density Estimation - If you create a kernel density
surface, you could slice the surface at some height (e.g., turning
it into a plateau), giving you a perimeter shape (the shape of the
plateau) around the points. The trick would be to slice it at the
right location though, because you could end up getting no points
outside of the shape, but with the right selection you could easily
get the green shape you drew. This approach will work well and give you the green shape in your example if you choose the slice point wisely (which may be difficult to do). The big drawback of this approach is that it is very computationally expensive. More information:
http://en.wikipedia.org/wiki/Multivariate_kernel_density_estimation
Use alpha shapes to get a general shape the wraps tightly around
the outside perimeter of the point set. Then erode the shape a
little to force some points outside of the shape. I don't have a lot of experience with alpha shapes, but this approach will also be quite computationally expensive. More info:
http://doc.cgal.org/latest/Alpha_shapes_2/index.html
OpenCV has a nice in-built ellipse-fitting algorithm called fitEllipse(const Mat& points)
However, it has some major shortcomings, limiting its usefulness. For example, it already requires selected points, so I already have to do a feature extraction myself. HoughCircles detects circles on a given image, pity there is no HoughEllipses.
The other major shortcoming, which stands in the center of my question, is that it does no provide any metric about how accurate the fitting was. It returns an ellipse which best fits the given points, even if the shape does not even remotely look like an ellipse. Is there a way to get the estimated error from the algorithm? I would like to use it as a threshold to filter out shapes which are not even close to be considered ellipses.
I asked this, because maybe there is a simple solution before I try to reinvent the wheel and write my very own fitEllipse function.
If you don't mind getting your hands dirty, you could actually modify the source code for fitEllipse(). The fitEllipse() function uses least-squares to determine the likely ellipses, and the least-squares solution is a tangible distance metric, which is what you want.
If that is something you're willing to do, it would be a very simple code change. Simply add a float whose value is passed back after the function call, where the float stores the current best least-squares value.
fitEllipse gives you the ellipse as a cv::RotatedRect and so you know the angle of rotation of the ellipse, its center and its two axes.
You can compute the sum of the square of the distances between your points and the ellipse, that sum is the metric you are looking for.
The distance between a point and an ellipse is described here http://www.geometrictools.com/Documentation/DistancePointEllipseEllipsoid.pdf and the code is here http://www.geometrictools.com/GTEngine/Include/Mathematics/GteDistPointHyperellipsoid.h
You need to go from OpenCV cv::RotatedRect to Ellipse2 of Geometric Tools Engine and then you can compute the distance.
Why don't you do a findContours() to reduce the memory space required? There's your selected points structure right there. If you want to further simplify you can run a ConvexHull() or ApproxPoly() on that. Fit the ellipse to those points, and then I suppose you can check similarity between the two structures to get some kind of estimate. A difference operator between the two Mats would be a (very) rough estimate?
Depending on the application, you might be able to use CAMShift (or mean shift), which fits an ellipse to a region with similar colors.