Papers have been written describing how the Hough transform can be generalised to detect shapes like circles and parabolas. I'm new to computer vision though and find these papers pretty tough going. There is also code out there that does this detection but this is more than I want. I was wondering if anyone could briefly describe in bullet points or pseudo-code really simply how Hough Transforms are used to detect parabolas in images. That would be amazing. Or if anyone knows any basic explanations online that I haven't come across than that would be good enough too :).
Thanks very much :).
Interesting question. This looks like a great resource. I included a summary (loosely quoted). Also see the source from Mathworks at the bottom of this answer - Matlab has houghlines and houghpeaks functions which will be useful for you. Hope it helps.
Run edge detection algorithm, such as the Canny edge detector, on subject image
Input edge/boundary points into Hough Transform (line detecting)
Generate a curve in polar space (radius, angle) for each point
in Cartesian space (also called
accumulator array)
Extract local maxima from the accumulator array, for example using a
relative threshold
In other words, we take only those local maxima in the accumulator
array whose values are equal to or
greater than some fixed percentage of
the global maximum value.
De-Houghing into Cartesian space yields a set of line descriptions of the image subject
cs.jhu.edu:
http://www.cs.jhu.edu/~misha/Fall04/GHT1.pdf
Code from Mathworks: http://www.mathworks.com/help/toolbox/images/ref/hough.html
Related
I realize there are many cans of worms related to what I'm asking, but I have to start somewhere. Basically, what I'm asking is:
Given two photos of a scene, taken with unknown cameras, to what extent can I determine the (relative) warping between the photos?
Below are two images of the 1904 World's Fair. They were taken at different levels on the wireless telegraph tower, so the cameras are more or less vertically in line. My goal is to create a model of the area (in Blender, if it matters) from these and other photos. I'm not looking for a fully automated solution, e.g., I have no problem with manually picking points and features.
Over the past month, I've taught myself what I can about projective transformations and epipolar geometry. For some pairs of photos, I can do pretty well by finding the fundamental matrix F from point correspondences. But the two below are causing me problems. I suspect that there's some sort of warping - maybe just an aspect ratio change, maybe more than that.
My process is as follows:
I find correspondences between the two photos (the red jagged lines seen below).
I run the point pairs through Matlab (actually Octave) to find the epipoles. Currently, I'm using Peter Kovesi's
Peter's Functions for Computer Vision.
In Blender, I set up two cameras with the images overlaid. I orient the first camera based on the vanishing points. I also determine the focal lengths from the vanishing points. I orient the second camera relative to the first using the epipoles and one of the point pairs (below, the point at the top of the bandstand).
For each point pair, I project a ray from each camera through its sample point, and mark the closest covergence of the pair (in light yellow below). I realize that this leaves out information from the fundamental matrix - see below.
As you can see, the points don't converge very well. The ones from the left spread out the further you go horizontally from the bandstand point. I'm guessing that this shows differences in the camera intrinsics. Unfortunately, I can't find a way to find the intrinsics from an F derived from point correspondences.
In the end, I don't think I care about the individual intrinsics per se. What I really need is a way to apply the intrinsics to "correct" the images so that I can use them as overlays to manually refine the model.
Is this possible? Do I need other information? Obviously, I have little hope of finding anything about the camera intrinsics. There is some obvious structural info though, such as which features are orthogonal. I saw a hint somewhere that the vanishing points can be used to further refine or upgrade the transformations, but I couldn't find anything specific.
Update 1
I may have found a solution, but I'd like someone with some knowledge of the subject to weigh in before I post it as an answer. It turns out that Peter's Functions for Computer Vision has a function for doing a RANSAC estimate of the homography from the sample points. Using m2 = H*m1, I should be able to plot the mapping of m1 -> m2 over top of the actual m2 points on the second image.
The only problem is, I'm not sure I believe what I'm seeing. Even on an image pair that lines up pretty well using the epipoles from F, the mapping from the homography looks pretty bad.
I'll try to capture an understandable image, but is there anything wrong with my reasoning?
A couple answers and suggestions (in no particular order):
A homography will only correctly map between point correspondences when either (a) the camera undergoes a pure rotation (no translation) or (b) the corresponding points are all co-planar.
The fundamental matrix only relates uncalibrated cameras. The process of recovering a camera's calibration parameters (intrinsics) from unknown scenes, known as "auto-calibration" is a rather difficult problem. You'd need these parameters (focal length, principal point) to correctly reconstruct the scene.
If you have (many) more images of this scene, you could try using a system such as Visual SFM: http://ccwu.me/vsfm/ It will attempt to automatically solve the Structure From Motion problem, including point matching, auto-calibration and sparse 3D reconstruction.
I'm trying to track little white dots on edges table. In most of case it works. I'm using cornerHarris function like it's used in this tutorial : http://docs.opencv.org/doc/tutorials/features2d/trackingmotion/harris_detector/harris_detector.html .
Sometimes, I have got a problem : reflection of the light on edges creates point of interest which I have to not consider.
For example :
I'm searching to the two nearest points of the top corners, as you can see on the right edges, i have find dots(red and green dots) and on the left edges, light noise is a problem (cyan and blue dots).
Does someone knows a method to keep only dots white on my picture ? Thankyou and sorry for my english
On the purely image processing part, I would recommend using some kind of shape feature analysis(like comparing the histogram in say 8x8 around your currently examined point of interest to precomputed ones of the features you want .
This would mean that you first look for points with Harris corners, then compare the features to dismiss unwanted ones ( euclidian distance in the 8x8 = 64D ?). This of course assumes the existence of a strong feature (read "taking time to find a good one")
It also assumes you already know what your feature points look like beforehand.
Alternative more on the computer vision side : use geometry of your corner points repartition to your advantage : you probably want a distorted rectangle, so make sure you find one ! Surely you can compute a function that gives the validity of the last feature point assuming 3 others ? (Distance of intersection of the 2 lines generated by the other 3 points ...)
The typical and coolest approach would then apply RANSAC to it : try random (but not all !) combinations of your points and check which one fits best using that function, and consider those as good.
If you intend on tracking over time or over several images, you will have to tune it a bit, as ransac can occasionally fail (statistics of random combinations ...), and you would then use points from your previously successful run to guestimate the position.
Last idea for the moment : use some color-aware derivation technique : do you compute Harris corner of the rgb image or of a flattened version to gray ? Some gradients use color information as extra tip to discern edges, and I'm not sure the corners you're finding use any of those. Then again it might mean reimplementing Harris corners algorithm (try it, it's fun, and not that hard if you have a good algebra library to do the heavy work)
I recommend the geometric test of fitting as it uses wisely model-info of your system rather than assumptions on how reflections look like.
Really funny introduction to RANSAC : danielwedge.com/ransac/
Edit : Trusty photoshop knows what I mean : I highlighted the invalid shapes
Valid grid, photoshop says so
Invalid grid, logical, right ?
I'm trying to detect a shape (a cross) in my input video stream with the help of OpenCV. Currently I'm thresholding to get a binary image of my cross which works pretty good. Unfortunately my algorithm to decide whether the extracted blob is a cross or not doesn't perform very good. As you can see in the image below, not all corners are detected under certain perspectives.
I'm using findContours() and approxPolyDP() to get an approximation of my contour. If I'm detecting 12 corners / vertices in this approximated curve, the blob is assumed to be a cross.
Is there any better way to solve this problem? I thought about SIFT, but the algorithm has to perform in real-time and I read that SIFT is not really suitable for real-time.
I have a couple of suggestions that might provide some interesting results although I am not certain about either.
If the cross is always near the center of your image and always lies on a planar surface you could try to find a homography between the camera and the plane upon which the cross lies. This would enable you to transform a sample image of the cross (at a selection of different in plane rotations) to the coordinate system of the visualized cross. You could then generate templates which you could match to the image. You could do some simple pixel agreement tests to determine if you have a match.
Alternatively you could try to train a Haar-based classifier to recognize the cross. This type of classifier is often used in face detection and detects oriented edges in images, classifying faces by the relative positions of several oriented edges. It has good classification accuracy on faces and is extremely fast. Although I cannot vouch for its accuracy in this particular situation it might provide some good results for simple shapes such as a cross.
Computing the convex hull and then taking advantage of the convexity defects might work.
All crosses should have four convexity defects, making up four sets of two points, or four vectors. Furthermore, if your shape was a cross then these four vectors will have two pairs of supplementary angles.
I am just starting to use OpenCV to detect specific curves in an image. First, I want to verify if there is a curve, and next, I would like to identify the type of curve according to vertical or horizontal convex or concave curve. Is there an available function in OpenCV? If not, can you give me some ideas about how can I possibly write such a function? Thanks! By the way, I'm using C++.
Template matching is not a robust way to solve this problem (its like looking at an object from a small pinhole) and edge detectors don't necessarily return you the true edges in the image; false edges such as those due to shadows are returned too. Further, you have to deal with the problem of incomplete edges and other problems that scales up with the complexity of the scene in your image.
The problem you posed, in general, is a very challenging one and, except for toy examples, there are no good solutions.
A rough attempt could be to first try to detect plausible edges using an edge detector (e.g. the canny edge detector suggested). Next, use RANSAC to try to fit a subset of the points in the detected edges to your curve model.
For e.g. let's say you are trying to detect a curve of the following form f(x) = ax^2 + bx + c. RANSAC will basically try to find from among the points in the detected edges, a subset of them that would best fit this curve model. To detect different curves, change f(x) accordingly and run RANSAC for each of them. You can then try to determine if the curve represented by f(x) really exists in your image using some heuristic applied to from the points that were assigned to it by RANSAC (e.g. if too few points were fitted to the model it is likely that the curve is not there. But how to determine a good threshold for the number of points?). You model will get more complex when you have to account for allowable transformation such as rotation etc.
The problem with this approach is you are basically trying fit what you think should be in the image to the points and sometimes, even if what you are looking for is not there, it will return you the "best possible" fit. For e.g. you have a whole bunch of points detected from a concentric circle. If you try to detect straight lines from these points, RANSAC will return you the best fit line! In fact, it could give you many different lines from different runs depending on which points it selected during its random initialization stage.
For more details on how to use RANSAC on this sort of problem, have a look at RANSAC for Dummies by Marco Zuliani. He also has a nice MATLAB toolbox to accompany this tech report, which you can probably port to the language of your choice.
Unless you know what you background looks like, or if you are in control of it e.g. by forcing a clean background, this is a very difficult problem to solve.
I am currently working on a data visualization project.My aim is to produce contour lines ,in other words iso-lines, from gridded data.Data can be temperature, weather data or any kind of other environmental parameters but only condition is it must be regularly spaced.
I searched in internet , however i could not find a good algorithm, pseudo-code or source code for producing contour lines from grids.
Does anybody knows a library, source code or an algorithm for producing contour lines from gridded data?
it will be good if your suggestion has a good run time performance, i don't want to wait my users so much :)
Edit: thanks for response but isolines have some constrains like they should not intersects
so just generating bezier curves does not accomplish my goal.
See this question: How to approximate a vector contour from an elevation raster?
It's a near duplicate, but uses quite different terminology. You'll find that cartography and computer graphics solve many of the same problems, but use different terminology for them.
there's some reasonably good contouring available in GNUplot - if you're able to use GPL code that may help.
If your data is placed at regular intervals, this can be done fairly easily (assuming I understand your problem correctly). First you need to determine at what interval you want your contours. Next create the grid you are going to use to store the contour information (i'm assuming just a simple on/off or elevation at this contour level type of data), which should be one interval smaller than the source data.
Now the trick here is to offset the 2 grids by 1/2 an interval (won't actually show up in code like this, but its the concept I'm dealing with here) and compare the 4 coordinates surrounding the current point in the contour data grid you are calculating. If any of the 4 points are in a different interval range, then that 'pixel' in the contour grid should be set to true (or the value of the contour range being crossed).
With this method, there will be a problem when the interval is too fine which will cause several contours to overlap onto each other.
As the link from Paul Tomblin suggests, Bezier curves (which are a subset of B-splines) are a ripe solution for your problem. If runtime performance is an issue, Bezier curves have the added benefit of being constructable via the very fast de Casteljau algorithm, instead of drawing them according to the parametric equations. On the off chance you're working with DirectX, it has a library function for the de Casteljau, but it should not be challenging to brew one yourself using the 1001 web pages that describe it.