I can successfully threshold images and find edges in an image. What I am struggling with is trying to extract the angle of the black edges accurately.
I am currently taking the extreme points of the black edge and calculating the angle with the atan2 function, but because of aliasing, depending on the point you choose the angle can come out with some degree of variation. Is there a reliable programmable way of choosing the points to calculate the angle from?
Example image:
For example, the Gimp Measure tool angle at 3.12°,
If you're writing your own library, then creating a robust solution for this problem will allow you to develop several independent chunks of code that you can string together to solve other problems, too. I'll assume that you want to find the corners of the checkerboard under arbitrary rotation, under varying lighting conditions, in the presence of image noise, with a little nonlinear pincushion/barrel distortion, and so on.
Although there are simple kernel-based techniques to find whole pixels as edge pixels, when working with filled polygons you'll want to favor algorithms that can find edges with sub-pixel accuracy so that you can perform accurate line fits. Even though the gradient from dark square to white square crosses several pixels, the "true" edge will be found at some sub-pixel point, and very likely not the point you'd guess by manually clicking.
I tried to provide a simple summary of edge finding in this older SO post:
what is the relationship between image edges and gradient?
For problems like yours, a robust solution is to find edge points along the dark-to-light transitions with sub-pixel accuracy, then fit lines to the edge points, and use the line angles. If you are processing a true camera image, and if there is an uncorrected radial distortion in the image, then there are some potential problems with measurement accuracy, but we'll ignore those.
If you want to find an accurate fit for an edge, then it'd be great to scan for sub-pixel edges in a direction perpendicular to that edge. That presupposes that we have some reasonable estimate of the edge direction to begin with. We can first find a rough estimate of the edge orientation, then perform an accurate line fit.
The algorithm below may appear to have too many steps, but my purpose is point out how to provide a robust solution.
Perform a few iterations of erosion on black pixels to separate the black boxes from one another.
Run a connected components algorithm (blob-finding algorithm) to find the eroded black squares.
Identify the center (x,y) point of each eroded square as well as the (x,y) end points defining the major and minor axes.
Maintain the data for each square in a structure that has the total area in pixels, the center (x,y) point, the (x,y) points of the major and minor axes, etc.
As needed, eliminate all components (blobs) that are too small. For example, you would want to exclude all "salt and pepper" noise blobs. You might also temporarily ignore checkboard squares that are cut off by the image edges--we can return to those later.
Then you'll loop through your list of blobs and do the following for each blob:
Determine the direction roughly perpendicular to the edges of the checkerboard square. How you accomplish this depends in part on what data you calculate when you run your connected components algorithm. In a general-purpose image processing library, a standard connected components algorithm will determine dozens of properties and measurements for each individual blob: area, roundness, major axis direction, minor axis direction, end points of the major and minor axis, etc. For rectangular figures, it can be sufficient to calculate the topmost, leftmost, rightmost, and bottommost points, as these will define the four corners.
Generate edge scans in the direction roughly perpendicular to the edges. These must be performed on the original, unmodified image. This generally assumes you have bilinear interpolation implemented to find the grayscale values of sub-pixel (x,y) points such as (100.35, 25.72) since your scan lines won't fall exactly on whole pixels.
Use a sub-pixel edge point finding technique. In general, you'll perform a curve fit to the edge points in the direction of the scan, then find the real-valued (x,y) point at maximum gradient. That's the edge point.
Store all sub-pixel edge points in a list/array/collection.
Generate line fits for the edge points. These can use Hough, RANSAC, least squares, or other techniques.
From the line equations for each of your four line fits, calculate the line angle.
That algorithm finds the angles independently for each black checkerboard square. It may be overkill for this one application, but if you're developing a library maybe it'll give you some ideas about what sub-algorithms to implement and how to structure them. For example, the algorithm would rely on implementations of these techniques:
Image morphology (e.g. erode, dilate, close, open, ...)
Kernel operations to implement morphology
Thresholding to binarize an image -- the Otsu method is worth checking out
Connected components algorithm (a.k.a blob finding, or the OpenCV contours function)
Data structure for blob
Moment calculations for blob data
Bilinear interpolation to find sub-pixel (x,y) values
A linear ray-scanning technique to find (x,y) gray values along a specific direction (which will also rely on bilinear interpolation)
A curve fitting technique and means to determine steepest tangent to find edge points
Robust line fit technique: Hough, RANSAC, and/or least squares
Data structure for line equation, related functions
All that said, if you're willing to settle for a slight loss of accuracy, and if you know that the image does not suffer from radial distortion, etc., and if you just need to find the angle of the parallel lines defined by all checkboard edges, then you might try..
Simple kernel-based edge point finding technique (Laplacian on Gaussian-smoothed image)
Hough line fit to edge points
Choose the two line fits with the greatest number of votes, which should be one set of horizontal-ish lines and the other set of vertical-ish lines
There are also other techniques that are less accurate but easier to implement:
Use a kernel-based corner-finding operator
Find the angles between corner points.
And so on and so on. As you're developing your library and creating robust implementations of standalone functions that you can string together to create application-specific solutions, you're likely to find that robust solutions rely on more steps than you would have guessed, but it'll also be more clear what the failure mode will be at each incremental step, and how to address that failure mode.
Can I ask, what C++ library are you using to code this?
Jerry is right, if you actually apply a threshold to the image it would be in 2bit, black OR white. What you may have applied is a kind of limiter instead.
You can make a threshold function (if you're coding the image processing yourself) by applying the limiter you may have been using and then turning all non-white pixels black. If you have the right settings, the squares should be isolated and you will be able to calculate the angle.
Once this is done you can use a path finding algorithm to find some edge, any edge will do. If you find a more or less straight path, you can use the extreme points as you are doing now to determine the angle. Since the checker-board rotation is only relevant within 90 degrees, your angle should be modulo 90 degrees or pi over 2 radians.
I'm not sure it's (anywhere close to) the right answer, but my immediate reaction would be to threshold twice: once where anything but black is treated as white, and once where anything but white is treated as black.
Find the angle for each, then interpolate between the two angles.
Your problem have few solutions but all have one very important issue which you seem to neglect. Note: When you are trying to make geometrical calculation in the image, the points you use must be as far as possible one from the other. You are taking 2 points inside a single square. Those points are very close one to another, so a slight error in pixel location of of the points leads to a large error in the angle. Why do you use only a single square, when you have many squares in the image?
Here are few solutions:
Find the line angle of every square. You have at least 9 squares in the image, 4 lines in each square which give you total of 36 angles (18 will be roughly at 3[deg] and 18 will be ~93[deg]). Remove the 90[degrees] and you get 36 different measurements of the angle. Sort them and take the average of the middle 30 (disregarding the lower 3 and higher 3 measurements). This will give you an accurate result
Second solution, find the left extreme point of the leftmost square and the right extreme point of the rightmost square. Now calculate the angle between them. The result will be much more accurate because the points are far away.
A third algorithm which will give you accurate results because it doesn't involve finding any points and no need for thresholding. Just smooth the image, calculate gradients in X and Y directions (gx,gy), calculate the angle of the gradient in each pixel atan(gy,gx) and make histogram of the angles. You will have 2 significant peaks near the 3[deg] and 93[deg]. Just find the peaks by searching the maximum in the histogram. This will work even if you have a lot of noise in the image, even with antialising and jpg artifacts, and even if you have other drawings on the image. But remember, you must smooth the image a lot before calculating the derivatives.
Related
I want to follow the rightmost edge in the following picture with a line following robot.
I tried simple "thresholding", but unfortunately, it includes the blurry white halo:
The reason I threshold is to obtain a clean line from the Sobel edge detector:
Is there a good algorithm which I can use to isolate this edge/move along this edge? The one I am using currently seems error prone, but it's the best one I've been able to figure out so far.
Note: The edge may curve or be aligned in any direction, but a point on the edge will always lie very close to the center of the image. Here's a video of what I'm trying to do. It doesn't follow the edge after (1:35) properly due to the halo screwing up the thresholding.
Here's another sample:
Here, I floodfill the centermost edge to separate it from the little bump in the bottom right corner:
Simplest method (vertical line)
If you know that your image will have black on the right side of the line, here's a simple method:
1) apply the Sobel operator to find the first derivative in the x direction. The result will be an image that is most negative where your gradient is strongest. (Use a large kernel size to average out the halo effect. You can even apply a Gaussian blur to the image first, to get even more averaging if the 7x7 kernel isn't enough.)
2) For each row of the image, find the index of the minimum (i.e. most negative) value. That's your estimate of line position in that row.
3) Do whatever you want with that. (Maybe take the median of those line positions, on the top half and the bottom half of the image, to get an estimate of 2 points that describe the line.)
Slightly more advanced (arbitrary line)
Use this if you don't know the direction of the line, but you do know that it's straight enough that you can approximate it with a straight line.
1)
dx = cv2.Sobel(grayscaleImg,cv2.cv.CV_32F,1,0,ksize=7)
dy = cv2.Sobel(grayscaleImg,cv2.cv.CV_32F,0,1,ksize=7)
angle = np.atan2(dy,dx)
magnitudeSquared = np.square(dx)+np.square(dy)
You now have the angle (in radians) and magnitude of the gradient at each point in your image.
2) From here you can use basic numpy operations to find the line: Filter the points to only keep points where magnitudeSquared > some threshold. Then grab the most common angle (np.bincount() is useful for that). Now you know your line's angle.
3) Further filter the points to only keep points that are close to that angle. You now have all the points on your line. Fit a line through the coordinates of those points.
Most advanced and brittle (arbitrary curve)
If you really need to handle a curve, here's one way:
1) Use your method above to threshold the image. Manually tune the threshold until the white/black division happens roughly where you want it. (Probably 127 is not the right threshold. But if your lighting conditions are consistent, you might be able to find a threshold that works. Confirm it works across multiple images.)
2) Use OpenCV's findcontours() to fit a curve to the white/black boundary. If it's too choppy, use approxPolyDP() to simplify it.
I have a set of point cloud, and I would like to test if there is a corner in a 3D room. So I would like to discuss my approach and if there is a better approach or not in terms of speed, because I want to test it on mobile phones.
I will try to use hough tranform to detect lines, then I will try to see if there are three lines that are intersecting and they make a two plane that are intersecting too.
If the point cloud data comes from a depth sensor, then you have a relatively dense sampling of your walls. One thing I found that works well with depth sensors (e.g. Kinect or DepthSense) is a robust version of the RANSAC procedure that #MartinBeckett suggested.
Instead of picking 3 points at random, pick one point at random, and get the neighboring points in the cloud. There are two ways to do that:
The proper way: use a 3D nearest neighbor query data structure, like a KD-tree, to get all the points within some small distance from your query point.
The sloppy but faster way: use the pixel grid neighborhood of your randomly selected pixel. This may include points that are far from it in 3D, because they are on a different plane/object, but that's OK, since this pixel will not get much support from the data.
The next step is to generate a plane equation from that group of 3D points. You can use PCA on their 3D coordinates to get the two most significant eigenvectors, which define the plane surface (the last eigenvector should be the normal).
From there, the RANSAC algorithm proceeds as usual: check how many other points in the data are close to that plane, and find the plane(s) with maximal support. I found it better to find the largest support plane, remove the supporting 3D points, and run the algorithm again to find other 'smaller' planes. This way you may be able to get all the walls in your room.
EDIT:
To clarify the above: the support of a hypothesized plane is the set of all 3D points whose distance from that plane is at most some threshold (e.g. 10 cm, should depend on the depth sensor's measurement error model).
After each run of the RANSAC algorithm, the plane that had the largest support is chosen. All the points supporting that plane may be used to refine the plane equation (this is more robust than just using the neighboring points) by performing PCA/linear regression on the support set.
In order to proceed and find other planes, the support of the previous iteration should be removed from the 3D point set, so that remaining points lie on other planes. This may be repeated as long as there are enough points and best plane fit error is not too large.
In your case (looking for a corner), you need at least 3 perpendicular planes. If you find two planes with large support which are roughly parallel, then they may be the floor and some counter, or two parallel walls. Either the room has no visible corner, or you need to keep looking for a perpendicular plane with smaller support.
Normal approach would be ransac
Pick 3 points at random.
Make a plane.
Check if each other point lies on the plane.
If enough are on the plane - recalculate a best plane from all these points and remove them from the set
If not try another 3 points
Stop when you have enough planes, or too few points left.
Another approach if you know that the planes are near vertical or near horizontal.
pick a small vertical range
Get all the points in this range
Try and fit 2d lines
Repeat for other Z ranges
If you get a parallel set of lines in each Z slice then they are probably have a plane - recalculate the best fit plane for the points.
I would first like to point out
Even though this is an old post, I would like to present a complementary approach, similar to Hough Voting, to find all corner locations, composed of plane intersections, jointly:
Uniformly sample the space. Ensure that there is at least a distance $d$ between the points (e.g. you can even do this is CloudCompare with a 'space' subsampling)
Compute the point cloud normals at these points.
Randomly pick 3 points from this downsampled cloud.
Each oriented point (point+plane) defines a hypothetical plane. Therefore, each 3 point picked define 3 planes. Those planes, if not parallel and not intersecting at a line, always intersect at a single point.
Create a voting space to describe the corner: The intersection of the 3 planes (the point) might a valid parameterization. So our parameter space has 3 free parameters.
For each 3 points cast a vote in the accumulator space to the corner point.
Go to (2) and repeat until all sampled points are exhausted, or enough iterations are done. This way we'll be casting votes for all possible corner locations.
Take the local maxima of the accumulator space. Depending on the votes, we'll be selecting the corners from intersection of the largest planes (as they'll receive more votes) to the intersection of small planes. The largest 4 are probably the corners of the room. If not, one could also consider the other local maxima.
Note that the voting space is a quantized 3D space and the corner location will be a rough estimate of the actual one. If desired, one could store the planes intersection at that very location and refine them (with iterative optimization similar to ICP or etc) to get a very fine corner location.
This approach will be quite fast and probably very accurate, given that you could refine the location. I believe it's the best algorithm presented so far. Of course this assumes that we could compute the normals of the point clouds (we can always do that at sample locations with the help of the eigenvectors of the covariance matrix).
Please also look here, where I have put out a list of plane-fitting related questions at stackoverflow:
3D Plane fitting algorithms
I have points in 3D which make 2 or 3 side of rectangle. How I can calculate the coordinates of the cube's corners? Is it possible?
Updated: https://github.com/CPIGroup/3d-Camera-scanDimensions
This is just an idea, not a proven method.
First, find the planes. Randomly select 3 points, find a plane that passes through them, normalize the 4 parameters. Repeat 1000 or so times. You will end up with 1000 4-tuples of numbers. Use one of the clustering analysis methods to find 2 or 3 groups of 4-tuples that are very close together. Average each of the groups. These will be, approximately, planes of your box's sides.
Now make them more precise. For each plane, find all points that are close to it but not close to other planes (for some value of "close", perhaps to be found using a clustering method too). For each such group of points, find a best fit plane using least squares.
If you have three planes, great; intersect them and you have a vertex and three edges. For two planes, you only have one edge. Either way, you can now try to find other edges. For simplicity, consider your plane to be an XY plane and your known edge an X axis. You now need to find the leftmost (rightmost) vertical line such that most of the points are to the left (resp. right) of it. Project all the points to the X axis. You now have a 1-dimensional case of your original problem: there is a lot of random points on some interval, find the interval. Use a clustering method again.
I'm not super experienced with this, but possibly you could use RANSAC ?
There seem to be many papers on the plane detection from pointclouds using RANSAC
Also you might want to have a look at the Point Clouds Library(PCL).It's a pretty impressive project with many useful features including also planar segmentation
As soon as the planes are detected, it should be a matter of finding the edges/corners which should be a lot simpler.
I have black and white image after binarization. After that I have image like below:
How can I remove the small lines parallel to the long curves using OpenCV?. I can remove them by removing all small objects, but I want to remove only the small parallel
lines.
This looks like a Canny artifact (or some kind of ringing artifact) to me. There are several ways to remove them.
An empiric but not too computing intensive method would be to locate all small features, and superimpose them with the same image shifted by [+/-]X, [+/-]Y. If the feature is completely coincident with the shifted image, i.e., all pixels in the white feature are also white in the shifted image, then you are probably looking at an artifact.
To evaluate "smallness" of feature, you can use a basic floodfill. This method is cheap because you can simulate shifting with pointers, without really allocating four shifted images. It is prone to false positives wherever you really have small parallel lines, and to false negatives if the artifacts are very large.
Another method would be to posterize twice the original image with different thresholds. While the "real" lines will stay together, the ringing artifacts will have a different strength. At that point you evaluate the image difference, and consider "artifact" all features that are farther than a given threshold from the image track. This is a bit more computation intensive, yields better results, but depends on what you have for an original image, i.e. what is your workflow.
It is possible that reevaluating the workflow (altering the edge detection phase) could avoid the creation of the artifacts altogether.
use cvBlobslib library to detect the white patches as blobs...the cvBlobslib library gives functions by which you can find out different features of the blobs like area , and ellipticity...so if you want only the smaller patches parallel to the long curve...then ..
Get the long curve on the basis of area covered by the blob or the preimeter i.e. contour length of the blob...
Get the ellipticity or the orientation of the major axis of the long curve after fitting an ellipse(cvBlobslib library will do that for you..!!)...
Filter all those blobs which are less than a threshold in terms of area or contour and have the same orientation as the long curve....
hope this might work..
If you know the orientation of your line in advance, you can do a morphological closing with a custom structuring element adapted to your needs.
See morphomat on wikipedia
See opencv documentation
Perhaps similar to what the others said, but in simpler words: since the small lines seem to have roughly half the thickness of the long ones, if you don't really care about preserving the long lines the way they are, you could apply several times a simple algorithm that "makes the lines thinner", until the small ones disappear. What you need to do is scan the image pixel by pixel and when you detect a white pixel above or below or to the left or to the right of a black pixel, you store its coordinates in a vector. After you traverse the entire image, you make all the pixels specified by the coordinates in the vector black. You could define some threshold empirically for the number of iterations of this algorithm.
Here are steps exploiting the fact that parallel lines are increasing edge density.
1) Apply adaptive Threshold on gray image to get many edges.
2) Erode 3x3 (or experiment but small) Morphological Operation.
3) Take Logical Not to get edge density.
4) Apply Dilate of like 3x3 or 5x5. It will dilate edges to merge and make a region.
5) Now Erode 7x7 (or experiment for higher then last dilate) Morphological Operation. It will remove most of the non-required region, long lines and small stray areas.
Output is is MASK for removal region. You can apply contour detection on original image and remove contour-object for matching position in mask high precision removal.
OR if you don't need high-precision result simply And with mask's NOT.
Why not doing something like:
Find the long curves (using findContours and filter by size).
Find the small curves
For each long curve, calculate the minimal distance between each point of every small curve and the long curve.
Calculate the mean and the standard deviation of these minimal distances.
Reject small curves for which either the mean minimal distance to the long curve is too large, or small curves for which the standard deviation of the minimal distances is large.
The result will probably be better (and faster) is you skeletonize the image first.
Good luck with it,
I'm doing some image processing, and am trying to keep track of points similar to those circled below, a very dark spot of a couple of pixels diameter, with all neighbouring pixels being bright. I'm sure there are algorithms and methods which are designed for this, but I just don't know what they are. I don't think edge detection would work, as I only want the small spots. I've read a little about morphological operators, could these be a suitable approach?
Thanks
Loop over your each pixel in your image. When you are done considering a pixel, mark it as "used" (change it to some sentinel value, or keep this data in a separate array parallel to the image).
When you come across a dark pixel, perform a flood-fill on it, marking all those pixels as "used", and keep track of how many pixels were filled in. During the flood-fill, make sure that if the pixel you're considering isn't dark, that it's sufficiently bright.
After the flood-fill, you'll know the size of the dark area you filled in, and whether the border of the fill was exclusively bright pixels. Now, continue the original loop, skipping "used" pixels.
How about some kind of median filtering? Sample values from 3*3 grid (or some other suitable size) around the pixel and set the value of pixel to median of those 9 pixels.
Then if most of the neighbours are bright the pixel becomes bright etc.
Edit: After some thinking, I realized that this will not detect the outliers, it will remove them. So this is not the solution original poster was asking.
Are you sure that you don't want to do an edge detection-like approach? It seems like a comparing the current pixel to the average value of the neighborhood pixels would do the trick. (I would evaluate various neighborhood sizes to be sure.)
Personally I like this corner detection algorithms manual.
Also you can workout naive corner detection algorithm by exploiting idea that isolated pixel is such pixel through which intensity changes drastically in every direction. It is just a starting idea to begin from and move on further to better algorithms.
I can think of these methods that might work with some tweaking of parameters:
Adaptive thresholds
Morphological operations
Corner detection
I'm actually going to suggest simple template matching for this, if all your features are of roughly the same size.
Just copy paste the pixels of one (or a few features) to create few templates, and then use Normalized Cross Correlation or any other score that OpenCV provides in its template matching routines to find similar regions. In the result, detect all the maximal peaks of the response (OpenCV has a function for this too), and those are your feature coordinates.
Blur (3x3) a copy of your image then diff your original image. The pixels with the highest values are the ones that are most different from their neighbors. This could be used as an edge detection algorithm but points are like super-edges so set your threshold higher.
what a single off pixel looks like:
(assume surrounding pixels are all 1)
original blurred diff
1,1,1 8/9,8/9,8/9 1/9,1/9,1/9
1,0,1 8/9,8/9,8/9 1/9,8/9,1/9
1,1,1 8/9,8/9,8/9 1/9,1/9,1/9
what an edge looks like:
(assume surrounding pixels are the same as their closest neighbor)
original blurred diff
1,0,0 6/9,3/9,0/9 3/9,3/9,0/9
1,0,0 6/9,3/9,0/9 3/9,3/9,0/9
1,0,0 6/9,3/9,0/9 3/9,3/9,0/9
Its been a few years since i did any image processing. But I would probably start by converting to a binary representation. It doesn't seem like you're overly interested in the grey middle values, just the very dark/very light regions, so get rid of all the grey. At that point, various morphological operations can accentuate the points you're interested in. Opening and Closing are pretty easy to implement, and can yield pretty nice results, leaving you with a field of black everywhere except the points you're interested in.
Have you tried extracting connected components using cvContours? First thresholding the image (using Otsu's method say) and then extracting each contour. Since the spots you wish to track are (from what I see in your image) somewhat isolated from neighborhood they will some up as separate contours. Now if we compute the area of the Bounding Rectangle of each contour and filter out the larger ones we'd be left with only small dots separate from dark neighbors.
As suggested earlier a bit of Morphological tinkering before the contour separation should yield good results.