I'm applying 3D graph cuts based on Yuri Boykov's implementation in C++, itk and boost for min cut/max flow. First I provide some foreground and background seeds. Then I create the graph and assign the weight to the edges using 3D neighborhood (boundary term):
weight=vcl_exp(-vcl_pow(pixelDifference,2)/(2.0*sigma*sigma)),
being sigma a noise function.
Then I assign the source/sink edges depending on the intensity probability histogram (regional term):
this->Graph->add_tweights(nodeIterator.Get(),
-this->Lambda*log(sinkHistogramValue),
-this->Lambda*log(sourceHistogramValue));
So the energy function is E= regional term+boundary term. Then, the cut is compute with Boycov's implementation, but I don't understand exactly how. Anyway, now I want to add a shape prior to the cut, but I have no clue on how to do it.
Do I have to change the weight of the edges?
Do I have to create another energy function? And if so, how?
How could I provide both functions to the mincut/max flow algorithm?
Hope my questions are easily understandable.
Thank you very much,
Karen
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I have got a binary image/contour containing four human beings, and I want to detect/count all humans. Since there are occlusions, so I think it is best to get the head/maxima in the contour of all the humans. In that case human can be counted.
I am able to get the global maxima\topmost point (in terms of calculus language), but I want to get all the local maximas
The code for finding the topmost point is as suggested by Adrian in his blogpost i.e.:
topmost = tuple(biggest_contour[biggest_contour[:,:,1].argmin()][0])
Can anyone please suggest how to get all the local maximas, instead of just topmost location?
Here is the sample of my Image:
The definition of "local maximum" can be tricky to pin down, but if you start with a simple method you'll develop an intuition to look further. Even if there are methods available on the web to do this work for you, it's worth implementing a few basic techniques yourself before you go googling.
One simple method I've used in the path goes something like this:
Find the contours as arrays/lists/containers of (x,y) coordinates.
At each element N (a pixel) in the list, get the pixels at N - D and N + D; that is the pixels D ahead of the current pixel and D behind the current pixel
Calculate the point-to-point distance
Calculate the distance along the contour from N-D to N+D
Calculate (distanceAlongContour)/(point-to-point distance)
...
There are numerous other ways to do this, but this is quick to implement from scratch, and I think a reasonable starting point: Compare the "geodesic" distance and the Euclidean distance.
A few other possibilities:
Do a bunch of curve fits to chunks of pixels from the contour. (Lots of details to investigate here.)
Use Ramer-Puecker-Douglas to render the outlines as polygons, then choose parameters to ensure those polygons are appropriately simplified. (Second time I've mentioned R-P-D today; it's handy.) Check for vertices with angles that deviate much from 180 degrees.
Try a corner detector. Crude, but easy to implement.
Implement an edge follower that moves from one pixel to the next in the contour list, and calculate some kind of "inertia" as the pixel shifts direction. This wouldn't be useful on a pixel-by-pixel basis, but you could compare, say, pixels N-1,N,N+1 to pixels N+1,N+2,N+3. Or just calculate the angle between them.
Currently I am working on a project of detecting defects of product line by comparing the pictures taken by camera. I tried to use OpenCV to extract the edges of the sample picture and the testing picture. However, I am not sure about the next step of comparison. How should I make a conclusion of ok? What measure should I use to compare the pictures?
What I come up in mind is using square difference of every pixels. However, it depends too much on the static environment. I saw the shape distance and Hausdoff distance provided by opencv. Which one should I use? For shape distance, where could I find the logic or methodology behind it? Thanks !!!
I tried to compare two identical pictures (bmp) (just copied from another). The shape distance calculated by shape distance is not zero .... It makes me difficult to set the threshold of shape distance. For Hausdoff distance, the distance calculated is even larger....
Thank you for your kind attention!!
I have a distribution of weighted 2D pose estimates (position + orientation) that are samples of an unknown PDF of a systems pose. All estimates and the underlying real position are constrained by a concave polygon.
The picture shows an exemplary distribution. The magenta colored circles are the estimates, the radius line indicates the estimated direction. The weights are indicated by the circles diameter. The red dot is the weighted mean, the yellow cirlce indicates the variance and the direction but is of no importance for the following problem:
From all estimates I want to derive the most likely position of the system.
Up to now I have evaluated the following approaches:
Using the estimate with the highest weight: Gives poor results since one estimate with a high weight outperforms several coinciding estimates with slightly lower weights.
Weighted Mean: Not applicable since the mean might lie outside the polygon as in the picture (red dot with yellow circle).
Weighted Median: Would work but does neglect potential clusters. E.g. in the image below two clusters are prominent of which one is more likely than the other.
Additionally I have looked into K-Means and K-Medoids. For K-Means I do not know the most efficient way to constrain the centers to the polygon. K-Medoids seems to work, but has poor performance (O(n^2)), which is important since I have a high number of estimates (contrary to explanatory picture)
What would be the ideal algorithm to solve this kind of problem ?
What complexity can be achieved ?
Are there readily available algorithms in c++ that solve this problem, or can be easily adapted to solve it?
k-means may also yield an estimate outside your polygons.
Such constraints are beyond the clustering use case. But nothing prevents you from devising a method to correct the estimates afterwards.
For non-convex data, DBSCAN may be worth a try. You could even incorporate line-of-sight into Generalized DBSCAN easily. But I'm not convinced that clustering will help for your overall objective.
I have some 3D Points that roughly, but clearly form a segment of a circle. I now have to determine the circle that fits best all the points. I think there has to be some sort of least squares best fit but I cant figure out how to start.
The points are sorted the way they would be situated on the circle. I also have an estimated curvature at each point.
I need the radius and the plane of the circle.
I have to work in c/c++ or use an extern script.
You could use a Principal Component Analysis (PCA) to map your coordinates from three dimensions down to two dimensions.
Compute the PCA and project your data onto the first to principal components. You can then use any 2D algorithm to find the centre of the circle and its radius. Once these have been found/fitted, you can project the centre back into 3D coordinates.
Since your data is noisy, there will still be some data in the third dimension you squeezed out, but bear in mind that the PCA chooses this dimension such as to minimize the amount of data lost, i.e. by maximizing the amount of data that is represented in the first two components, so you should be safe.
A good algorithm for such data fitting is RANSAC (Random sample consensus). You can find a good description in the link so this is just a short outline of the important parts:
In your special case the model would be the 3D circle. To build this up pick three random non-colinear points from your set, compute the hyperplane they are embedded in (cross product), project the random points to the plane and then apply the usual 2D circle fitting. With this you get the circle center, radius and the hyperplane equation. Now it's easy to check the support by each of the remaining points. The support may be expressed as the distance from the circle that consists of two parts: The orthogonal distance from the plane and the distance from the circle boundary inside the plane.
Edit:
The reason because i would prefer RANSAC over ordinary Least-Squares(LS) is its superior stability in the case of heavy outliers. The following image is showing an example comparision of LS vs. RANSAC. While the ideal model line is created by RANSAC the dashed line is created by LS.
The arguably easiest algorithm is called Least-Square Curve Fitting.
You may want to check the math,
or look at similar questions, such as polynomial least squares for image curve fitting
However I'd rather use a library for doing it.
Finding Circle Edges :
Here are the two sample images that i have posted.
Need to find the edges of the circle:
Does it possible to develop one generic circle algorithm,that could find all possible circles in all scenarios ?? Like below
1. Circle may in different color ( White , Black , Gray , Red)
2. Background color may be different
3. Different in its size
http://postimage.org/image/tddhvs8c5/
http://postimage.org/image/8kdxqiiyb/
Please suggest some idea to write a algorithm that should work out on above circle
Sounds like a job for the Hough circle transform:
I have not used it myself so far, but it is included in OpenCV. Among other parameters, you can give it a minimum and maximum radius.
Here are links to documentation and a tutorial.
I'd imagine your second example picture will be very hard to detect though
You could apply an edge detection transformation to both images.
Here is what I did in Paint.NET using the outline effect:
You could test edge detect too but that requires more contrast in the images.
Another thing to take into consideration is what it exactly is that you want to detect; in the first image, do you want to detect the white ring or the disc inside. In the second image; do you want to detect the all the circles (there are many tiny ones) or just the big one(s). These requirement will influence what transformation to use and how to initialize these.
After transforming the images into versions that 'highlight' the circles you'll need an algorithm to find them.
Again, there are more options than just one. Here is a paper describing an algoritm
Searching the web for image processing circle recognition gives lots of results.
I think you will have to use a couple of different feature calculations that can be used for segmentation. I the first picture the circle is recognizeable by intensity alone so that one is easy. In the second picture it is mostly the texture that differentiates the circle edge, in that case a feature image based based on some kind of texture filter will be needed, calculating the local variance for instance will result in a scalar image that can segment out the circle. If there are other features that defines the circle in other scenarios (different colors for background foreground etc) you might need other explicit filters that give a scalar difference for those cases.
When you have scalar images where the circles stand out you can use the circular Hough transform to find the circle. Either run it for different circle sizes or modify it to detect a range of sizes.
If you know that there will be only one circle and you know the kind of noise that will be present (vertical/horizontal lines etc) an alternative approach is to design a more specific algorithm e.g. filter out the noise and find center of gravity etc.
Answer to comment:
The idea is to separate the algorithm into independent stages. I do not know how the specific algorithm you have works but presumably it could take a binary or grayscale image where high values means pixel part of circle and low values pixel not part of circle, the present algorithm also needs to give some kind of confidence value on the circle it finds. This present algorithm would then represent some stage(s) at the end of the complete algorithm. You will then have to add the first stage which is to generate feature images for all kind of input you want to handle. For the two examples it should suffice with one intensity image (simply grayscale) and one image where each pixel represents the local variance. In the color case do a color transform an use the hue value perhaps? For every input feed all feature images to the later stage, use the confidence value to select the most likely candidate. If you have other unknowns that your algorithm need as input parameters (circle size etc) just iterate over the possible values and make sure your later stages returns confidence values.