I have some data points which I have devided into them into some clusters with some clustering algorithms as the picture below:(it might takes some time for the image to appear)
alt text http://www.freeimagehosting.net/uploads/05a807bc42.png
Each color represents different cluster. I have to draw polygons around each cluster. I use convhull for this reason. But as you can see the polygon for the red cluster is very big and covers a lot of areas, which is not the one I am looking for. I need to draw lines(ploygons) exactly around my data sets. For example in the picture above I want a polygon that is drawn exactly the same(and around) as the red cluster with the 3 branches. In other words, in this case I need a polygon with 3 branches to cover my red clusters not that big polygon that covers the whole area. Can anyone help me with this?
Please Note that the solution should be general, because the clusters will change in each run of the algorithm, so it needs to be in a way that is general.
I am not sure this is a fully specified question. I see this variants on this question come up quite often.
Why this can not really be answered here: Imagine six points, three in an equilateral triangle with another three in an equilateral triangle inside it in the same orientation.
What is the correct hull around this? Is it just the convex hull? Is it the inner triangle with three line spurs coming out from it? Does it matter what the relative sizes of the triangles are? Should you have to specify that parameter then?
If your clusters are very compact, you could try the following:
Create a grid, say with a spacing of 0.1.
Set every pixel in the grid to 1 if there's at least one data point covering it, set the pixel to 0 if there is no data point covering the pixel.
You may need to run imclose on your mask in order to fill little holes inside that have not been colored due to sheer bad luck.
Extract the border pixels using, e.g. bwperim. This is the outline of the polygon you're looking for.
Related
I have a markered robot with circular markers and two images from different perspective as shown: (Circular white rings are the markers)
I want to match the markers in the two images, by matching I mean the bottommost marker of 1st image should be treated as correspondence point of bottom most marker of 2nd image and so on.
The finger-like robot given in the image can bend in any direction given in space (can also bend in a U-like manner).
If it helps, the camera geometry is fixed and known beforehand.
I am lost, as simple correspondence algorithm would not work, since the perspectives are very different. How should I go about matching the two images?
You can start like this:
You know the position of the mounting point on the base panel for each perspective.
You know the positions of the white rings for each perspective as discussed here.
You can derive the direction of the arm at each ring by its tilt.
So you can easily determine the sequence of the positions starting with the mounting point stepping from ring to ring even if the arm is bent. With this you can match the rings from both images. If you have any situation where this fails, please add an according example to your question!
Unfortunately, you don't have matching points but matching curves. You might try to fit ellipses on the rings and take the ellipse centers for points to be matched.
This is an approximation, as the center of a circle does not exactly project as the center of the ellipse, but I don't think that this will be the major source of error: as you only see half circles, the fitting will not be that accurate.
If all nine circles remain visible and are ordered vertically, the matching of the centers is trivial. If they are not ordered but don't form a loop, you can probably start from the lowest and follow the chain of nearest neighbors.
I'm working on MATLAB on some regions inside an image. I'm at a point in which I would like to be able to separate regions which exhibit some kind of regularity (e.g., being circle-ish or square-ish) from regions which does not resemble any known figure and which for my application are mere noise. I'll illustrate this using a descriptive MS Paint image:
Is there any tool that, most of the times (or even less, I know this can't be 100/100) will recognize the red thing as being different?
I'll deal with many shapes in a single image, so I don't mind if I carry on some red monsters along the way, as long as the majority of them is kicked out. Of course I know the indices of these regions, so I can manipulate them in MATLAB.
Many algorithms come to mind, e.g., getting the boundary and checking for its regularity/the number of times it changes curvature/..., checking for variations in vertical length through different columns (nearly 0 for the linear feature, really high for the red stuff), ...
However I was hoping in some help from a tool out there. It doesn't matter if this tool won't cover all cases (for example, will kick out circles), I've been very broad to get the maximum number of inputs from you guys - any tool will be inspiring and helpful (and, however, we can't expect a perfect answer for the deeper question - recognizing regular shapes - which seems more like a AI field of research). I also think that, while being broad, this is totally non-subjective so should fit in SO. Thank you.
Side note 1: I'll deal mostly with elongated, extended features like the top-right one, so circles are not that relevant.
Side note 2: To be 100% clear, I would need something (be it an already existant tool, or some ideas pointed out by you) that acts on the indices of the shapes, in terms of rows-columns into the original image, or on the boundary of the shape itself.
Side note 3: Apart from tools/suggestions/ideas, you are welcomed to write down some lines of code ;) I'm getting the regions as connected components from bwconncomp.
I had to solve a similar problem recently that involved counting the number of indentations on blobs within in an image (basically, the connected components returned by bwconncomp). The method I used was to look at curvature changes along the boundary calculated via the FFT. In your case, the red blobs would have a large number of curvature variations, whereas the black regions would not. It's a pretty easy calculation and relatively fast. The code is on github here:
https://github.com/mjsottile/blobdents
The file of interest is src/countindents.m. A short description of the approach is here:
http://arxiv.org/abs/1501.07692
I went for the easier road as suggested by #Mikhail in comments.
I found out regionprops has a really helpful tool called Solidity. Quoting docs,
Returns a scalar specifying the proportion of the pixels in the convex hull that are also in the region. Computed as Area/ConvexArea.
Convex hull is defined as the smallest convex polygon that can contain the region. So Solidity goes up to 1 if the shape is kind of regular and has no convexity changes; down to 0 for my red shape, which leaves space between itself and the convex polygon.
Of course it never reaches 0, lowest value should belong to a kind of +-shaped sign.
The problem I have is that there are rectangles within rectangles. Think of a map, except with the following traits with the key point being: rectangles with similar density often share similar dimensions and similar position on the x axis with other rectangles, but sometimes the distance between these rectangles may be big but usually small. If the position on x axis or dimensions are clearly way off, they would not be similar.
rectangles do not intersect, smaller rectangles are completely inside a larger rectangle.
rectangles often have similar x position and similar dimensions
(similar height and width), and have smaller rectangles inside it. The rectangle itself would be considered a cluster of it's own.
Sometimes the distance of these cluster from another cluster may be quite
big (think of islands). Often these clusters share the same or
similar dimension and same or similar density of sub rectangles. if so, they should be considered as part of the same cluster despite a distance between the two clusters.
The more dense a rectangle is (smaller rectangles inside), the more likely there is a similar or same dense rectangle sharing same or similar dimension nearby.
I've attached a diagram to describe the situation more clearly:
Red border means those groups are outliers, not part of any cluster
and are ignored.
Blue border has many clusters (black borders containing black solid
rectangles). They form a group of clusters that are similar due to
the criteria mentioned above (similar width, similar X position,
similar density). Even the clusters towards the bottom right corner
is still considered part of this group because of the criteria
(similar width, similar X position, similar density).
Turquois border has many clusters (black borders containing black
solid rectangles). However, these clusters differ in dimension, x
position, and density, from the ones in Blue border. They are
considered a group of their own.
So far I found density clustering such as DBSCAN which seems to be perfect since it takes noise (outliers) into consideration, and you do not need to know ahead of time how many clusters there will be.
However, you need to define the minimum number of points needed to form a cluster and a threshold distance. What happens if you don't know these two and it can vary based on the problem described above?
Another seemingly plausible solution would be hierarchial (agglomerative) clustering (r-tree), but I'm concerned that I would still need to know the cutoff point in the tree depth level to determine if it's a cluster.
You certainly will need to take all your constraints into account.
In general, your task looks more like constraint satisfaction to me than clustering.
Maybe some constraint clustering approaches are useful to you, but I'm not sure if they allow your kind of constraints. Usually, they only support must-link and must-not-link constraints.
But of course you should try DBSCAN (in particular also: generalized DBSCAN, since the generalization might allow you to add the constraints you have!) and R-trees (which aren't actually a clustering algorithm, but a data index).
Note that R-trees will put the "outliers" into some leaf, to ensure minimum fill.
As is, I cannot give you more detailed recommendations, because even from above sketch, your constraints are not well defined IMHO. Try putting them into pseudocode. You probably only have a small number of rectangles (say, 100); so you can afford to run really expensive algorithms, such as linkage clustering with a customized linkage criterion. Putting your criterions into code may already be 99% of the effort!
The following problem:
Given is an arbitrary polygon. It shall be covered 100% with the minimum number of circles of a given radius.
Note:
1) Naturally the circles have to overlap.
2) I try to solve the problem for ARBITRARY polygons. But also solutions for CONVEX polygons are appreciated.
3) As far as Im informed, this problem is NP-hard ( an algorithm to find the minimum size set cover for the Set-cover problem )
Choose: U = polygon and S1...Sk = circles with arbitrary centers.
My solution:
Ive already read some papers and tried a few things on my own. The most promising idea that I came up with was in fact one already indicated in Covering an arbitrary area with circles of equal radius.
So I guess it’s best I quickly try to describe my own idea and then refine my questions.
The picture gives you already a pretty good idea of what I do
IDEA and Problem Formulation
1. I approximate the circles with their corresponding hexagons and tessellate the whole R2, i.e. an sufficiently large area; keyword hexagonally closest packaging. (cyan … tessellation, red dotted, centers of the cyan hexagons)
2. I put the polygon somewhere in the middle of this tessellated area and compute the number of hexagons that are needed to cover the polygon.
In the following Im trying to minimize N, which is number ofhexagons needed to cover the polygon, by moving the polygon around step by step, after each step “counting” N.
Solving the problem:
So that’s when it gets difficult (for me). I don’t know any optimizers that solve this problem properly, since they all terminate after moving the polygon around a bit and not observing any change.
My solution is the following:
First note that this is a periodic problem:
1. The polygon can be moved in horizontal direction x with a period of 3*r (side length = radius r) of the hexagon.
2. The polygon can be moved in vertical direction y with a period of r^2+r^2-2*rrcos(2/3*pi) of the hexagon.
3. The polygon can be rotated phi with a period of 2/3*pi.
That means, one has to search a finite area of possible solutions to find the optimal solution.
So what I do is, I choose a stepsize for (x,y,phi) and simply brute force compute all possible solutions, picking out the optimum.
Refining my questions
1) Is the problem formulated intelligently? Right now im working on an algorithm that only tessellates a very small area, so that as little hexagons as possible have to be computed.
2) Is there a more intelligent optimizer to solve the problem?
3) FINALLY: I also have difficulties finding appropriate literature, since I don’t guess I don’t know the right keywords to look for. So if anybody can provide me with literature, it would also be appreciated a lot.
Actually I could go on about other things ive tried but I think no one of u guys wants to spend the whole afternoon just reading my question.
Thx in advance to everybody who takes the time to think about it.
mat
PS i implement my algorithms in matlab
I like your approach! When you mention your optimization I think a good way to go about it is by rotating the hexagonal grid and translating it till you find the least amount of circles that cover the region. You don't need to rotate 360 since the pattern is symmetric so just 360/6.
I've been working on this problem for a while and have just published a paper that contains code to solve this problem! It uses genetic algorithms and BFGS optimization. You can find a link to the paper here: https://arxiv.org/abs/2003.04839
Edit: Answer rewritten (there's no limitation that circles couldn't go outside the polygon).
You might be interested in Covering a simple polygon with circles. I think the algorithm works or is extendable also to complex polygons.
1.Inscribe the given polygon in a minimum sized rectangle
2.Cover the rectangle optimally by circles (algorithm is available)
I have an image which looks like this:
I have a task in which I should circle all the bottles around their opening. I created a simple algorithm and started working it. My algorithm follows:
Threshold the original image
Do some morphological opening in it
Fill the empty holes
Separate the portion of the image using region props such that only the area equivalent to the mouth of the bottles is selected.
Find the centroid for each and draw circle around each bottle.
I did according to the algorithm above and but I have some portion of the image around which I draw a circle. This is because I have selected the area since the area of the mouth of bottle and the remained noise is almost same. And so I yielded a figure like this.
The processing applied on the image look like this:
And my final image after plotting the circle over the original image is like this:
I think I can deal with the extra circle, that is, because of some white portion of the image remained as shown in the figure 2 below. This can be filtered out using regionproping for eccentricity. Is that a good idea or there are some other approaches to this? How would I deal with other bottles behind the glass and select them?
Nice example images you provide for your question!
One thing you can use to detect the remaining bottles (if there are any) is the well defined structure of the placement of the bottles.
The 4 by 5 grid of the bottle should be relatively easy to locate, and when the grid is located you can test if a bottle is detected at each expected bottle location.
With respect to the extra detected bottle, you can use shape features like
eccentricity,
the first Hu moment
a ratio between the perimeter length squared over the area (which is minimized for a circle) details here
If you are able to detect the grid, it should be easy to located it as an outlier (far from an expected bottle location) and discard accordingly.
Good luck with your project!
I've used the same approach as midtiby's third suggestion using the ratio between area and perimeter called shape factor:
4π * Area /perimeter^2
to detect circles from a contour traced image (from the thresholded image) to great success;
http://www.empix.com/NE%20HELP/functions/glossary/morphometric_param.htm
Regarding the 4 unfound bottles, this is rather tricky without some a priori knowledge of what it is you're looking at (as discussed using the 4 x 5 grid, then looking from the centre of each cell). I did think that from the list of contours, most would be of the bottle tops (which you can test using the shape factor stuff), however, one would be of a large rectangle. If you could find the extremities of the rectangle (from the largest contour in terms of area), then remove it from the third image, you'd be left with partial circles. If you then contour traced those partial circles and used a mixture of shape factor/curve detection etc. may help? And yes, good luck again!