I am interested in using the CGContextEOFillPath feature provided by apple. I am guessing with the way the EOFill works, it probably has a way to take the filled in areas and calculate an area.
So my question is does anyone know of a way to use CGContextEOFillPath and find the area of the filled in sections.
If this isn't something that is easily done, maybe some pointers to a better way of doing this would be helpful. Though I need to use the EO style graphing.
Thanks.
What do you mean "Calculate the area"?
As in calculate the surface area of a complex shape?
It depends on your shapes.
Are they all polygons?
What about circles?
There are well known formulas for calculating the area of a polygon. (Wikipedia has it) Part of that calculation involves using an ABS() function because shapes drawn "counterclockwise" have the opposite sign as those drawn "clockwise". If you're looking to simulate the EO behavior, you can simply ignore the sign change, because, for you, it's desirable.
If you have more complicated shapes that involve curves, then you need to break the problem down into multiple parts - one part to solve for polygons - one to solve for circles - one to solve for other shapes, etc.
Related
I have two sets of 2D Points (shown in images below).
And I would like to find some high confidence correspondence between these dots.
These dots are extracted feature points from 2 camera images from different angles. Two images are relatively well rectified, though not perfect. However, there will be distortion/warp caused by depth in the scene, the number of points might not be the same, there might be outliers, etc.
One approach could be using a sliding window that contains multiple dots and try block matching. But that might be kind of slow. I feel like there should be a relatively straight forward solution to this problem.
For example, this paper might be addressing a similar problem.
You can use each dot/point in one of the images, and search for its "neighbors" in the other image.
Just a few days ago someone asked a similar question here, and got a very sophisticated (accepted) answer:
How to calculate the nearest neighbors using weka from the command line?
But maybe your problem is so common in image processing that there are even better solutions, but you might try this one (implemented in java).
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 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 am able to draw shapes using the UIBezierPath object. Now I want to identify different shapes drawn using this eg. Rectangle , Square , Triangle , Circle etc. Then next thing I want to do is that user should be able to select a particular shape and should be able to move the whole shape to different location on the screen. The actual requirement is even more complex , but If I could make this much then I can work out on the rest.
Any suggestion or links or points on how do I start with this is welcome . I am thinking of writing a separate view to handle every shape but not getting how do I do that..
Thank You all in advance !!
I recommend David Gelphman’s Programming with Quartz.
In his chapter “Drawing with Paths” he has a section on “Path Construction Primitives” which provides a crossroads:
If you use CGContextAddLineToPoint your user could make straight lines defined by known Cartesian points. You would use basic math to deduce the geometric shapes defined by those points.
If you use CGContextAddCurveToPoint your user could make curved lines defined by known points, and I’m pretty sure that those lines would run through the points, so you could still use basic math to determine at least an approximation of the types of shapes formed.
But if you use CGContextAddQuadCurveToPoint, the points define a framework outside of the drawn curve. You’d need more advanced math to determine the shapes formed by curves along tangents.
Gelphman also discusses “Path Utility Functions,” like getting a bounding box and checking whether a given point is inside the path.
As for moving the completed paths, I think you would use CGContextTranslateCTM.
I am trying to make an iPhone application which can draw a path between two points (similar to Google Maps) but instead of the map i want to use any other image as a background, this path between the two points might not be straight and there might be multiple paths to get from one point to another then I want to draw the shortest path between the two points.
I tried using the CGContext & CGPath but I got stacked.
Can you help me plz.
Thanx,
Ghaith
I think you're looking for UIBezierPath. You can add simple lines/polygons with something like:
UIBezierPath* path = [UIBezierPath bezierPath];
[aPath moveToPoint:CGPointMake(50.0, 50.0)];
[aPath addLineToPoint:CGPointMake(10.0, 10.0)];
[aPath addLineToPoint:CGPointMake(10.0, 50.0)];
[aPath closePath];
You can also, of course, add curves (bezier ones!) and other shapes. Then to draw it use the [aPath stroke] call in your view's drawRect method.
For more information see the iPad Programming Guide
This seems like a problem that's not really related to drawing the route.
You want to find the shortest path from one point to another, given certain criteria - where you can and cannot move, for example. I don't see this problem as something you can solve with drawing, but with actually calculating the different possible ways and then compare them. When you have decided which is the best route. Drawing is pretty simple.
How you would go by deciding I'm actually not sure - sorry 'bout that. But you should probably have a look at some shortest path algorithms. But that probably means you have to represent the underlying image as a pattern, or a series of nodes but graphical problems are not my cup of tea, so I'm not really sure how.
Just a side note - If the number of possible ways of getting from point A to point B are great, this can become a computational problem, and you have to make sure that the iPhone can manage.
(this should probably be a comment somewhere, but since I can't yet and I still wanted to share my two cents, it became an answer.)
Edit:
I just thought of really naive aproach! - for fun mostly, but I couldn't keep myself from posting.
Suppose you have a representation of the image. What parts can't be traveled on and what parts can be. Each pixel that can be travelled on is represented by a 1, and every other pixel is represented by a 0. Thus the pixels represented by 1s can be seen as nodes on which we can travel.
Each node can reach, at most, 8 other nodes - the adjacent pixels. And the weight of travelling between any two nodes could be set as 1. But we have to account that travelling in a diagonal is a greater distance so that weight should be sqrt(2).
Now we have a great bunch of nodes - each with weights in between them. From here we can apply a djikstra-algorithm to find the best route. (maybe some other algorithm is more beneficial at this point - but djikstras is the only one I'm familiar with).
hum, wonder how bad of a solution this would be. ... again, you probably don't want this solution...
EDIT 2:
I will say this again that this is probably not the best way to do this! You should seriously ask someone with more experience in algorithms and in graphical problems. - This was something I thought of at 3am and was mostly for laughs.
If your question is about calculating routes instead of drawing routes, that's a whole different problem. The standard algorithm for finding efficient routes through a given space are the "A*" (pronounced A-star) algorithms, which are typically what real-time strategy games use when you click a unit and tell it to "go there". It's also got many uses in AI when searching for a transition through a space.
It's not easy to get right, though. It might be easier to find a good game engine that already includes an A* implementation and integrate that into your software.