I have a bit of a difficult algorithm question, I can't find any suitable algorithm from a lot of searching, so I am hoping that someone here on stackoverflow might know the answer.
I have a set of x,y coordinates for a vehicle as it moves through a 2D space, the coordinates are recorded at "decision points" in the time period (i.e. they have stopped and made a determination of where to move next).
What I want to do is find a mechanism for comparing these trails efficiently (i.e. not going through each point individually). Compounding this is that I am interested in the "pattern" of their movement, not necessarily the individual points they went to. This means that the "path" is considered the same if you reflect it around an axis, or if you rotate it by 90,180 or 270 degrees.
Basically I am trying to distil some sort of "behaviour" to the way they move through the space, then examine the different "behaviours" for classification purposes.
Cheers,
Aidan
This may be way more complicated than you're looking for, but it sounds like what the guys did at astrometry.net may be similar to what you're looking for. Essentially, you can upload a picture of some stars, and it will figure out the position in the sky it belongs, along with rotation, you may be able to use similar pattern matching in what you're looking for.
They have a great pdf explaining how it works here, and apparently you can email them and they'll send you the source code (details are in the pdf).
Edit: apparently you can download the code directly here.
Hope it helps.
there are several approaches you could make:
Using vector paths and translation matricies together with two algorithms, The A* (a star) algorithm ( to locate best routes from what are called greedy functions ), and the "nearest neighbour" algorithm --- these are both commonly used for comparing path efficiencies for routes.
you may not know it but the issue you have is known as the "travelling salesman" problem and has many many approaches.
so look up
traveling salesman problem
A*
Nearest neighbour
also look at
Random walk algorithm - for the most basic approach
for a learned behaviour approach try neural networks "ANN" or genetic algorithms
the mathematics for this type of problem are covered under what is called "graph theory"
It seems that basically what is needed is some metric to compare two(N in general) paths and choose the best one?
If that's the case then I'd suggest plain statistics. I'd start with heading(orientation) histogram, relative(relative to previous heading) heading histogram and so on. Other thing comes to mind - distance/orientation between points covariance. Or just simply make up some kind of "statistics"(number of turns, etc.) and compare those paths using that.
Related
I'm faced with a problem where I have to solve puzzles.
E.g. I have an (variable) area of 20x20 (meters for example). There are a number of given set pieces having variable sizes. Such as 4x3, 4x2, 1x5 pieces etc. These pieces can also be turned to add more pain to my problem. The point of the puzzle is to fill the entire area of 20x20 with the given pieces.
What would be a good starting algorithm to achieve such a feat?
I'm thinking of using a heuristic that calculates the open space (for efficiency purposes).
Thanks in advance
That's an Exact Cover problem, with a nice structure too, usually, depending on the pieces. I don't know about any heuristic algorithms, but there are several exact options that should work well.
As usual with Exact Covers, you can use Dancing Links, a way to implement Algorithm X efficiently.
Less generally, you can probably solve this with zero-suppressed decision diagrams. It depends on the tiles though. As a bonus, you can represent all possible solutions and count them or generate one with some properties, all without ever explicitly storing the entire (usually far too large) set of solutions.
BDDs would work about as well, using more nodes to accomplish the same thing (because the solutions are very sparse, as in, using few of the possible tile-placements - ZDDs like that but BDDs like symmetry better than sparseness).
Or you could turn it into a SAT problem, then you get less information (no solution count for example), but faster if there are easy solutions.
I am working on a project which determines the indoor position of an object which moves in 3D space (e.g. a quadcopter).
I have built some prototypes which use a combination of gyroscope, accelerometer and compass. However the results were far from being satisfactory, especially related to the moved distance, which I calculated using the accelerometer. Determining the orientation using a fusion of gyroscope and compass was close to perfect.
In my opinion I am missing some more sensors to get some acceptable results. Which additional sensors would I need for my purpose? I was thinking about adding one or more infrared cameras/distance sensors. I have never worked with such sensors and I am not sure which sensor would lead to better results.
I appreciate any suggestions, ideas and experiences.
The distance checking would decidedly help. The whole algorithm of any surface geo survey is based on the conception of start/final check. You know the start, then you add erroneous steps, and come to the finish that you know, too. But you have collected some sum error by the way. Then you distribute the error found among all steps done, with the opposite sign, of course.
What is interesting, in most cases you not only somewhat diminish the effect of arbitrary mistakes, but almost eliminate the systematical ones. Because they mostly are linear or close to linear and such linear distribution of found error will simply kill them.
That is only the illustration idea. Any non-primitive task will contain collecting all data and finding their dependencies, linearizing them and creating parametrical or correlational systems of equations. The solving of them you get the optimal changes in the measured values. By parametrical method you can also easily find approximate errors of these new values.
The utmost base of these methods is the lesser squares method of Gauss. The more concrete methodics can be found in old books on geodesy/geomatic/triangulation/ geodesy nets. The books after introduction of GPS are for nothing, because everything was terribly simplified by it. Look for the books with matrix formulaes for lesser squares solutions.
Sorry if I had translated some terms into English with errors.
I'm working on a project with a virtual robot (Turtles in the ComputerCraft mod for Minecraft), where the robot would be in a maze of tunnels and have to navigate around in them. The world is conveniently already divided into tiles (a 2D Cartesian graph of them, with a boolean passable/nonpassable value for each), and the robot building the tunnels will map them as he goes.
In addition, there are teleporter "shortcuts" scattered around in areas where robots need to get between them quickly.
The question is: What's the best way to have the robot pathfind to his destination? How would the system identify areas that need teleporters? A* is the most famous algorithm, but are there others that might suit the application better? Please keep in mind that I have very little experience with pathfinding algorithms, so you might have to break things down into base terms for me to understand. Any suggestions?
The only problem with using A* is finding an admissible heuristic for your problem. Fortunately, this has already been answered here.
How would the system identify areas that need teleporters?
That depends on where the turtle is actually moving to/from. If he's always moving to/from the same start/end points, the answer is trivial: add teleports at the start and finish. For more complicated setups, my guess would be that this is NP-hard; if true, you'll have to look into global-optimization strategies (or just try a bunch of random positions and take the best one).
I am working on edge detection in images and would like to evaluate the performance of algorithm, if any any one could give me a reference or method on how to proceed it will be really helpful. :)
I do not have ground truth and data set includes color as well as gray images.
Thank you.
Create a synthetic data set with known edges, for example by 3D rendering, by compositing 2D images with precise masks (as may be obtained in royalty free photosets), or by introducing edges directly (thin/faint lines). Remember to add some confounding non-edges that look like edges, of a type appropriate for what you're tuning for.
Use your (non-synthetic) data set. Run the reference algorithms that you want to compare against. Also produce combinations of the reference algorithms, for example by voting (majority, at least K out of N, etc). Calculate stats on your algo vs reference algo performance, in terms of (a) number of points your algo classifies as edge which each reference algo, or the combination, does not classify as edge (false positive), or (b) number of points which the reference algo classifies as edge that your algo does not (false negative). You can also calculate a rank correlation-type number for algos by looking at each point and looking at which algos do (or don't) classify that as an edge.
Create ground truth manually. Use reference edge-finding algos as a starting point, then fix up by hand. Probably valuable to do for a small number of images in any case.
Good luck!
For comparisons, quantitative measures like what #Alex I explained is best. To do so, you need to define what is "correct" with a ground truth set and a way to consistently determine if a given image is correct or on a more granular level, how correct (some number like a percentage) it is. #Alex I gave a way to do that.
Another option that is often used in graphics research where there is no ground truth is user studies. Usually less desirable as they are time consuming and often more costly. However, if it is a qualitative improvement that you are after or if a quantitative measurement is just too hard to do, a user study is an appropriate solution.
When I mean user study I mean to poll people on how well a result is given the input image. You could give them a scale to rate things on and randomly give them samples from both your results and the results of another algorithm
And of course, if you still want more ideas, be sure to check out edge detection papers to see how they measured their results (I'd actually look here first as they've already gone through this same process and determined what was best for them: google scholar).
This is a long shot, but I thought I might try before starting the dirty work.
I've got a project to build an application which will, for a defined input stations (vertices) and lines (edges), that is, a real map of some public transportation, schematize a given map into a metro map. I've done some research on the problem and it's an NP-complete problem equivalent to the 3-SAT problem. I also have some theoretic ideas on how to generate such a map, but they aren't detailed enough.
What I'm looking for is any other existing solution of this problem, some sort of pseudo-code, some real code in (almost) any other programming language etc, anything that would reduce the time I need to spend working on the algorithm itself, which will in return give me more time to work on other aspects of the application.
If anyone has ever seen anything that can help me, I'd appreciate it very much.
If you google for "metro map layout problem" and "metro map line crossing" you'll find a lot of references, since it has been researched very actively in the past 10 years.
The problem seems no trivial at all, and translating the "artistic" features to mathematical constraints is seemingly one of the most difficult tasks.
Anyway here are three publications that I found interesting to start with (among many, many others):
Metro Map Layout Using Multicriteria Optimization
Line Crossing Minimization on Metro Maps
The Metro Map Layout Problem
HTH!
Research that's similar to your topic: http://graphics.stanford.edu/papers/routemaps/
This is just some suggestion with handwaving - take with a pinch of salt.
My notion of a "metro" map is one where lines tend to one of the eight cardinal directions and stations are regularly spaced.
I'm assuming you're trying to convert a set of real coordinates into "metro" coordinates.
I would start with your main route (e.g., a city loop), then incrementally add other routes in order of importance.
For each route you want to find the nearest approximation that uses the fewest number of straight lines travelling in the eight cardinal directions. You might do this by starting with the bounding box for the real coordinates, splitting that into a grid, then finding a "metro" route from grid square to grid square, then successively refining that route to reduce the number of bends without distorting the map too much and without introducing crossings with other routes if at all possible.
Having done that, scale each line so that consecutive stations are the same distance apart on the "metro" view.
My guess is you'll still want to support manual tweaking of the result.
Good luck!
Feels like a planning problem.
Looks like your hard constraints are:
Every station must be on a point. A points are on a grid with a distance of X between points (I'd make this static on 2cm)
There should not be 2 stations on the same spot
There should be enough room to draw the station label. Note that the label can be assigned different directions from the point to which the station is assigned.
There should be enough room to draw the subway lines.
Looks like your soft constraints are:
For each station, minimize the actually geographical location distance to the point assigned to the station.
Then throw something like Drools Planner on it, here's an example of hard and soft constraints for nurse rostering.