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I was curious if it would be possible to count the number of things in a picture, let's say the number of ducks, by first taking a sample picture and then seeing where it matched in a separate picture. So to clarify, we would have 2 pictures (one picture with a single duck, and one picture with 4 ducks for the sake of the argument) and the program would see how many matches it could make in the 4 duck picture by overlaying the one duck picture--thereby counting how many ducks there are in the picture. I've been reading up on computer vision a little bit, and I know that opencv's site talked about using a Fourier transform to break an image into its magnitude and phase. I was hoping to possibly take the magnitude of the one duck picture into a matrix and then compare it to a series of matrices from the four duck picture.
I imagine this would be quite difficult, seeing as how I would have to somehow tell the program the shape of the initial duck and then store that duck's broken down image information into a matrix and then compare that to matrices broken down from the other picture. Any ideas/suggestions? I thought this would be a good learning experience, since I'm an electrical engineering student and I learned Fourier Transforms, DFTs, etc. last semester--it'd just be cool to actually apply them to something.
You are talking about object recognition - one of fundamental problems in computer vision. Your main idea - take a picture of the object, get some features from it and then find same set of features on other image - is correct. However, pixel by pixel comparison (no matter in time or frequency domain) is very error-prone and normally gives poor results. In most cases more high-level features give much better results.
To get started, take a look at Cascade Classifier in OpenCV which uses Haar-like features (small rectangles with particular gray level). It is most well-known for face detection and recognition, but can also be trained for other objects.
You may also be interested in SURF method, which searches for points with similar characteristics, or even AAMs, which try to model shape and appearance of an object.
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This is my first post. I'm the lead programmer on a FIRST robotics team, and this year's competition is about throwing Frisbees. I was wondering if there was some sort of "grand unified equation" for the trajectory that takes into account the air resistance, initial velocity, initial height, initial angle, etc. Basically, I would like to acquire data from an ultrasonic rangefinder, the encoders that determine the speed of our motors, the angle of our launcher, the rotational force (should be pretty constant. We'll determine this on our own) and the gravitational constant, and plug it into an equation in real time as we're lining up shots to verify/guesstimate whether or not we'll be close. If anyone has ever heard of such a thing, or knows where to find it, I would really appreciate it! (FYI, I have already done some research, and all I can find are a bunch of small equations for each aspect, such as rotation and whatnot. It'll ultimately be programmed in C++). Thanks!
I'm a mechanical engineer who writes software for a living. Before moving to tech startups, I worked for Lockheed Martin writing simulation software for rockets. I've got some chops in this area.
My professional instinct is that there is no such thing as a "grand unified equation". In fact, this is a hard enough problem that there might not be very good theoretical models for this even if they are correct: for instance, one of your equations will have to be the lift generated from the frisbee, which will depend on its cross-section, speed, angle of attack, and assumptions about the properties of the air. Unless you're going to put your frisbee in a wind tunnel, this equation will be, at best, an approximation.
It gets worse in the real world: will you be launching the frisbee where there is wind? Then you can kiss your models goodbye, because as casual frisbee players know, the wind is a huge disturbance. Your models can be fine, but the real world can be brutal to them.
The way this complexity is handled in the real world is that almost all systems have feedback: a pilot can correct for the wind, or a rocket's computer removes disturbances from differences in air density. Unless you put a microcontroller with control surfaces on the frisbee, you're just not going to get far with your open loop prediction - which I'm sure is the trap they're setting for you by making it a frisbee competition.
There is a solid engineering way to approach the problem. Give Newton a boot and do they physics equations yourselves.
This is the empirical modeling process: launch a frisbee across a matrix of pitch and roll angles, launch speeds, frisbee spin speeds, etc... and backfit a model to your results. This can be as easy as linear interpolation of the results of your table, so that any combination of input variables can generate a prediction.
It's not guess and check, because you populate your tables ahead of time, so can make some sort of prediction about the results. You will get much better information faster than trying the idealized models, though you will have to keep going to fetch your frisbee :)
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I am trying to fit some points to an inverse parabola, in the form of F(x)=1/(ax^2+bx+c).
My objective is to program a function in c++ that would take a set of 10-30 points and fit them to the inverse parabola.
I started trying to get an analytical expression using Least squares, but I can't reach to get a result. I tried by hand (little crazy) and then I tried to solve analytically the expressions for a,b and c, but mupad doesn't give me a result (I am pretty new to Matlab's mupad so maybe i am not doing it correctly).
i don't know anymore how to approach the problem.
Can I get a analytical expression for this specific problem? I have also seen algorithms for general least squares fitting but I don't need a so complicated algorithm, I just need it for this equation.
If not, how would StackOverflow people approach the problem?
If needed I can post the equations, and the small Mupad code I've tried, but I think is unnecessary.
EDIT: some example
Im sorry the image is a little bit messy but it is the thing i need.
The data is in blue (this data is particularly noisy). I need to use only the data that is between the vertical lines (a bunch of data in the left and another one in the right).
The result of the fit is in de red line.
all this has been made with matlab, but I need to make it in c++.
I'll try to post some data...
Edit 2: I actually did the fitting in Matlab as follows (not the actual code):
create linear system Ax = b, with
A = [x² x 1]
x = [a; b; c]
b = 1/y;
It should work, shouldn't it? I can solve then using Moore-Penrose pseudoinv calculated with SVD. Isn't it?
There is no analytic solution of least squares; it is an minimisation problem, and requires clever iterative methods to solve. (nonlinear LS - thanks #insilico)
You could try a Newton style iterative method (by rearranging your equation) but I don't think it will converge easily for your function -- which is going to be highly nonlinear at two points!
I'd recommend using a library for this. such as nelder-mead search
http://www.codecogs.com/code/maths/optimization/nelder.php
you simply provide your error function - which is
sum( pow(F(x) - dataY(x), 2) )
and provide a set of initial values (a stab in the dark at the solution);
I've had good success with nelder-mead.
I don't think you will find a good plain-coded solution.
If I understand you correctly, you just need to know the formula for a fit for a particular data set, right?
If so, then you just need to get a curve fitting program and fit the curve using your desired method. Then, implement the formula shown by the curve fit.
There are a few curve fit programs out there:
Curve Expert
http://www.curveexpert.net/
* Eurequa *
http://creativemachines.cornell.edu/eureqa
Additionally, some spreadsheet packages may have the curve fitting facilities you need.
I would be happy to try to do a fit for you if you provide the data. No guarantees on getting the fit you want.
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There are several open source implementations of conditional random fields (CRFs) in C++, such as CRF++, FlexCRF, etc. But from the manual, I can only understand how to use them for 1-D problems such as text tagging, it's not clear how to apply them in 2-D vision problems, suppose I have computed the association potentials at each node and the interaction potentials at each edge.
Did anyone use these packages for vision problems, e.g., segmentation? Or they simply cannot be used in this way?
All in all, is there any open source packages of CRFs for vision problems?
Thanks a lot!
The newest version of dlib has support for learning pairwise Markov random field models over arbitrary graph structures (including 2-D grids). It estimates the parameters in a max-margin sense (i.e. using a structural SVM) rather than in a maximum likelihood sense (i.e. CRF), but if all you want to do is predict a graph labeling then either method is just as good.
There is an example program that shows how to use this stuff on a simple example graph. The example puts feature vectors at each node and the structured SVM uses them to learn how to correctly label the nodes in the graph. Note that you can change the dimensionality of the feature vectors by modifying the typedefs at the top of the file. Also, if you already have a complete model and just want to find the most probable labeling then you can call the underlying min-cut based inference routine directly.
In general, I would say that the best way to approach these problems is to define the graphical model you want to use and then select a parameter learning method that works with it. So in this case I imagine you are interested in some kind of pairwise Markov random field model. In particular, the kind of model where the most probable assignment can be found with a min-cut/max-flow algorithm. Then in this case, it turns out that a structural SVM is a natural way to find the parameters of the model since a structural SVM only requires the ability to find maximum probability assignments. Finding the parameters via maximum likelihood (i.e. treating this as a CRF) would require you to additionally have some way to compute sums over the graph variables, but this is pretty hard with these kinds of models. For this kind of model, all the CRF methods I know about are approximations, while the SVM method in dlib uses an exact solver. By that I mean, one of the parameters of the algorithm is an epsilon value that says "run until you find the optimal parameters to within epsilon accuracy", and the algorithm can do this efficiently every time.
There was a good tutorial on this topic at this year's computer vision and pattern recognition conference. There is also a good book on Structured Prediction and Learning in Computer Vision written by the presenters.
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I have a school project to build an AI for a 2D racing game in which it will compete with several other AIs.
We are given a black and white bitmap image of the racing track, we are allowed to choose basic stats for our car (handling, acceleration, max speed and brakes) after we receive the map. The AI connects to the game's server and gives to it several times a second numbers for the current acceleration and steering. The language I chose is C++, by the way.
The question is
What is the best strategy or algorithm (since I want to try and win)? I currently have in mind some ideas found on the net and one or two of my own, but I would like before I start to code that my perspective is one of the best.
What good books are there on that matter?
What sites should I refer to?
There's no "right answer" for this problem - it's pretty open-ended and many different options might work out.
You may want to look into reinforcement learning as a way of trying to get the AI to best determine how to control the car once it's picked the different control statistics. Reinforcement learning models can train the computer to try to work toward a good system for making particular maneuvers in terms of the underlying control system.
To determine what controls you'll want to use, you could use some flavor of reinforcement learning, or you may want to investigate supervised learning algorithms that can play around with different combinations of controls and see how good of a "fit" they give for the particular map. For example, you might break the map apart into small blocks, then try seeing what controls do well in the greatest number of blocks.
In terms of plotting out the path you'll want to take, A* is a well-known algorithm for finding shortest paths. In your case, I'm not sure how useful it will be, but it's the textbook informed search algorithm.
For avoiding opponent racers and trying to drive them into trickier situations, you may need to develop some sort of opponent modeling system. Universal portfolios are one way to do this, though I'm not sure how useful they'll be in this instance. One option might be to develop a potential field around the track and opponent cars to help your car try to avoid obstacles; this may actually be a better choice than A* for pathfinding. If you're interested in tactical maneuvers, a straightforward minimax search may be a good way to avoid getting trapped or to find ways to trap opponents.
I am no AI expert, but I think the above links might be a good starting point. Best of luck with the competition!
What good books are there on that matter?
The best book I have read on this subject is "Programming Game AI by Example" by Mat Buckland. It has chapters on both path planning and steering behaviors, and much more (state machines, graph theory, the list goes on).
All the solutions above are good, and people have gone to great length to test them out. Look up "Togelius and Lucas" or "Loiacono and Lanzi". They have tries things like neuroevolution, imitation (done via reinforcement learning), force fields, etc. From my point of view the best way to go is center line. That will take an hour to implement. In contrast, neuroevolution (for example) is neither easy nor fast. I did my dissertation on that and it can easily take several months full time, if you have the right hardware.
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I'm interested in creating a game that uses fractal maps for more realistic geography. However, the only fractal map programs I have found are Windows-only, for example Fractal Mapper. Needless to say, they are also not open-sourced.
Are there any open-sourced fractal map creators available, preferably in Python or C/C++? Ideally I would like something that can be "plugged into" a program, rather then being standalone.
Fracplanet may be of use.
Basic terrain generation involves creating a height map (an image) and rendering it using the pixel colour as height. So you may find image or texture generation code useful. This is a good tutorial.
For the terrain aspect take a look at libnoise.
It's packaged for Debian, and has excellent documentation with a chapter on terrain generation with example C++ code.
Of course there's a lot more to "maps" than slapping some colours on a height field (for example Fracplanet adds rivers and lakes). And the sort of terrain you get from these methods isn't actually that realistic; continents don't generally ramp up from the coast into a rocky hinterland, so maybe simulating continental drift and mountain building and erosion processes would help (alternatively, fake it). And then if you want vegetation, or the artefacts of lifeforms (roads and towns, say) to populate your map you might want to look at cellular automata or other "artificial life" tools. Finally, the Virtual Terrain Project is well worth a browse for more links and ideas.
I'd highly recommend purchasing a copy of
Texturing & Modeling: A Procedural Approach
I see it's now in it's third edition (I only have the second) but it's packed full of useful articles about the use of procedural texturing including several chapters on their use in fractal terrains. It starts out with extensive discussion of noise algorithms too - so you have everything from the basics upwards. The authors include Musgrave, Perlin and Worley, so you really can't do better.
If you want truely realistic geography, you could use NASA's SRTM dataset, perhaps combined with OpenStreetMap features. :-)
A very simple implementation would be to use the midpoint displacement fractal, http://en.wikipedia.org/wiki/Diamond-square_algorithm, or the somewhat more complicated Diamond-Squares algorithm.
http://www.gameprogrammer.com/fractal.html#diamond
These are similar algorithms to the "Difference cloud" in Photoshop.