I am hacking a vacuum cleaner robot to control it with a microcontroller (Arduino). I want to make it more efficient when cleaning a room. For now, it just go straight and turn when it hits something.
But I have trouble finding the best algorithm or method to use to know its position in the room. I am looking for an idea that stays cheap (less than $100) and not to complex (one that don't require a PhD thesis in computer vision). I can add some discrete markers in the room if necessary.
Right now, my robot has:
One webcam
Three proximity sensors (around 1 meter range)
Compass (no used for now)
Wi-Fi
Its speed can vary if the battery is full or nearly empty
A netbook Eee PC is embedded on the robot
Do you have any idea for doing this? Does any standard method exist for these kind of problems?
Note: if this question belongs on another website, please move it, I couldn't find a better place than Stack Overflow.
The problem of figuring out a robot's position in its environment is called localization. Computer science researchers have been trying to solve this problem for many years, with limited success. One problem is that you need reasonably good sensory input to figure out where you are, and sensory input from webcams (i.e. computer vision) is far from a solved problem.
If that didn't scare you off: one of the approaches to localization that I find easiest to understand is particle filtering. The idea goes something like this:
You keep track of a bunch of particles, each of which represents one possible location in the environment.
Each particle also has an associated probability that tells you how confident you are that the particle really represents your true location in the environment.
When you start off, all of these particles might be distributed uniformly throughout your environment and be given equal probabilities. Here the robot is gray and the particles are green.
When your robot moves, you move each particle. You might also degrade each particle's probability to represent the uncertainty in how the motors actually move the robot.
When your robot observes something (e.g. a landmark seen with the webcam, a wifi signal, etc.) you can increase the probability of particles that agree with that observation.
You might also want to periodically replace the lowest-probability particles with new particles based on observations.
To decide where the robot actually is, you can either use the particle with the highest probability, the highest-probability cluster, the weighted average of all particles, etc.
If you search around a bit, you'll find plenty of examples: e.g. a video of a robot using particle filtering to determine its location in a small room.
Particle filtering is nice because it's pretty easy to understand. That makes implementing and tweaking it a little less difficult. There are other similar techniques (like Kalman filters) that are arguably more theoretically sound but can be harder to get your head around.
A QR Code poster in each room would not only make an interesting Modern art piece, but would be relatively easy to spot with the camera!
If you can place some markers in the room, using the camera could be an option. If 2 known markers have an angular displacement (left to right) then the camera and the markers lie on a circle whose radius is related to the measured angle between the markers. I don't recall the formula right off, but the arc segment (on that circle) between the markers will be twice the angle you see. If you have the markers at known height and the camera is at a fixed angle of inclination, you can compute the distance to the markers. Either of these methods alone can nail down your position given enough markers. Using both will help do it with fewer markers.
Unfortunately, those methods are imperfect due to measurement errors. You get around this by using a Kalman estimator to incorporate multiple noisy measurements to arrive at a good position estimate - you can then feed in some dead reckoning information (which is also imperfect) to refine it further. This part is goes pretty deep into math, but I'd say it's a requirement to do a great job at what you're attempting. You can do OK without it, but if you want an optimal solution (in terms of best position estimate for given input) there is no better way. If you actually want a career in autonomous robotics, this will play large in your future. (
Once you can determine your position you can cover the room in any pattern you'd like. Keep using the bump sensor to help construct a map of obstacles and then you'll need to devise a way to scan incorporating the obstacles.
Not sure if you've got the math background yet, but here is the book:
http://books.google.com/books/about/Applied_optimal_estimation.html?id=KlFrn8lpPP0C
This doesn't replace the accepted answer (which is great, thanks!) but I might recommend getting a Kinect and use that instead of your webcam, either through Microsoft's recently released official drivers or using the hacked drivers if your EeePC doesn't have Windows 7 (presumably it does not).
That way the positioning will be improved by the 3D vision. Observing landmarks will now tell you how far away the landmark is, and not just where in the visual field that landmark is located.
Regardless, the accepted answer doesn't really address how to pick out landmarks in the visual field, and simply assumes that you can. While the Kinect drivers may already have feature detection included (I'm not sure) you can also use OpenCV for detecting features in the image.
One solution would be to use a strategy similar to "flood fill" (wikipedia). To get the controller to accurately perform sweeps, it needs a sense of distance. You can calibrate your bot using the proximity sensors: e.g. run motor for 1 sec = xx change in proximity. With that info, you can move your bot for an exact distance, and continue sweeping the room using flood fill.
Assuming you are not looking for a generalised solution, you may actually know the room's shape, size, potential obstacle locations, etc. When the bot exists the factory there is no info about its future operating environment, which kind of forces it to be inefficient from the outset.
If that's you case, you can hardcode that info, and then use basic measurements (ie. rotary encoders on wheels + compass) to precisely figure out its location in the room/house. No need for wifi triangulation or crazy sensor setups in my opinion. At least for a start.
Ever considered GPS? Every position on earth has a unique GPS coordinates - with resolution of 1 to 3 metres, and doing differential GPS you can go down to sub-10 cm range - more info here:
http://en.wikipedia.org/wiki/Global_Positioning_System
And Arduino does have lots of options of GPS-modules:
http://www.arduino.cc/playground/Tutorials/GPS
After you have collected all the key coordinates points of the house, you can then write the routine for the arduino to move the robot from point to point (as collected above) - assuming it will do all those obstacles avoidance stuff.
More information can be found here:
http://www.google.com/search?q=GPS+localization+robots&num=100
And inside the list I found this - specifically for your case: Arduino + GPS + localization:
http://www.youtube.com/watch?v=u7evnfTAVyM
I was thinking about this problem too. But I don't understand why you can't just triangulate? Have two or three beacons (e.g. IR LEDs of different frequencies) and a IR rotating sensor 'eye' on a servo. You could then get an almost constant fix on your position. I expect the accuracy would be in low cm range and it would be cheap. You can then map anything you bump into easily.
Maybe you could also use any interruption in the beacon beams to plot objects that are quite far from the robot too.
You have a camera you said ? Did you consider looking at the ceiling ? There is little chance that two rooms have identical dimensions, so you can identify in which room you are, position in the room can be computed from angular distance to the borders of the ceiling and direction can probably be extracted by the position of doors.
This will require some image processing but the vacuum cleaner moving slowly to be efficiently cleaning will have enough time to compute.
Good luck !
Use Ultra Sonic Sensor HC-SR04 or similar.
As above told sense the walls distance from robot with sensors and room part with QR code.
When your are near to a wall turn 90 degree and move as width of your robot and again turn 90deg( i.e. 90 deg left turn) and again move your robot I think it will help :)
Related
I have a web cam that takes a picture every N seconds. This gives me a collection of images of the same scene over time. I want to process that collection of images as they are created to identify events like someone entering into the frame, or something else large happening. I will be comparing images that are adjacent in time and fixed in space - the same scene at different moments of time.
I want a reasonably sophisticated approach. For example, naive approaches fail for outdoor applications. If you count the number of pixels that change, for example, or the percentage of the picture that has a different color or grayscale value, that will give false positive reports every time the sun goes behind a cloud or the wind shakes a tree.
I want to be able to positively detect a truck parking in the scene, for example, while ignoring lighting changes from sun/cloud transitions, etc.
I've done a number of searches, and found a few survey papers (Radke et al, for example) but nothing that actually gives algorithms that I can put into a program I can write.
Use color spectroanalisys, without luminance: when the Sun goes down for a while, you will get similar result, colors does not change (too much).
Don't go for big changes, but quick changes. If the luminance of the image changes -10% during 10 min, it means the usual evening effect. But when the change is -5%, 0, +5% within seconds, its a quick change.
Don't forget to adjust the reference values.
Split the image to smaller regions. Then, when all the regions change same way, you know, it's a global change, like an eclypse or what, but if only one region's parameters are changing, then something happens there.
Use masks to create smart regions. If you're watching a street, filter out the sky, the trees (blown by wind), etc. You may set up different trigger values for different regions. The regions should overlap.
A special case of the region is the line. A line (a narrow region) contains less and more homogeneous pixels than a flat area. Mark, say, a green fence, it's easy to detect wheter someone crosses it, it makes bigger change in the line than in a flat area.
If you can, change the IRL world. Repaint the fence to a strange color to create a color spectrum, which can be identified easier. Paint tags to the floor and wall, which can be OCRed by the program, so you can detect wheter something hides it.
I believe you are looking for Template Matching
Also i would suggest you to look on to Open CV
We had to contend with many of these issues in our interactive installations. It's tough to not get false positives without being able to control some of your environment (sounds like you will have some degree of control). In the end we looked at combining some techniques and we created an open piece of software named OpenTSPS (Open Toolkit for Sensing People in Spaces - http://www.opentsps.com). You can look at the C++ source in github (https://github.com/labatrockwell/openTSPS/).
We use ‘progressive background relearn’ to adjust to the changing background over time. Progressive relearning is particularly useful in variable lighting conditions – e.g. if lighting in a space changes from day to night. This in combination with blob detection works pretty well and the only way we have found to improve is to use 3D cameras like the kinect which cast out IR and measure it.
There are other algorithms that might be relevant, like SURF (http://achuwilson.wordpress.com/2011/08/05/object-detection-using-surf-in-opencv-part-1/ and http://en.wikipedia.org/wiki/SURF) but I don't think it will help in your situation unless you know exactly the type of thing you are looking for in the image.
Sounds like a fun project. Best of luck.
The problem you are trying to solve is very interesting indeed!
I think that you would need to attack it in parts:
As you already pointed out, a sudden change in illumination can be problematic. This is an indicator that you probably need to achieve some sort of illumination-invariant representation of the images you are trying to analyze.
There are plenty of techniques lying around, one I have found very useful for illumination invariance (applied to face recognition) is DoG filtering (Difference of Gaussians)
The idea is that you first convert the image to gray-scale. Then you generate two blurred versions of this image by applying a gaussian filter, one a little bit more blurry than the first one. (you could use a 1.0 sigma and a 2.0 sigma in a gaussian filter respectively) Then you subtract from the less-blury image, the pixel intensities of the more-blurry image. This operation enhances edges and produces a similar image regardless of strong illumination intensity variations. These steps can be very easily performed using OpenCV (as others have stated). This technique has been applied and documented here.
This paper adds an extra step involving contrast equalization, In my experience this is only needed if you want to obtain "visible" images from the DoG operation (pixel values tend to be very low after the DoG filter and are veiwed as black rectangles onscreen), and performing a histogram equalization is an acceptable substitution if you want to be able to see the effect of the DoG filter.
Once you have illumination-invariant images you could focus on the detection part. If your problem can afford having a static camera that can be trained for a certain amount of time, then you could use a strategy similar to alarm motion detectors. Most of them work with an average thermal image - basically they record the average temperature of the "pixels" of a room view, and trigger an alarm when the heat signature varies greatly from one "frame" to the next. Here you wouldn't be working with temperatures, but with average, light-normalized pixel values. This would allow you to build up with time which areas of the image tend to have movement (e.g. the leaves of a tree in a windy environment), and which areas are fairly stable in the image. Then you could trigger an alarm when a large number of pixles already flagged as stable have a strong variation from one frame to the next one.
If you can't afford training your camera view, then I would suggest you take a look at the TLD tracker of Zdenek Kalal. His research is focused on object tracking with a single frame as training. You could probably use the semistatic view of the camera (with no foreign objects present) as a starting point for the tracker and flag a detection when the TLD tracker (a grid of points where local motion flow is estimated using the Lucas-Kanade algorithm) fails to track a large amount of gridpoints from one frame to the next. This scenario would probably allow even a panning camera to work as the algorithm is very resilient to motion disturbances.
Hope this pointers are of some help. Good Luck and enjoy the journey! =D
Use one of the standard measures like Mean Squared Error, for eg. to find out the difference between two consecutive images. If the MSE is beyond a certain threshold, you know that there is some motion.
Also read about Motion Estimation.
if you know that the image will remain reletivly static I would reccomend:
1) look into neural networks. you can use them to learn what defines someone within the image or what is a non-something in the image.
2) look into motion detection algorithms, they are used all over the place.
3) is you camera capable of thermal imaging? if so it may be worthwile to look for hotspots in the images. There may be existing algorithms to turn your webcam into a thermal imager.
We are making a robot that shoots basketballs into hoops.
From an image and our knowledge of the camera's angle and the target's dimensions (the targets are coated with retroreflective tape), we know how far away we are, X and Y (distance being Z, more or less)
This is fed into the machine learning algorithm, which should spit out
Speed to be sent to the canon
Horizontal tilt
Vertical tilt
What kind of machine learning algorithm is this, and how would you train it?
Machine Learning is probably not appropriate for this task. At least, not by itself. Use physics. You should be able to get a rough formula for this out of a first-semester physics textbook, though you'll need to decide whether you're aiming for the middle of the hoop or the board behind it.
Your physics formulae should tell you the angle and force to use, but your model of the system will have some inaccuracies. Different balls may have different mass, and you might not want to explicitly account for air resistance, and so on. A search through the space of offsets based on how close the previous shot was could work. The choice of search methods is up to you - simulated annealing could work well, as Mencel said.
One possible use for machine learning here might be to remember and extrapolate these offsets. A function approximator (such as a neural network) could be used to learn the offsets from experience. Once your search method succeeds at putting the ball in the hoop, use this as a training example for an approximator that learns to map from what the physics model says to use to the offsets that made the shot work. Then, for the next shot (from whatever position), the function approximator would be used to guess the offsets to use. If that shot misses, repeat the search until correct offsets are found. Update the function approximator, rinse, and repeat. Also, it would probably be beneficial if your function approximator were initialized in such a way that it initially always says to apply no offsets - after all, the best first guess should be to just use what the physics model tells you to use.
I would recommend a reinforcement learning approach. It'll be slow ; so maybe you could initialize the solution with your own estimate (basic physics) and refine it with reinforcement learning.
I am thinking of implement a image processing based solution for industrial problem.
The image is consists of a Red rectangle. Inside that I will see a matrix of circles. The requirement is to count the number of circles under following constraints. (Real application : Count the number of bottles in a bottle casing. Any missing bottles???)
The time taken for the operation should be very low.
I need to detect the red rectangle as well. My objective is to count the
items in package and there are no
mechanism (sensors) to trigger the
camera. So camera will need to capture
the photos continuously but the
program should have a way to discard
the unnecessary images.
Processing should be realtime.
There may be a "noise" in image capturing. You may see ovals instead of circles.
My questions are as follows,
What is the best edge detection algorithm that matches with the given
scenario?
Are there any other mechanisms that I can use other than the edge
detection?
Is there a big impact between the language I use and the performance of
the system?
AHH - YOU HAVE NOW TOLD US THE BOTTLES ARE IN FIXED LOCATIONS!
IT IS AN INCREDIBLY EASIER PROBLEM.
All you have to do is look at each of the 12 spots and see if there is a black area there or not. Nothing could be easier.
You do not have to do any edge or shape detection AT ALL.
It's that easy.
You then pointed out that the box might be rotatated, things could be jiggled. That the box might be rotated a little (or even a lot, 0 to 360 each time) is very easily dealt with. The fact that the bottles are in "slots" (even if jiggled) massively changes the nature of the problem. You're main problem (which is easy) is waiting until each new red square (crate) is centered under the camera. I just realised you meant "matrix" literally and specifically in the sentence in your original questions. That changes everything totally, compared to finding a disordered jumble of circles. Finding whether or not a blob is "on" at one of 12 points, is a wildly different problem to "identifying circles in an image". Perhaps you could post an image to wrap up the question.
Finally I believe Kenny below has identified the best solution: blob analysis.
"Count the number of bottles in a bottle casing"...
Do the individual bottles sit in "slots"? ie, there are 4x3 = 12 holes, one for each bottle.
In other words, you "only" have to determine if there is, or is not, a bottle in each of the 12 holes.
Is that correct?
If so, your problem is incredibly easier than the more general problem of a pile of bottles "anywhere".
Quite simply, where do we see the bottles from? The top, sides, bottom, or? Do we always see the tops/bottoms, or are they mixed (ie, packed top-to-tail). These issues make huge, huge differences.
Surf/Sift = overkill in this case you certainly don't need it.
If you want real time speed (about 20fps+ on a 800x600 image) I recommend using Cuda to implement edge detection using a standard filter scheme like sobel, then implement binarization + image closure to make sure the edges of circles are not segmented apart.
The hardest part will be fitting circles. This is assuming you already got to the step where you have taken edges and made sure they are connected using image closure (morphology.) At this point I would proceed as follows:
run blob analysis/connected components to segment out circles that do not touch. If circles can touch the next step will be trickier
for each connected componet/blob fit a circle or rectangle using RANSAC which can run in realtime (as opposed to Hough Transform which I believe is very hard to run in real time.)
Step 2 will be much harder if you can not segment the connected components that form circles seperately, so some additional thought should be invested on how to guarantee that condition.
Good luck.
Edit
Having thought about it some more, I feel like RANSAC is ideal for the case where the circle connected components do touch. RANSAC should hypothetically fit the circle to only a part of the connected component (due to its ability to perform well in the case of mostly outlier points.) This means that you could add an extra check to see if the fitted circle encompasses the entire connected component and if it does not then rerun RANSAC on the portion of the connected component that was left out. Rinse and repeat as many times as necessary.
Also I realize that I say circle but you could just as easily fit an ellipse instead of circles using RANSAC.
Also, I'd like to comment that when I say CUDA is a good choice I mean CUDA is a good choice to implement the sobel filter + binirization + image closing on. Connected components and RANSAC are probably best left to the CPU, but you can try pushing them onto CUDA though I don't know how much of an advantage a GPU will give you for those 2 over a CPU.
For the circles, try the Hough transform.
other mechanisms: dunno
Compiled languages will possibly be faster.
SIFT should have a very good response to circular objects - it is patented, though. GLOHis a similar algorithm, but I do not know if there are any implementations readily available.
Actually, doing some more research, SURF is an improved version of SIFT with quite a few implementations available, check out the links on the wikipedia page.
Sum of colors + convex hull to detect boundary. You need, mostly, 4 corners of a rectangle, and not it's sides?
No motion, no second camera, a little choice - lot of math methods against a little input (color histograms, color distribution matrix). Dunno.
Java == high memory consumption, Lisp == high brain consumption, C++ == memory/cpu/speed/brain use optimum.
If the contrast is good, blob analysis is the algorithm for the job.
I'm trying to write a simple tracking routine to track some points on a movie.
Essentially I have a series of 100-frames-long movies, showing some bright spots on dark background.
I have ~100-150 spots per frame, and they move over the course of the movie. I would like to track them, so I'm looking for some efficient (but possibly not overkilling to implement) routine to do that.
A few more infos:
the spots are a few (es. 5x5) pixels in size
the movement are not big. A spot generally does not move more than 5-10 pixels from its original position. The movements are generally smooth.
the "shape" of these spots is generally fixed, they don't grow or shrink BUT they become less bright as the movie progresses.
the spots don't move in a particular direction. They can move right and then left and then right again
the user will select a region around each spot and then this region will be tracked, so I do not need to automatically find the points.
As the videos are b/w, I though I should rely on brigthness. For instance I thought I could move around the region and calculate the correlation of the region's area in the previous frame with that in the various positions in the next frame. I understand that this is a quite naïve solution, but do you think it may work? Does anyone know specific algorithms that do this? It doesn't need to be superfast, as long as it is accurate I'm happy.
Thank you
nico
Sounds like a job for Blob detection to me.
I would suggest the Pearson's product. Having a model (which could be any template image), you can measure the correlation of the template with any section of the frame.
The result is a probability factor which determine the correlation of the samples with the template one. It is especially applicable to 2D cases.
It has the advantage to be independent from the sample absolute value, since the result is dependent on the covariance related with the mean of the samples.
Once you detect an high probability, you can track the successive frames in the neightboor of the original position, and select the best correlation factor.
However, the size and the rotation of the template matter, but this is not the case as I can understand. You can customize the detection with any shape since the template image could represent any configuration.
Here is a single pass algorithm implementation , that I've used and works correctly.
This has got to be a well reasearched topic and I suspect there won't be any 100% accurate solution.
Some links which might be of use:
Learning patterns of activity using real-time tracking. A paper by two guys from MIT.
Kalman Filter. Especially the Computer Vision part.
Motion Tracker. A student project, which also has code and sample videos I believe.
Of course, this might be overkill for you, but hope it helps giving you other leads.
Simple is good. I'd start doing something like:
1) over a small rectangle, that surrounds a spot:
2) apply a weighted average of all the pixel coordinates in the area
3) call the averaged X and Y values the objects position
4) while scanning these pixels, do something to approximate the bounding box size
5) repeat next frame with a slightly enlarged bounding box so you don't clip spot that moves
The weight for the average should go to zero for pixels below some threshold. Number 4 can be as simple as tracking the min/max position of anything brighter than the same threshold.
This will of course have issues with spots that overlap or cross paths. But for some reason I keep thinking you're tracking stars with some unknown camera motion, in which case this should be fine.
I'm afraid that blob tracking is not simple, not if you want to do it well.
Start with blob detection as genpfault says.
Now you have spots on every frame and you need to link them up. If the blobs are moving independently, you can use some sort of correspondence algorithm to link them up. See for instance http://server.cs.ucf.edu/~vision/papers/01359751.pdf.
Now you may have collisions. You can use mixture of gaussians to try to separate them, give up and let the tracks cross, use any other before-and-after information to resolve the collisions (e.g. if A and B collide and A is brighter before and will be brighter after, you can keep track of A; if A and B move along predictable trajectories, you can use that also).
Or you can collaborate with a lab that does this sort of stuff all the time.
In a multi-touch environment, how does gesture recognition work? What mathematical methods or algorithms are utilized to recognize or reject data for possible gestures?
I've created some retro-reflective gloves and an IR LED array, coupled with a Wii remote. The Wii remote does internal blob detection and tracks 4 points of IR light and transmits this information to my computer via a bluetooth dongle.
This is based off Johnny Chung Lee's Wii Research. My precise setup is exactly like the graduate students from the Netherlands displayed here. I can easily track 4 point's positions in 2d space and I've written my basic software to receive and visualize these points.
The Netherlands students have gotten a lot of functionality out of their basic pinch-click recognition. I'd like to take it a step further if I could, and implement some other gestures.
How is gesture recognition usually implemented? Beyond anything trivial, how could I write software to recognize and identify a variety of gestures: various swipes, circular movements, letter tracing, etc.
Gesture recognition, as I've seen it anyway, is usually implemented using machine learning techniques similar to image recognition software. Here's a cool project on codeproject about doing mouse gesture recognition in c#. I'm sure the concepts are quite similar since you can likely reduce the problem down to 2D space. If you get something working with this, I'd love to see it. Great project idea!
One way to look at it is as a compression / recognition problem. Basically, you want to take a whole bunch of data, throw out most of it, and categorize the remainder. If I were doing this (from scratch) I'd probably proceed as follows:
work with a rolling history window
take the center of gravity of the four points in the start frame, save it, and subtract it out of all the positions in all frames.
factor each frame into two components: the shape of the constellation and the movement of it's CofG relative to the last frame's.
save the absolute CofG for the last frame too
the series of CofG changes gives you swipes, waves, etc.
the series of constellation morphing gives you pinches, etc.
After seeing your photo (two points on each hand, not four points on one, doh!) I'd modify the above as follows:
Do the CofG calculation on pairs, with the caveats that:
If there are four points visible, pairs are chosen to minimize the product of the intrapair distances
If there are three points visible, the closest two are one pair, the other one is the other
Use prior / following frames to override when needed
Instead of a constellation, you've got a nested structure of distance / orientation pairs (i.e., one D/O between the hands, and one more for each hand).
Pass the full reduced data to recognizers for each gesture, and let them sort out what they care about.
If you want to get cute, do a little DSL to recognize the patterns, and write things like:
fire when
in frame.final: rectangle(points)
and
over frames.final(5): points.all (p => p.jerk)
or
fire when
over frames.final(3): hands.all (h => h.click)
A video of what has been done with this sort of technology, if anyone is interested?
Pattie Maes demos the Sixth Sense - TED 2009
Most simple gesture-recognition tools I've looked at use a vector-based template to recognize them. For example, you can define right-swipe as "0", a checkmark as "-45, 45, 45", a clockwise circle as "0, -45, -90, -135, 180, 135, 90, 45, 0", and so on.
Err.. I've been working on gesture recognition for the past year or so now, but I don't want to say too much because I'm trying to patent my technology :) But... we've had some luck with adaptive boosting, although what you're doing looks fundamentally different. You only have 4 points of data to process, so I don't think you really need to "reduce" anything.
What I would investigate is how programs like Flash turn a freehand drawn circle into an actual circle. It seems like you could track the points for duration of about a second, and then "smooth" the path in some fashion, and then you could probably get away with hardcoding your gestures (if you make them simple enough). Otherwise, yes, you're going to want to use a learning algorithm. Neural nets might work... I don't know. Just tossing out ideas :) Maybe look at how OCR is done too... or even Hough transforms. It looks to me like this is a problem of recognizing shapes more than it is of recognizing gestures.
I'm not very well versed in this type of mathematics, but I have read somewhere that people sometimes use Markov Chains or Hidden Markov Models to do Gesture Recognition.
Perhaps someone with a little more background in this side of Computer Science can illuminate it further and provide some more details.