I got the code of Snakes algorithm from here (Implemented in MatLab)
http://www.mathworks.com/matlabcentral/fileexchange/28109-snakes-active-contour-models
when you give it the initial indices surrounding the contour, It runs perfectly. but, unfortunately that isn't what I want.
Imagine that there is a mountain, I want to detect it's contour. But, I only have the index of the top of the mountain. So, the initial indices are the indices surrounding this pixel. But when running the algorithm, the snake is getting smaller and smaller till vanishing.
I want the snake to grow up till it founds the contour. Is that feasible?
I'm not an expert, but I have done a little reading on this topic. From what I understand many snake algorithms tend to shrink in the absence of any image forcing because they punish the first derivative (the integral of |x'|^2) and that inadvertently punishes area.
If you can access it, they talk about this problem in this paper and try and alter it to get an expanding snake by adding a volume term to the cost function.
http://www.springerlink.com/index/10.1007/s00791-012-0178-8
Hope that helps.
You want to increment the weight of External Forces (the force field generated by the mountain contour upon the snake points) and decrease the weight of Internal Forces (the elasticity of the snake, the "rubber band" effect).
If you do that, the snake will be less elastic (less of a rubber band) and more plastic (more like a string of beads).
Related
I have an application where I need to move a number of objects around on the screen in a random fashion and they can not bump into each other. I'm looking for an algorithm that will allow me to generate the paths that don't create collisions and can continue for an indefinite time (i.e.: the objects keep moving around until a user driven event removes them from the program).
I'm not a game programmer but I think this looks like an AI problem and you guys probably solve it with your eyes closed. From what I've read A* seems to be the recommended 'basic idea' but I don't really want to invest a lot of time into it without some confirmation.
Can anyone shed some light on an approach? Anti-gravity movement maybe?
This is to be implemented on iOS, if that is important
New paths need to be generated at the end of each path
There is no visible 'grid'. Movement is completely free in 2D space
The objects are insects that walk around the screen until they are killed
A* is an algorithm to find the shortest path between a start and a goal configuration (in terms of whatever you define as short: common are e.g. euclidean distance, cost or time, angular distance...). Your insects seem not to have a specific goal, they don't even need a shortest path. I would certainly not go for A*. (By the way, since you are having a dynamic environment, D* would have been an idea - still it's meant to find a path from A to B).
I would tackle the problem as follows:
Random Paths and following them
For the random paths I see two methods. The first would be a simple random walk (click here to see a nice 2D animation with explanations), which can suffer from jittering and doesn't look too nice. The second one needs a little bit more detailed explanations.
For each insect generate four random points around them, maybe starting on a sinusoid. With a spline interpolation generate a smooth curve between those points. Take care of having C1 (in 2D) or C2 (in 3D) continuity. (Suggestion: Hermite splines)
With Catmull-Rom splines you can find your configurations while moving along the curve.
An application of a similar approach can be found in this blog post about procedural racetracks, also a more technical (but still not too technical) explanation can be found in these old slides (pdf) from a computer animations course.
When an insect starts moving, it can constantly move between the second and third point, when you always remove the first and append a new point when the insect reaches the third, thus making that the second point.
If third point is reached
Remove first
Append new point
Recalculate spline
End if
For a smoother curve add more points in total and move somewhere in the middle, the principle stays the same. (Personally I only used this in fixed environments, it should work in dynamic ones as well though.)
This can, if your random point generation is good (maybe you can use an approach similar to the one provided in the above linked blog post, or have a look at algorithms on the PCG Wiki), lead to smooth paths all over the screen.
Avoid other insects
To avoid other insects, three different methods come to my mind.
Bug algorithms
Braitenberg vehicles
An application of potential fields
For the potential fields I recommend reading this paper about dynamic motion planning (pdf). It's from robotics, but fairly easy to apply to your problem as well. You can just use the robots next spline point as the goal and set its velocity to 0 to apply this approach. However, it might be a bit too much for your simple game.
A discussion of Braitenberg vehicles can be found here (pdf). The original idea was more of a technical method (drive towards or away from a light source depending on how your motor is coupled with the photo receptor) and is often used to show how we apply emotional concepts like fear and attraction to other objects. The "fear" behaviour is an approach used for obstacle avoidance in robotics as well.
The third and probably simplest method are bug algorithms (pdf). I always have problems with the boundary following, which is a bit tricky. But to avoid another insect, these algorithms - no matter which one you use (I suggest Bug 1 or Tangent Bug) - should do the trick. They are very simple: Move towards your goal (in this application with the catmull-rom splines) until you have an obstacle in front. If the obstacle is close, change the insect's state to "obstacle avoidance" and run your bug algorithm. If you give both "colliding" insects the same turn direction, they will automatically go around each other and follow their original path.
As a variation you could just let them turn and recalculate a new spline from that point on.
Conclusion
Path finding and random path generation are different things. You have to experiment around what looks best for your insects. A* is definitely meant for finding shortest paths, not for creating random paths and following them.
You cannot plan the trajectories ahead of time for an indefinite duration !
I suggest a simpler approach where you just predict the next collision (knowing the positions and speeds of the objects allows you to tell if they will collide and when), and resolve it by changing the speed or direction of either objects (bounce before objects touch).
Make sure to redo a check for collisions in case you created an even earlier collision !
The real challenge in your case is to efficiently predict collisions among numerous objects, a priori an O(N²) task. You will accelerate that by superimposing a coarse grid on the play field and look at objects in neighboring cells only.
It may also be possible to maintain a list of object pairs that "might interfere in some future" (i.e. considering their distance and relative speed) and keep it updated. Checking that a pair may leave the list is relatively easy; efficiently checking for new pairs needing to enter the list is not.
Look at this and this Which described an AI program to auto - play Mario game.
So in this link, what the author did was using a A* star algorithm to guide Mario Get to the right border of the screen as fast as possible. Avoid being hurt.
So the idea is for each time frame, he will have an Environment which described the current position of other objects in the scene and for each action (up, down left, right and do nothing) , he calculate its cost function and made a decision of the next movement based on this.
Source: http://www.quora.com/What-are-the-coolest-algorithms
For A* you would need a 2D-Grid even if it is not visible. If I get your idea right you could do the following.
Implement a pathfinding (e.g. A*) then just generate random destination points on the screen and calculate the path. Once your insect reaches the destination, generate another destination point/grid-cell and proceed until the insect dies.
As I see it A* would only make sence if you have obstacles on the screen the insect should navigate around, otherwise it would be enough to just calculate a straight vector path and maybe handle collision with other insects/objects.
Note: I implemented A* once, later I found out that Lee's Algorithm
pretty much does the same but was easier to implement.
Consider a Hamiltonian cycle - the idea is a route that visits all the positions on a grid once (and only once). If you construct the cycle in advance (i.e. precalculate it), and set your insects off with some offset between them, they will never collide, simply because the path never intersects itself.
Also, for bonus points, Hamiltonian paths tend to 'wiggle about', and because it's a loop you can predict (and precalculate) the path into the indefinite future.
You can always use the nodes of the grid as knot points for a spline to smooth the movement, or even randomly shift all the points away from their strict 2d grid positions, until you have the desired motion.
Example Hamiltonian cycle from Wikimedia:
On a side note, if you want to generate such a path, consider constructing a loop through many points and just moving the points around in such a manner that they never intersect an existing edge. With some encouragement to move into gaps and away from each other, they should settle into some long, never-intersecting path. Store the result and use for your loop.
I am making a game and i have come across a hard part to implement into code. My game is a tile-bases platformer with lots of enemies chasing you. basically, in theory, I want my enemies to be able to, every frame/second/2 seconds, find the realistic, and shortest path to my player. I originally thought of A-star as a solution, but it leads the enemies to paths that defy gravity, which is not good. Also, multiple enemies will be using it every second to get the latest path, and then walk the first few tiles of it. So they will be discarding the rest of the path every second, and just following the first few tiles of it. I know this seems like a lot, to calculate a new path every second, all at the same time, if their is more than one enemy, but I don't know any other way to achieve what i want.
This is a picture of what I want:
Explanation: The green figure is the player, the red one is an enemy. the grey tiles are regular, open, nothing there tiles, the brown tiles being ones that you can stand on. And finally the highlighted yellow tiles represents the path that i want my enemy to be able to find, in order to realistically get to the player.
SO, the question is: What realistic path-finding algorithm can i use to acquire this? While keeping it fast?
EDIT*
I updated the picture to represent the most complicated map that their could be. this map represents what the player of my game actually sees, they just use WASD and can move around and they see themselves move through this 2d plat-former view. Their will be different types of enemies, all with different speeds and jump heights. but all will have enough jump height and speed to make the jumps in this map, and maneuver through it. The maps are generated by simply reading an XML file that has the level data in it. the data is then parsed and different types of tiles are placed in the tile holding sprite, acording to what the XML says. EX( XML node: (type="reg" graphic="grass2" x="5" y="7") and so the x and y are multiplied by the constant gridSize (like 30 or something) and they are placed down accordingly. The enemies get their frame-by-frame instruction from an AI class attached to them. This class is responsible for producing this path and return the first direction to the enemy, this should only happen every second or so, so that the enemies don't follow a old, wrong path. Please let me know if you understand my concept, and you have some thought/ideas or maybe even the answer that i'm looking for.
ALSO: the physics in this game is separate from the pathfinding, they work just fine, using a AABB vs AABB concept (the player and enemies also being AABBs).
The trick with using A* here is how you link tiles together to form available paths. Take for example the first gap the red player would need to cross. The 'link' to the next platform (aka brown tile to the left) is actually a jump action, not a move action. Additionally, it's up to you to determine how the nodes connect together; I'd add a heavy penalty when moving from a gray tile over a brown tile to a gray tile with nothing underneath just for starters (without discouraging jumps that open a shortcut).
There are two routes I see personally: running a quick prediction of how far the player can jump and where they'd jump and adjusting how the algorithm determines node adjacency or accept the path and determine when parts of the path "hang" in the air (no brown tile immediately below) and animate the enemy 'jumping' to the next part of the path. The trick is handling things when the enemy may pass through brown tiles in the even the path isn't a parabola.
I am not versed in either solution; just something I've thought about.
You need to give us the most complicated case of map, player and enemy behaviour (including jumping up and across speed) that you are going to either automatically create or manually create so we can give relevant advice. The given map is so simple, put the map in an 2-dimensional array and then the initial player location as an element of that map and then first test whether lower number column on the same row is occupied by brown if not put player there and repeat until false then same row higher column and so on to move enemy.
Update: from my reading of the stage generation- its sometime you create- not semi-random.
My suggestion is the enemy creates clones of itself with its same AI but invisible and each clone starts going in different direction jump up/left/right/jump diagonal right/left and every time it succeeds it creates a new clone- basically a genetic algorithm. From the map it seems an enemy never need to evaluate one path over another just one way fails to get closer to the player's initial position and other doesn't.
my problem is that I have a large set of GPS tracks from different GPS loggers used in cars. When not turned off these cheap devices log phantom movements even if standing still:
As you can see in the image above, about a thousand points get visualized in a kind of congestion. Now I want to remove all of these points so that the red track coming from the left ends before the jitter starts.
My approach is to "draw" two or three circles around each point in the track, check how many other points are located within these circles and check the ratio:
(#points / covered area) > threshold?
If the threshold exceeds a certain ratio (purple circles), I could delete all points within. So: easy method, but has huge disadvantages, e.g. computation time, deleting "innocent" tracks only passing through the circle, doesn't detect outliers like the single points at the bottom of the picture).
I am looking for a better way to detect large heaps of points like in the picture. It should not remove false positives (of perhaps 5 or 10 points, these aggregations don't matter to me). Also, it should not simplify the rest of the track!
Edit: The result in given example should look like this:
My first step would be to investigate the speeds implied by the 'movements' of your stationary car and the changes in altitude. If either of these changes too quickly or too slowly (you'll have to decide the thresholds here) then you can probably conclude that they are due to the GPS jitter.
What information, other than position at time, does your GPS device report ?
EDIT (after OP's comment)
The problem is to characterise part of the log as 'car moving' and part of the log as 'car not moving but GPS location jittering'. I suggested one approach, Benjamin suggested another. If speed doesn't discriminate accurately enough, try acceleration. Try rate of change of heading. If none of these simple approaches work, I think it's time for you to break out your stats textbooks and start figuring out autocorrelation of random processes and the like. At this point I quietly slink away ...
Similarly to High Performance Mark's answer, you could look for line intersections that happen within a short number of points. When driving on a road, the route of the last n points rarely intersects with itself, but it does in your stationary situation because of the jitter. A single intersection could be a person doubling-back or circling around a block, but multiple intersections should be rarer. The angle of intersection will also be sharper for the jitter case.
What is the data interval of the GPS Points, it seems that these are in seconds. There may be one other way to add to the logic previously mentioned.
sum_of_distance(d0,d1,d2....dn)>=80% of sum_of_distance(d0,dn)
This 0 to n th value can iterate in smaller and larger chunks, as the traveled distance within that range will not be much. So, you can iterate over may be 60 points of data initially, and within that data iterate in 10 number of data in each iteration.
I have some map files consisting of 'polylines' (each line is just a list of vertices) representing tunnels, and I want to try and find the tunnel 'center line' (shown, roughly, in red below).
I've had some success in the past using Delaunay triangulation but I'd like to avoid that method as it does not (in general) allow for easy/frequent modification of my map data.
Any ideas on how I might be able to do this?
An "algorithm" that works well with localized data changes.
The critic's view
The Good
The nice part is that it uses a mixture of image processing and graph operations available in most libraries, may be parallelized easily, is reasonable fast, may be tuned to use a relatively small memory footprint and doesn't have to be recalculated outside the modified area if you store the intermediate results.
The Bad
I wrote "algorithm", in quotes, just because I developed it and surely is not robust enough to cope with pathological cases. If your graph has a lot of cycles you may end up with some phantom lines. More on this and examples later.
And The Ugly
The ugly part is that you need to be able to flood fill the map, which is not always possible. I posted a comment a few days ago asking if your graphs can be flood filled, but didn't receive an answer. So I decided to post it anyway.
The Sketch
The idea is:
Use image processing to get a fine line of pixels representing the center path
Partition the image in chunks commensurated to the tunnel thinnest passages
At each partition, represent a point at the "center of mass" of the contained pixels
Use those pixels to represent the Vertices of a Graph
Add Edges to the Graph based on a "near neighbour" policy
Remove spurious small cycles in the induced Graph
End- The remaining Edges represent your desired path
The parallelization opportunity arises from the fact that the partitions may be computed in standalone processes, and the resulting graph may be partitioned to find the small cycles that need to be removed. These factors also allow to reduce the memory needed by serializing instead of doing calcs in parallel, but I didn't go trough this.
The Plot
I'll no provide pseudocode, as the difficult part is just that not covered by your libraries. Instead of pseudocode I'll post the images resulting from the successive steps.
I wrote the program in Mathematica, and I can post it if is of some service to you.
A- Start with a nice flood filled tunnel image
B- Apply a Distance Transformation
The Distance Transformation gives the distance transform of image, where the value of each pixel is replaced by its distance to the nearest background pixel.
You can see that our desired path is the Local Maxima within the tunnel
C- Convolve the image with an appropriate kernel
The selected kernel is a Laplacian-of-Gaussian kernel of pixel radius 2. It has the magic property of enhancing the gray level edges, as you can see below.
D- Cutoff gray levels and Binarize the image
To get a nice view of the center line!
Comment
Perhaps that is enough for you, as you ay know how to transform a thin line to an approximate piecewise segments sequence. As that is not the case for me, I continued this path to get the desired segments.
E- Image Partition
Here is when some advantages of the algorithm show up: you may start using parallel processing or decide to process each segment at a time. You may also compare the resulting segments with the previous run and re-use the previous results
F- Center of Mass detection
All the white points in each sub-image are replaced by only one point at the center of mass
XCM = (Σ i∈Points Xi)/NumPoints
YCM = (Σ i∈Points Yi)/NumPoints
The white pixels are difficult to see (asymptotically difficult with param "a" age), but there they are.
G- Graph setup from Vertices
Form a Graph using the selected points as Vertex. Still no Edges.
H- select Candidate Edges
Using the Euclidean Distance between points, select candidate edges. A cutoff is used to select an appropriate set of Edges. Here we are using 1.5 the subimagesize.
As you can see the resulting Graph have a few small cycles that we are going to remove in the next step.
H- Remove Small Cycles
Using a Cycle detection routine we remove the small cycles up to a certain length. The cutoff length depends on a few parms and you should figure it empirically for your graphs family
I- That's it!
You can see that the resulting center line is shifted a little bit upwards. The reason is that I'm superimposing images of different type in Mathematica ... and I gave up trying to convince the program to do what I want :)
A Few Shots
As I did the testing, I collected a few images. They are probably the most un-tunnelish things in the world, but my Tunnels-101 went astray.
Anyway, here they are. Remember that I have a displacement of a few pixels upwards ...
HTH !
.
Update
Just in case you have access to Mathematica 8 (I got it today) there is a new function Thinning. Just look:
This is a pretty classic skeletonization problem; there are lots of algorithms available. Some algorithms work in principle on outline contours, but since almost everyone uses them on images, I'm not sure how available such things will be. Anyway, if you can just plot and fill the sewer outlines and then use a skeletonization algorithm, you could get something close to the midline (within pixel resolution).
Then you could walk along those lines and do a binary search with circles until you hit at least two separate line segments (three if you're at a branch point). The midpoint of the two spots you first hit, or the center of a circle touching the three points you first hit, is a good estimate of the center.
Well in Python using package skimage it is an easy task as follows.
import pylab as pl
from skimage import morphology as mp
tun = 1-pl.imread('tunnel.png')[...,0] #your tunnel image
skl = mp.medial_axis(tun) #skeleton
pl.subplot(121)
pl.imshow(tun,cmap=pl.cm.gray)
pl.subplot(122)
pl.imshow(skl,cmap=pl.cm.gray)
pl.show()
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.