I am planning a kids' version of Mahjong Solitaire (starting with just the Turtle board layout and working my way from there). I am trying to wrap my head around how to store the data for each layer of the Turtle layout tileset. See here for an example: http://icarus.cs.weber.edu/~dab/cs3230/labs/lab.5/tile_layers.pdf
Ordinarily I'd use a 2D array for each layer, and a 1D array of the layers, from 0 (bottom-most) to 4 (topmost), with the allowance for layers above that (5, 6, ...). However, there are the tiles that occupy more than one row and/or column at once. For example, in Layer 0 (bottom-most), the far left tile and the 2 far right tiles occupy two rows at once, and the single tile in Layer 4 (topmost) occupies two columns and two rows at the same time.
What is the best data model to store this sort of tileset? Should each tile have a flag for shifting it halfway into the next row and column?
I'm thinking, there is a Tile object, each instance of which represents 1 of the 144 tiles on the board. Then all tiles are arranged in layers as I described above (2D array for each layer, all layers stored in a 1D array).
Note: I am considering using Javascript & HTML5 for this project. It won't be something I release to the public, just a programming exercise.
Is this the best method? Am I missing something?
I would indeed use a finer grid as alikox suggested. I would use a 2 times finer grid, give each tile an unique id, so one regular tile now uses four squares of the grid, when you have to delete one tile, you only have to check for surrounding squares with the same id and delete them as well.
There would be more than one way to implement this, you can set x, y and z coordinates of each tile for example.
class Tile {
int x
int y
int z
}
Related
I use set of images for image processing in which each image generates unique code (Freeman chain code). The size of array for each image varies. However the value ranges from 0 to 7. For e.g. First image creates array of 3124 elements. Second image creates array of 1800 elements.
Now for further processing, I need a fixed size of those array. So, is there any way to Normalize it ?
There is a reason why you are getting different sized arrays when applying a chain code algorithm to different images. This is because the contours that represent each shape are completely different. For example, the letter C and D will most likely contain chain codes that are of a different length because you are describing a shape as a chain of values from a starting position. The values ranging from 0-7 simply tell you which direction you need to look next given the current position of where you're looking in the shape. Usually, chain codes have the following convention:
3 2 1
4 x 0
5 6 7
0 means to move to the east, 1 means to move north east, 2 means to move north and so on. Therefore, if we had the following contour:
o o x
o
o o o
With the starting position at x, the chain code would be:
4 4 6 6 0 0
Chain codes encode how we should trace the perimeter of an object given a starting position. Now, what you are asking is whether or not we can take two different contours with different shapes and represent them using the same number of values that represent their chain code. You can't because of the varying length of the chain code.
tl;dr
In general, you can't. The different sized arrays mean that the contours that are represented by those chain codes are of different lengths. What you are actually asking is whether or not you can represent two different and unrelated contours / chain codes with the same amount of elements.... and the short answer is no.
What you need to think about is why you want to try and do this? Are you trying to compare the shapes between different contours? If you are, then doing chain codes is not the best way to do that due to how sensitive chain codes are with respect to how the contour changes. Adding the slightest bit of noise would result in an entirely different chain code.
Instead, you should investigate shape similarity measures instead. An authoritative paper by Remco Veltkamp talks about different shape similarity measures for the purposes of shape retrieval. See here: http://www.staff.science.uu.nl/~kreve101/asci/smi2001.pdf . Measures such as the Hausdorff distance, Minkowski distance... or even simple moments are some of the most popular measures that are used.
I made a photo mosaic script (PHP). This script has one picture and changes it to a photo buildup of little pictures. From a distance it looks like the real picture, when you move closer you see it are all little pictures. I take a square of a fixed number of pixels and determine the average color of that square. Then I compare this with my database which contains the average color of a couple thousand of pictures. I determine the color distance with all available images. But to run this script fully it takes a couple of minutes.
The bottleneck is matching the best picture with a part of the main picture. I have been searching online how to reduce this and came a cross “Antipole Clustering.” Of course I tried to find some information on how to use this method myself but I can’t seem to figure out what to do.
There are two steps. 1. Database acquisition and 2. Photomosaic creation.
Let’s start with step one, when this is all clear. Maybe I understand step 2 myself.
Step 1:
partition each image of the database into 9 equal rectangles arranged in a 3x3 grid
compute the RGB mean values for each rectangle
construct a vector x composed by 27 components (three RGB components for each rectangle)
x is the feature vector of the image in the data structure
Well, point 1 and 2 are easy but what should I do at point 3. How do I compose a vector X out of the 27 components (9 * R mean, G mean, B mean.)
And when I succeed to compose the vector, what is the next step I should do with this vector.
Peter
Here is how I think the feature vector is computed:
You have 3 x 3 = 9 rectangles.
Each pixel is essentially 3 numbers, 1 for each of the Red, Green, and Blue color channels.
For each rectangle you compute the mean for the red, green, and blue colors for all the pixels in that rectangle. This gives you 3 numbers for each rectangle.
In total, you have 9 (rectangles) x 3 (mean for R, G, B) = 27 numbers.
Simply concatenate these 27 numbers into a single 27 by 1 (often written as 27 x 1) vector. That is 27 numbers grouped together. This vector of 27 numbers is the feature vector X that represents the color statistic of your photo. In the code, if you are using C++, this will probably be an array of 27 number or perhaps even an instance of the (aptly named) vector class. You can think of this feature vector as some form of "summary" of what the color in the photo is like. Roughly, things look like this: [R1, G1, B1, R2, G2, B2, ..., R9, G9, B9] where R1 is the mean/average of red pixels in the first rectangle and so on.
I believe step 2 involves some form of comparing these feature vectors so that those with similar feature vectors (and hence similar color) will be placed together. Comparison will likely involve the use of the Euclidean distance (see here), or some other metric, to compare how similar the feature vectors (and hence the photos' color) are to each other.
Lastly, as Anony-Mousse suggested, converting your pixels from RGB to HSB/HSV color would be preferable. If you use OpenCV or have access to it, this is simply a one liner code. Otherwise wiki HSV etc. will give your the math formula to perform the conversion.
Hope this helps.
Instead of using RGB, you might want to use HSB space. It gives better results for a wide variety of use cases. Put more weight on Hue to get better color matches for photos, or to brightness when composing high-contrast images (logos etc.)
I have never heard of antipole clustering. But the obvious next step would be to put all the images you have into a large index. Say, an R-Tree. Maybe bulk-load it via STR. Then you can quickly find matches.
Maybe it means vector quantization (vq). In vq the image isn't subdivide in rectangles but in density areas. Then you can take a mean point of this cluster. First off you need to take all colors and pixels separate and transfer it to a vector with XY coordinate. Then you can use a density clustering like voronoi cells and get the mean point. This point can you compare with other pictures in the database. Read here about VQ: http://www.gamasutra.com/view/feature/3090/image_compression_with_vector_.php.
How to plot vector from adjacent pixel:
d(x) = I(x+1,y) - I(x,y)
d(y) = I(x,y+1) - I(x,y)
Here's another link: http://www.leptonica.com/color-quantization.html.
Update: When you have already computed the mean color of your thumbnail you can proceed and sort all the means color in a rgb map and using the formula I give to you to compute the vector x. Now that you have a vector of all your thumbnails you can use the antipole tree to search for a thumbnail. This is possbile because the antipole tree is something like a kd-tree and subdivide the 2d space. Read here about antipole tree: http://matt.eifelle.com/2012/01/17/qtmosaic-0-2-faster-mosaics/. Maybe you can ask the author and download the sourcecode?
I want to rig a Rubik's cube in Maya, so it can rotate in any direction and any number of times. Any rotation would be in 90 degree increments. These are the objects in my Outliner:
26 blocks (the center block of the cube is not necessary)
9 rotation controllers (3 for the rows/columns of height/width/depth)
1 root controller
The trick is passing the control of the individual blocks from one controller to the next. At any given time, a block can be influenced by 3 different controllers. However, after rotation, the controllers change.
I suppose I need to create a series of matrices (2D arrays), 9 of them - one for each controller. Assign the blocks to them, and then reassign after a rotation. I suppose I would need a temporary matrix for swapping. Beyond this, I don't know how to go about this. Should these matrices be a parameter of the root controller? Probably.
Any help in this matter would help. I am new to MEL but I have background in C/C++ and such. How would you rig a functional Rubik's cube?
Here is working Rubic's cube tool for download http://www.geonak.com/downloads/RubixCube.zip
All you need is to turn the rotation interpolation to quaternion interpolation for your rotation, then key one packet at a time. Just make sure never go backwards when your keying the sequence tough.
You can also do it by blending constraint weights. The 6 center pieces are your controls. Parent constrain all the other cubes to all 6 controls. Each cube will now have a constraint node with 6 weight inputs that you can key. Set the weight for the controller you're going to rotate to 1 and all others to 0 for the cubes one the face you're rotating. Set all the weights to 0 for cubes that aren't involved in the current move.
If you want to get fancier, create a master layout control for the whole thing, add an attribute to set which controller is active with options 1 to 6, and have it update the weights on all the cubes when it gets changed. You can probably determine if a cube should be deactivated completely (all weights -> 0) by looking at its distance to the currently active controller cube; adjacent cubes on the active face will all be close, all others will be further away.
In hashlife the field is typically treated as a theoretically infinite grid, with the pattern in question centered near the origin. A quadtree is used to represent the field. Given a square of 2^(2k) cells, 2k on a side, at the kth level of the tree, the hash table stores the 2^(k-1) by 2^(k-1) square of cells in the center, 2^(k-2) generations in the future. For example, for a 4x4 square it stores the 2x2 center, 1 generation forward; and for an 8x8 square it stores the 4x4 center, 2 generations forward.
So given a 8x8 initial configuration we get a 4x4 square 1 generation forward centered w.r.t. the 8x8 square and a 2x2 square 2 generations forward (1 generation forward w.r.t the 4x4 square) centered w.r.t the 8x8 square. With every new generation our view of the grid reduces, in-turn we get the next state of the automata. We canot go any further after getting the inner most 2x2 square 2^(k-2) generations forward.
So how does the hashlife in Golly go on forever? Also its view of the field never seems to reduce. It seems to show the state of the whole automata after 2^(k-2) generations. More so given a starting configuration which expands with time, the view of the algorithm seems to increase. The view of the grid zooms out to show the expanding automata?
There's a good article on Dr. Dobb's which goes into detail about how HashLife works. The basic answer is that you don't merely run the algorithm on the existing nodes, you also use new shifted nodes to get the next generation.
To be clear (because your ^ symbols were missing), you are asking:
Given a square of 2^(2k) cells, 2^k on a side, at the kth level of the
tree, the hash table stores the 2^(k-1)-by-2^(k-1) square of cells in
the center, 2^(k-2) generations in the future. [...]
So given a 8x8 initial configuration [...] With every new generation
our view of the grid reduces, in-turn we get the next state of the
automata. We canot go any further after getting the inner most 2x2
square 2^k-2 generations forward.
So how does the hashlife in Golly go on forever? Also its view of the
field never seems to reduce.
Instead of starting with your 8x8 pattern, imagine instead that you start with a bigger pattern that happens to contain your 8x8 pattern inside it. For example, you could start with a 16x16 pattern that has your 8x8 pattern in the center, and a 4-row margin of blank cells all around the edges. Such a pattern is easy to construct, by assembling blank 4x4 nodes with the 4x4 subnodes of your 8x8 start pattern.
Given such a 16x16 pattern, the HashLife algorithm can give you an 8x8 answer, 4 generations in the future.
You want more? Okay, start with a 32x32 pattern that contains mostly blank space, with the 8x8 pattern in the center. With this you can get a 16x16 answer that is 8 generations into the future.
What if your pattern contains moving objects that move fast enough that they go outside that 16x16 area after 8 generations? Simple -- start with a 64x64 start pattern, but instead of trying to run it for a whole 16 generations, just run it for 8 generations.
In general, all cases of arbitrarily large, possibly expanding patterns, over arbitrarily long periods of time, can be handled (and in fact are handled in Golly) by adding as much blank space as needed around the outside of the pattern.
The centered squares are only the precomputed stuff. The algorithm indeed keeps the whole universe at all times and updates all parts of it, not just the centers.
I need to do a program that does this: given an image (5*5 pixels), I have to search how many images like that exist in another image, composed by many other images. That is, i need to search a given pattern in an image.
The language to use is C. I have to use parallel computing to search in the 4 angles (0º, 90º, 180º and 270º).
What is the best way to do that?
Seems straight forward.
Create 4 versions of the image rotated by 0°, 90°, 180°, and 270°.
Start four threads each with one version of the image.
For all positions from (0,0) to (width - 5, height - 5)
Comapare the 25 pixels of the reference image with the 25 pixels at the current position
If they are equal enough using some metric, report the finding.
Use normalized correlation to determine a match of templates.
#Daniel, Daniel's solution is good for leveraging your multiple CPUs. He doesn't mention a quality metric that would be useful and I would like to suggest one quality metric that is very common in image processing.
I suggest using normalized correlation[1] as a comparison metric because it outputs a number from -1 to +1. Where 0 is no correlation 1 would be output if the two templates were identical and -1 would be if the two templates were exactly opposite.
Once you compute the normalized correlation you can test to see if you have found the template by doing either a threshold test or a peak-to-average test[2].
[1 - footnote] How do you implement normalized correlation? It is pretty simple and only has two for loops. Once you have an implementation that is good enough you can verify your implementation by checking to see if the identical image gets you a 1.
[2 - footnote] You do the ratio of the max(array) / average(array_without_peak). Then threshold to make sure you have a good peak to average ratio.
There's no need to create the additional three versions of the image, just address them differently or use something like the class I created here. Better still, just duplicate the 5x5 matrix and rotate those instead. You can then linearly scan the image for all rotations (which is a good thing).
This problem will not scale well for parallel processing since the bottleneck is certainly accessing the image data. Having multiple threads accessing the same data will slow it down, especially if the threads get 'out of sync', i.e. one thread gets further through the image than the other threads so that the other threads end up reloading the data the first thread has discarded.
So, the solution I think will be most efficient is to create four threads that scan 5 lines of the image, one thread per rotation. A fifth thread loads the image data one line at a time and passes the line to each of the four scanning threads, waiting for all four threads to complete, i.e. load one line of image, append to five line buffer, start the four scanning threads, wait for threads to end and repeat until all image lines are read.
5 * 5 = 25
25 bits fits in an integer.
each image can be encoded as an array of 4 integers.
Iterate your larger image, (hopefully it is not too big),
pulling out all 5 * 5 sub images, convert to an array of 4 integers and compare.