SMorFix is an algorithm which generates interesting textures. It currently only generates binary textures but could be extended to generate either continuously-valued or n-ary textures. The current implementation generates tilable textures.
I enjoy having textured desktop backgrounds which change regularly. When I started to use such backgrounds, it was important not to use a lot of the limited 8-bit colormap for the background, so I would generate tilable binary textures by hand in various image processing programs/frameworks. When my desktop starts up, a randomly chosen texture, with randomly chosen foreground and background colors, is used as my desktop background.
Eventually, I became tired of making these textures manually, and designed SMorFix, an algorithm which automatically generates a large variety of textures.
It is possible to use SMorFix for many other things which I thought of afterwards, like: texture gradients, animated textures, texture compression. I haven't had time to intensively test SMorFix in these applications, so YMMV.
Some binary textures are very rigid and deterministic, e.g., solid 1's, solid 0's, or a perfect checkerboard pattern of 1's and 0's. These textures do not resemble (in my eyes) natural textures. Natural textures contain "flaws", like natural crystals. When thinking about what characterizes such textures, what popped up in my mind was "stochastic texure rule", i.e., that in each small neighborhood the texture satisfied a texture "rule", randomly chosen from a given probability distribution of texture "rules".
I then mapped the fuzzy concept of "texture rule" to "fixed point of a binary morphological operator" and decided that the natural textures are the "fixed points" of applying stochastic morphological operators to random noise.
"Fixed point" in this case is not the strong, deterministic mathematical concept of fixed point, it instead is a perceptual, subjective fixed point. In other words, if we apply the operator to the current instance of the texture, we will obtain a different instance of what seems to be the same texture. For example, if the texture in question looks like a certain kind of tree bark, after applying the operator to an image containing the texture we obtain a different image, which could plausibly be the same kind of tree bark, just taken from a different part of the same tree...
If you've come here expecting to find a rigorous, mathematical model for textures, I'm sorry, you've come to the wrong place. I have not bothered to develop such a framework. I was just interested in generating textures, and after the weak-minded, hand-waving line of reasoning described above led me to an algorithm which works, I did not pursue the more theoretical aspects.
Currently the algorithmic framework includes:
Well, check out the gallery, which includes only a small part of the possible textures. Contact me if you generate a new texture which you think deserves to be added (you will have to submit the operator file also).
Any method which converts a vector of real numbers to a texture in a continuous fashion can be used to accomplish these things. A SMO is collection of numbers, some of which are real numbers. If we take one of these real numbers and let it vary continuously in space, we will get a texture gradient. If we let it vary continuously in time, we get an animated texture. If we have many parameters and discover a method for efficiently searching the parameter space for a texture which is sufficiently close to a given texture, that texture can be compressed into the set of parameters which generates the similar texture and the (presumably small) difference (or lossily compressed by forgetting about the difference).
A method of continuously parametrizing textures also enables the transformation of a gray-level image into one where gray-levels have been mapped continuously into textures.
When talking about texture animation, the continuous variation I speak about can express itself in two ways. In one version, the same random initial noise is processed with the same algorithmic parameters (random sequence of application sites, number of SMO applications, etc.) by SMO's which continuously vary frame by frame. Another possibiilty, which much more strongly depends on the texture really being a "fixed point", is that every frame is generated from the previous one by random application of the SMO associated with that frame.
YMMV, the only direction I've investigated here is texture animation, and up to now, I haven't come across anything particularly noteworthy. This might change if the set of SMOs is extended.
As far as I know, the SMorFix algorithm and the other associated algorithms discussed here have not been patented. One of the reasons this web page exists is to provide prior art which will hopefully prevent these algorithms from being patented in the future.
Even though I don't know of any such patents, I am not in a position to promise anything. I suggest that any company considering using this technology do a professional patent search. And I would appreciate being told about any significant patents which you discover.
There are many possible ways to continue the work on SMorFix. The programmatic direction includes:
The source code will be released under the GNU Public License, v.2. Details will follow.
Currently only the standalone generator is available via Subversion. I need to review all of the GIMP plugin files before I upload them.
SMorFix is only one of several personal projects I work on in my rather scanty "spare time". I'm planning on submitting it to SourceForge, after it is accepted I will start to see how I will organize any help which is volunteered.
In the meantime, take the code and play with it.