I should be doing work

Two days behind and I'm just pointing the web-cam back at the computer screen.

Image Analogies

Some awesome stuff here. Check out the "texture-by-numbers" examples in particular.

Conformal maps on photography

I just found a Flickr set with some cool examples of applying conformal maps to photography.

More screenshots

Here's the latest.

Edit: I've added some more screenshots to the gallery, with tasty vertical symmetry imposed by mirroring.


Here I'm trying out some different maps, and also incorporating a camera feed, which is what gives it the more fuzzy, organic look. The geometric patterns with n-way radial symmetry come from z' = z*c, which gives simple scaling and rotation. The squished circles come from z' = sin(real(p) + t) + i*sin(imag(p)), where p = z^2 + c and t is a real parameter.

More fractal video feedback

I've been working on a new implementation of the fractal video feedback idea. Unlike the previous attempts, the code is nice and modular, so complicated bits of OpenGL hackery get encapsulated in an object with a simple interface. It's still very much a work in progress, but I thought I'd share some results now. Feedback (no pun intended) is very much appreciated.

Video:

Shoving the video through the YouTubes kills the quality. I have some higher quality screenshots in a Flickr gallery. Some of my favorites:

The basic idea is the same as Perceptron: take the previous frame, map it through some complex function, draw stuff on top, repeat. In this case, the "stuff on top" consists of a colored border around the buffer that changes hue, plus some moving polygons that can be inserted by the user (which aren't used in the video, but are in some of the stills). In these examples, the map is a convex combination of complex functions; in the video it's z' = a*log(z)*c + (1-a)*(z²+c). Here z is the point being rendered, z' is the point in the previous frame where we get its color, c is a complex parameter, and a is a real parameter between 0 and 1.

There are two modes: interactive and animated. In interactive mode, c and a are controlled with a joystick (which makes it feel like a flight simulator on acid). The user can also place control points in this (c,a) space. In animated mode, the parameters move smoothly between these control points along a Catmull-Rom spline, which produces a nice C1 continuous curve.

The feedback loop is rendered offscreen at 4096x4096 pixels. Since colors are inverted every time through the loop, only every other frame is drawn to the screen, to make it somewhat less seizuretastic. At this resolution, the system has 48MB of state. On my GeForce 8800GTS I can get about 100 FPS in this loop; by a conservative estimate of the operations involved, this is about 60 GFLOPS. I bow before NVIDIA. Now if only I had one of these...

Microrobotically fabricated biological scaffolds for tissue engineering

My first paper credit! This was a bio-engineering project. We explored a new fabrication method for building submicron-scale fibrous constructs out of the biodegradable polymer polylactic acid (PLA). 

Designing fibrous, biodegradable, patterned substrates is relevant for tissue engineering: they provide a mechanical substrate to guide the structural development of the tissue. We cultured the mouse myoblast (muscle building) C2C12 cell line (which has been immortalized since 1977) on the constructs. The cells adhered to the fibers and replicated happily.

You can download the conference paper here.

We took some beautiful confocal and electron microscopy images:

The C2C12 cells were modified so that the structural protein α-tubulin is attached to a green fluorescent protein. This protein is a component of the cytoskeletal microtubules. These structural elements are especially prominent during cytokinesis, just before the cells divide (below).

Below is a false-color confocal image of the cells proliferating on the scaffold. The PLA fibers (blue) were imaged in brightfield. The α-tubulin-GFP fluorescence is in green, with fine structures highlighted in yellow.

Here are a few more fluorescence and electron microscopy images (click on thumbnail to view full size):

If you would like to reproduce or refer to these images, you can cite the paper as:

Nain, A.S., Chung, F., Rule, M., Jadlowiec, J.A., Campbell, P.G., Amon, C. and Sitti, M., 2007, April. Microrobotically fabricated biological scaffolds for tissue engineering. In Proceedings 2007 IEEE International Conference on Robotics and Automation (pp. 1918-1923). IEEE.