I attended a symposium entitled Mathematics and Science in Digital Media, Technology and Entertainment yesterday held at Raffles City Convention Centre (link). It was a full-day event. Lunch was not provided ,much to my disappointment (I really love the food that RCCC caters).

As indicated by the title, the symposium centres around the use of Maths and Science (primarily Maths) together with a touch of computer science, in fields like animation and image processing (which would constitute the Digital Media part). Four entertaining and very qualified speakers were invited to talk about their research, almost all of them having one breakthrough or another.

And I FORGOT to bring my camera, so no photos…

The Talks

Here is a list of the talks and their speakers:

• Mathematics of Entertainment
  Douglas Roble, Digital Domain
• Meshes for Geometric Modelling and Animation
  Peter Schröder, California Institute of Technology
• A Start-Up from Mathematics for Television
  Stéphane Mallat, Ecole Polytechnique and Let it Wave
• Compressive Sensing
  Emmanuel Candes, California Institute of Technology

The first talk titled Mathematics of Entertainment was about Douglas Roble’s company Digital Domain. The company does 3D effects for well known movies like Titanic and Pirates 2: Dead Man’s Chest. Note that this is not to be confused with full 3D animation that companies like Pixar do. DD creates landscapes, lots of water (tsunami in Day After Tomorrow), animates explosions, and a ton of other stuff entirely using 3D graphics. He talked a lot about how the 3D effects were created without delving too much in the technicalities, showed us lots of cool videos, and was very animated about it all.

The second talk titled Meshes for Geometric Modelling and Animation was a rather technical talk on a dry topic, and it didn’t really interest me. The speaker was a cool looking guy, though. Unfortunately, I fell asleep halfway and didn’t catch much of it.

I do recall the speaker how it all started with the Mercator projection, and way in which cartographers could represent the globe of the world on the map whilst retaining the angles. The trade off is that the land masses are all skewed out of proportion, but it was more important for sailors to be able to take accurate bearings in order to find their way around. Similarly, 2D textures and images can then be mapped onto 3D meshes using a variation of this technique. Then I lost consciousness…

The third talk titled A Start-Up from Mathematics for Television was by far the most entertaining of the four. Why? Because a French guy was speaking. Seriously, if you’ve got a company and you need a spokesman or a PR guy, get a French one. They are so amusing, especially with the accent. You would have had to hear this guy speak to understand what I’m trying to say. Effectively, the whole audience was laughing for a good portion of the time.

I enjoyed this one tremendously, because it dealt with two of my greatest interests: compression and image processing. This guy Stéphane and his team of four friends created a new algorithm for image processing. They basically went one step further, and instead of using wavelets as the primary source of data for the compression, they used bandlets. (I bet you didn’t understand that, but that’s not the point)

This led to extremely efficient compression even at low sizes (it beat JPEG-2000 hands down—a 500 bytes image which you could hardly recognise with JPEG-2000, was sharp and clear using their technique). It also allowed for fast and effective filtering in video, such as denoising, inter-frame interpolation, edge detection. And it blew the minds of companies that they approached, who had never seen anything accomplish such amazing results with imaging and video.

It’s a pity that these four geniuses created a company to ultimately profit from it, but if they do make millions I think they deserve it completely. However, it have been fantastic if we could see a new compression algorithm replace the ageing and ineffective JPEG-2000 that we find everywhere. It could be made into a filter for use with video encoding (pre-processing like denoising and all that stuff) and playback (post-processing like upscaling to the size of your monitor). What we have available to everyone for free usage is already very good, though what is commercially available is even better. These boys beat the commercial products, so you can imagine how good their product is.

The last talk titled Compressive Sensing rang true with my interests as well. Emmanuel’s work is absolutely brilliant. When we employ compression (lossy), what we’re actually doing is only keeping the data that really matter. If I had an image of 1 megapixel (1000 x 1000), and I created an orthonormal wavelet plot of the coefficients of the pixel values against their frequency of occurrence, I would be able to see only a narrow range of coefficients (out of a million) constitute the majority of the image, and I only need to keep these 3% of the data. This reduces the size tremendously, and yet the compressed image looks almost the same as the original. This is also roughly how JPEG works.

Yet, our sensors, that do the conversion from analog to digital, take everything in. This is a waste of resources, since you’re going to throw away 97% of the input data with compression (e.g. in a digital camera). Emmanuel then proposes, why don’t we create sensors that read in only what we need, and we can then exploit the incoherence of the signals to extrapolate (decompress) the full signal. This sounds crazy, but he’s figured out how to do it. What followed was a very technical explanation about how this is done.

The applications for such an approach are countless. It can be used to make MRIs snappy and cheaper. Right now, MRIs are so time-consuming that hospitals need to schedule them. He also showed the workings of a 1-pixel camera (consisting of just ONE photo-detector), and how using compressive sensing a sharp image could be replicated digitally. This will allow cameras to become even smaller and cheaper, especially for security cameras.

Annoyances

Nothing is perfect. I found the emcees for this symposium extremely lacking. I do wished they had asked some younger people, who probably would have been able to at least read the script fluently. The place was extremely cold, that I found myself shivering during the Forum. And have I mentioned that lunch was NOT provided?

Last Words

I really wouldn’t expect many people to be able to spend their entire Sunday sitting through a technical symposium, and still find it enriching. One of the conditions is that you really need to have a strong interest in whatever is being covered. It became evident that many in the audience lacked this, as by the time the Forum was held (last event of the day), the audience had dwindled to a quarter (or less) of it’s original size.