Lies - Damn Lies - Mathematics: How-to lie with an image instead of 1000 words
Thirty years ago image processing was a tiny, exotic part of electrical engineering, today it is a technology that has changed the live-style of many of its users. In the last few years analog photography has almost disappeared, new cameras are all digital, and cameras are found everywhere from mobile phones to surveillance. Many experts predict that the next step will be new combinations of optical elements and computers: computational photography. In this approach the optics and the sensors act as an encoder of light distributions and the algorithms in the computer map this encoded information into conventional images.
This allows completely new solutions since the encoding is not necessary a conventional image. Two examples: (1) light stage: Here a combination of a large number of different light sources and a large number of conventional cameras is used to create a database showing the object (usually an actor) in many different positions under many different illuminations. The images in the database can later be used to show the object or several copies of it in computationally generated scenes. This is used in movie productions. (2) Cameras using mirrors encoding distorted views of the scene. The distortions can later be compensated by software to generate conventional images. Using this technique very wide fields of views can be covered. (3) In cases where we have models describing the optical properties of our objects it is possible to modify the captured images to simulate new views. This is used by cosmetic companies and in publishing.
Many of these applications are not only technologically challenging but
they also require sophisticated mathematical tools. Some examples: (1)
combining lenses, mirrors and sensors requires sophisticated geometrical
models to describe the encoding. Since many of these systems generate large
quantities of redundant data it is also necessary to develop new signal
processing and compression techniques. (2) The interaction of light with
scattering media like paper or skin is very complex and models that
describe the processes involved are complicated and not yet fully
understood. (3) Today, large databases can contain 1-2 Gimages and managing
such databases is a difficult problem. This becomes even more difficult
when the description, stored in the database, can be converted to different
conventional images that can have quite different appearance.
Senast uppdaterad: 2014-10-14