Dr. John F. Hamilton, Jr.

Photographic Science and Technology Center
Kodak Research Labs
Rochester, NY 14650-2120
Phone: 585-477-5047
E-mail: john.f.hamilton@kodak.com

A graduate of Cornell University, John Hamilton received his Ph.D. in mathematics at Indiana University. In 1974, he accepted a position at the Kodak Research Laboratories where he applied mathematics to various problems in graphic arts (printing), medical imaging, clinical diagnostic imaging, and electronic digital imaging. He is a Research Fellow, a recipient of the Eastman Innovation Award (2003), a recipent of the Rochester Intellectual Property Law Association (RIPLA) Distinguished Inventor of the Year Award (2005), and a member of Kodak’s Distinguished Inventors Gallery with 38 patents in the area of digital image processing. Currently, he is developing novel image processing algorithms for Kodak's digital camera business, Kodak's sensor business, and related applications.

Blur filters are often used in digital imaging systems to suppress the sampling artifact known as "aliasing". One type of blur filter is called a phase noise filter which blurs the image by introducing random phase shifts into the image prior to its capture. In the process of designing such a filter, it is helpful to have a math model to predict the effect the filter would have on any given image.

The talk includes a brief description of digital cameras and a demonstration of the problem of color aliasing. Additional topics briefly described are: linear shift-invariant operations, the Fourier Transform, and the modulation transfer function (MTF). An integral representation of an MTF is then analyzed and reduced to known functions and a single unknown autocorrelation function. The final portion of the talk discusses a computational method by which this unknown function can be approximated, and compares the resulting model to measured data.

Digital imaging systems need three values (red, green, blue) in every picture element (pixel) to produce a color image. While some systems use three sensors to measure all these values directly, other systems use a single sensor to measure only a third of them. The rest of the color values must then be computed from the measured values. This color reconstruction step is called color interpolation.

The talk takes the audience through some of the steps required to get good reconstructed images. Image artifacts are shown before and after each algorithm step is taken so that the impact of each step may be seen.

This talk is about the kind of problems found in "industry" and the role played by mathematicians in solving them. Most industrial problems are multi-disciplinary in nature and require the efforts of several people to find a solution. While math modeling is an important problem-solving skill, other "non-math" skills are equally important. These include good communication and the ability to deal with people from other areas of science and business.

A quick summary is presented of actual problems encountered at Kodak.