Linear Algebra and Forensics
Donna Beers, Ph.D.
Simmons College
Have you taken a selfie? Or have you ever doctored a photo of yourself so that you look taller or thinner or free of blemishes or other imperfections? With the ready availability of digital technology, we have all become photographers; and, free, online photo editing tools allow us to alter our pictures to suit our pleasure. The downside of this, however, is that when we look at photos, whether in tabloids or on the Web, we wonder: Is this a fake? For, just as you can alter pictures to make yourself look more attractive, so, too, politicians, advertisers, and others with particular agendas are using digital imaging tools to manipulate photos to create false impressions. Determining whether a photo has been doctored is just one of the many questions that photo forensics tries to answer.
The good news is that linear algebra offers powerful tools for carrying out digital photo forensics. In this talk we will explore two applications: detection of explicit images through use of the RGB color model and image reconstruction from compressed data files using the Inverse Discrete Cosine Transform.
An algebraist, Donna Beers, who is Professor of Mathematics at Simmons College, teaches a range of courses including linear and modern algebra, discrete mathematics, calculus and real analysis, and mathematics for elementary school teachers. Her research publications are in the areas of group theory and group algebras of infinite abelian groups. Her scholarly interests also include inquiry into student learning to strengthen teaching. Promoting undergraduate research is a vital aspect of her teaching and she has supervised numerous independent studies and internships. To honor the accomplishments of Simmons College students in mathematics, she initiated and serves as adviser to the Massachusetts Theta Chapter of Pi Mu Epsilon. In October 2012, she was honored as the inaugural recipient of the Toby Sloane Award for Student-Centeredness in Teaching.
