The talk describes (dis)similarity distances between pairs of two-dimensional surfaces (embedded in three-dimensional space) that use both local structures and global information in the surfaces. This is work done in collaboration with Yaron Lipman.
These are motivated by the need of biological morphologists to compare different phenotypical structures. At present, scientists using physical traits to study evolutionary relationships among living and extinct animals analyze data extracted from carefully defined anatomical correspondence points (landmarks). Identifying and recording these landmarks is time consuming and can be done accurately only by trained morphologists. This necessity renders these studies inaccessible to non-morphologists and causes phenomics to lag behind genomics in elucidating evolutionary patterns.
Unlike other algorithms presented for morphological correspondences, our approach does not require any preliminary marking of special features or landmarks by the user. It also differs from other seminal work in computational geometry in that our algorithms are polynomial in nature and thus faster, making pairwise comparisons feasible for significantly larger numbers of digitized surfaces.
The approach is illustrated using three datasets representing teeth and different bones of primates and humans; it is shown that it leads to highly accurate results.
About the Speaker:
Ingrid Daubechies is a member of the United States’ National Academy of Sciences, was a MacArthur Fellow, and is President of the International Mathematical Union.
Professor Daubechies was born and educated in Belgium. She moved to the United States in 1987 where she first worked for Bell Laboratories and then at Princeton University where she was full Professor of Mathematics from 1993-2011. She is best known for her discovery and mathematical analysis of compactly supported wavelets, which are used in image compression, for example in JPEG 2000 for both both lossless and lossy compression. She was awarded the Steele Prize for mathematical exposition in 1994 for her book, Ten Lectures on Wavelets.
One focus of Daubechies’ current research is the development of analytic and geometric tools for the comparison of surfaces. Her new approach, developed with Yaron Lipmon uses conformal mapping to define a metric between surfaces. Comparison of surfaces plays a central role in many scientific disciplines and in the construction of video animations, and it is also a crucial step in many medical and biological applications. In an earlier collaboration, she worked with paleontologists to develop a quantitative method to characterize the complexity of molar tooth surfaces, in an effort to reconstruct the diet of various extinct taxa.