Research
My
main research interest is in the area of statistical 3D curve shape
analysis of structures of Nucleotides and Amino-Acids. This research
area is multidisciplinary in that it involves statistics,
differential geometry, functional analysis, group algebra, computer
image analysis and bioinformatics.
I am currently working on developing
methods for shape analysis of parameterized 3D open curves for which
added sequence/secondary structure information can be jointly
compared. This requires the adjustment of Elastic Shape Analysis
(ESA) methods in that we can use neither equally spaced 3D points
nor same number points in a pair of structures to be able to compare
them. It also needs a biologically relevant way to incorporate such
additional information through a correct choice of auxiliary
function.
ESA has been applied mostly on equally re-sampled versions of original curves but we aim to eliminate this re-sampling step, this will enable us to incorporate sequences/secondary structure information more naturally into auxiliary post 3D coordinates. The ESA framework requires a Riemannian metric that allows: (1) re-parameterizations of curves by isometries, and (2) efficient computations of geodesic paths between curves. These tools allow for computing Karcher means and covariances (using tangent PCA) for shape classes, and a probabilistic classification of curves. To solve these problems we first introduced a mathematical representation of curves, called q-functions, and we used the L2 metric on the space of q-functions to induce a Riemannian metric on the space of parameterized curves. This process requires optimal registration of curves and achieves a superior alignment on them. Mean Shapes and their Covariance structures can be used to specify a normal probability model on shape classes, which can then be used for classifying test shapes. We have achieved comparable classification rate to state-of-the art methods on their RNA and Protein benchmark sets.
ESA has been applied mostly on equally re-sampled versions of original curves but we aim to eliminate this re-sampling step, this will enable us to incorporate sequences/secondary structure information more naturally into auxiliary post 3D coordinates. The ESA framework requires a Riemannian metric that allows: (1) re-parameterizations of curves by isometries, and (2) efficient computations of geodesic paths between curves. These tools allow for computing Karcher means and covariances (using tangent PCA) for shape classes, and a probabilistic classification of curves. To solve these problems we first introduced a mathematical representation of curves, called q-functions, and we used the L2 metric on the space of q-functions to induce a Riemannian metric on the space of parameterized curves. This process requires optimal registration of curves and achieves a superior alignment on them. Mean Shapes and their Covariance structures can be used to specify a normal probability model on shape classes, which can then be used for classifying test shapes. We have achieved comparable classification rate to state-of-the art methods on their RNA and Protein benchmark sets.
Please visit our research group web page:
Statistical Shape and Modeling Group