Projective shapes of 3D configurations, not their Kendall type similarity shapes, are the most appropriate objects for general image analysis in machine vision and robotics. The present project will develop registration free nonparametric inference by constructing an appropriate equivariant embedding of the full projective shape manifold, and by providing two-sample and multi-sample inference procedures based on the extrinsic mean under the embedding. On the other hand, data analysis on size-and-shape reflection-similarity manifolds are important in virtual reconstructions of proteins and of various configurations of bone structures in humans. Another focus of the project is on certain special spaces which are not manifolds, but are spaces with manifold stratification, and which arise in many applications, e.g., in geometric representations of phylogenetic trees. Apart from the landmarks based shape analysis as described above, continuous shapes such as given by boundary contours in 2D will be investigated as elements of infinite dimemsional (Hilbert) manifolds. Finally, proposed nonparametric Bayesian procedures for density estimation, regression and classification on shape manifolds will be a significant point of departure from nonparametric inference based so far primarily on Fre'chet means and dispersions. Together these projects aim at providing comprehensive robust procedures for shapes which are of wide applicability in many fields of science and technology.

Digital images today play a vital role in science and technology, in intelligence gathering and defense, and in many aspects of everyday life. The present proposal seeks to advance the analysis of digital camera images via the statistical study of shapes and other non-Euclidean objects. Nonparametric statistical methods developed by the PIs and others over the past twelve years have had a significant impact on statistical inference for 3D scene recognition from regular digital cameras, on medical diagnostics, and on many other forms of image analysis. The proposal aims not only to consolidate this theory. The objective is also to develop new methodologies for machine vision and robotics, for dynamic scene recognition, for medical diagnostics from CT scans for planning reconstructive surgery for the severely injured, and for the detection of elusive health impairments from DNA sequences via shape configurations of proteins.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Application #
1107053
Program Officer
Gabor J. Szekely
Project Start
Project End
Budget Start
2011-07-01
Budget End
2014-06-30
Support Year
Fiscal Year
2011
Total Cost
$180,000
Indirect Cost
Name
University of Arizona
Department
Type
DUNS #
City
Tucson
State
AZ
Country
United States
Zip Code
85721