| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
|
| Initial Amendment Date: | May 9, 2011 |
| Latest Amendment Date: | April 25, 2013 |
| Award Number: | 1107053 |
| Award Instrument: | Continuing Grant |
| Program Manager: |
Gabor Szekely
DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
| Start Date: | July 1, 2011 |
| End Date: | June 30, 2015 (Estimated) |
| Total Intended Award Amount: | $180,000.00 |
| Total Awarded Amount to Date: | $180,000.00 |
| Funds Obligated to Date: |
FY 2012 = $59,700.00 FY 2013 = $60,834.00 |
| History of Investigator: |
|
| Recipient Sponsored Research Office: |
845 N PARK AVE RM 538 TUCSON AZ US 85721 (520)626-6000 |
| Sponsor Congressional District: |
|
| Primary Place of Performance: |
845 N PARK AVE RM 538 TUCSON AZ US 85721 |
| Primary Place of
Performance Congressional District: |
|
| Unique Entity Identifier (UEI): |
|
| Parent UEI: |
|
| NSF Program(s): | STATISTICS |
| Primary Program Source: |
01001213DB NSF RESEARCH & RELATED ACTIVIT 01001314DB NSF RESEARCH & RELATED ACTIVIT |
| Program Reference Code(s): | |
| Program Element Code(s): |
|
| Award Agency Code: | 4900 |
| Fund Agency Code: | 4900 |
| Assistance Listing Number(s): | 47.049 |
ABSTRACT
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.
PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH
Note:
When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external
site maintained by the publisher. Some full text articles may not yet be available without a
charge during the embargo (administrative interval).
Some links on this page may take you to non-federal websites. Their policies may differ from
this site.
PROJECT OUTCOMES REPORT
Disclaimer
This Project Outcomes Report for the General Public is displayed verbatim as submitted by the Principal Investigator (PI) for this award. Any opinions, findings, and conclusions or recommendations expressed in this Report are those of the PI and do not necessarily reflect the views of the National Science Foundation; NSF has not approved or endorsed its content.
The PI in collaboration with his Ph.D. students and former students has developed a new model-independent statistical methodology for analysis of various forms of image data that are now available thanks to advances in digital imaging technologies. Model-independence means that no assumptions are made about the nature of uncertainty or randomness of the data. Indeed, the data analysis using this methodology has repeatedly outperformed earlier so-called parametric methods which assumed a probability model from which the data arose, where the only uncertainty lay in a finite set of unknown parameters. These earlier methods perform poorly if the model is misspecified, which is often the case in dealing with high dimensional image data.
As an illustration one may consider the problem of medical diagnostics based on MRI (magnetic resonance imaging) or DTI (diffusion tensor imaging) digital images. Physicians specializing in the treatment of a particular disease may be generally aware that the disease produces some deformation in certain organs. The methodology developed by the project provides a precise quantification of these possible deformations. Comparing images of two different groups of people -one diseased and one normal- one can then set benchmarks to diagnose the presence or onset of a disease. Such diagnosis has been found to be much sharper using the new model-independent methods than the older model-dependent, or parametric, methods. Several examples of this phenomenon have been presented in a research monograph published under the grant-- Nonparametric Inference on Manifolds-with Applications to Shape Spaces (2012), Cambridge University Press.. These cover some forms of schizophrenia, glaucoma, etc. Further applications based on DTI data of the brain's cortex have the potential for providing vital diagnostic tools for identifying the onset and/or progression of diseases such as Parkinson's disease, Alzheimer's, etc.
Aside from the expected benefits to healthcare as described above, the project has aimed at providing training and education of students and scientists in the new methodology and its applications. The findings of the project have been broadly disseminated among US and international scholars through publications and seminars and colloquia. In addition, two graduate students have received their Ph.D. degrees (in 2012 and 2015) under the supervision of the PI with support from the grant.
Last Modified: 08/16/2015
Modified by: Rabindra Bhattacharya
Please report errors in award information by writing to: awardsearch@nsf.gov.
