The need to estimate signals from their deformed versions arises in a wide range of engineering problems. Such deformations may be due to inherent physical effects or due to the measurement process. As an example consider two images of a single object taken from different viewpoints and distances. These images are deformed versions of each other. Any attempt to compare these images requires transforming one or both so that corresponding elements in the images appear at the same coordinates. In the one-dimensional case consider the case of a signal measured in the presence of (possibly time-varying) delay and Doppler which causes a distortion of the time axis and a corresponding deformation of the signal shape. The difficulty of these problems is their non-linear and high-dimensional nature.
This research provides a fundamental mathematical solution to a class of signal deformation problems. The solution involves a certain parametric model of the family of possible transformations (or rather, their inverses). Using this model the original problem is transformed into an equivalent problem expressed in the form of a linear system of equations in the low dimensional space. In other words, the method converts a computationally prohibitive estimation problem into a set of linear equations in the unknown parameters of the deformation model. In the case of affine transforms an exact closed form solution of the deformation parameters is obtained. In the more general case of homeomorphic deformations the solution is approximate, but high accuracy is achievable. The focus of the research is on evaluating the performance of this approach in the presence of noise and other uncertainties, and the optimal design of certain basis functions used by the algorithm. This research has applications to a wide range of image and video processing systems, in particular to medical imaging systems, and video/image based security systems.
%%%%%%%%%%%%%%%%%%%%%%%%%% > 3. A level of effort statement.
At the recommended level of support, the PI will make every effort to address all of the issues related to the basic operation of the proposed technique as described in the proposal, with emphasis on its performance in the presence of noise and various uncertainties, and the optimal design of the basis functions. Because of the greatly reduced budget and period of performance the specific applications of the technique will not be addressed in any detail.
