Reconstruction of Target Reflecting Surface Using Differential Geometry

A procedure based on the envelope concept of differential geometry is described that permits the reconstruction of the contour of a smooth, moving, conducting target, satisfying the geometrical optics approximation. The target reflections are assumed to be specular in nature with either one reflection point or multiple resolvable reflection points. The time variation of the range to the reflection point of the target (assumed derivable from a high-resolution radar) and the general motion of the target (assumed derivable from tracking or trajectory information) are employed to reconstruct the contour of that portion of the assumed target surface that is illuminated by the radar. The reconstruction is accomplished by the simultaneous solution of two nonlinear differential equations which are derived using the envelope concept of differential geometry. Several reconstruction examples based on computer analysis are presented which indicate the results obtainable using this method.     

Image Registration: Similarity Measure and Preprocessing Method Comparisons

An experimental comparison of several similarity measures and preprocessing techniques used for the registration of temporally differing images is carried out. It is found that preprocessing of the images via a gradient operator improves the registration performance. This is in agreement with a derived optimal processor (described in the Appendix) based upon image and temporal difference characteristics.     

Optimum Constrained Image Restoration Filters

An optimum image restoration filter is described which minimizes the radius of gyration of the corrected or composite system point-spread function subject to constraints on the radius of gyration of the restoration fitter point-spread function, the total noise power in the restored image, and the shape of the composite system frequency spectrum. The filter function is obtained as the solution to a set of simultaneous differential equations subject to nonlinear integral constraints. Except for an assumption regarding the general shape of noise spectral density, the filter design is data independent. By constraining the radius of gyration of the restoration filter point-spread function, truncation errors resulting from edge effects are controlled. An iterative technique is introduced which virtually eliminates the sidelobes of the composite system point-spread function. The resulting suboptimal restoration filter effectively suppresses undesirable secondary oscillations which may otherwise appear in the composite system point-spread function and introduce "ghosts" in the restored data. A detailed study of the restoration filter performance as a function of its parameter variations is described and a number of examples are provided to demonstrate the fundamental properties of the restoration filter.