Partial Differential Equations for Image Processing

摘要

This report, prepared for the Rapid Retargeting Accelerated CapabilitiesInitiative, provides a high-level description of how partial differential variational techniques are applied to image processing. The overall scientific theme is modeling image processing using the versatile mathematics of variational methods solved by partial differential equations (PDEs). This model is new within the last decade and generates both new and superior methods and useful generalizations of known methods. These generalizations allow both better insight into the methods and better performance. A case can be made that these generalizations have sparked a renewal in the theory-borrowing from computational fluid dynamics and differential geometry-and numerics of a class of nonlinear PDEs. The report gives selected examples of the major types of investigation going on and illustrates them with sample imagery. The report also describes how these investigations can be connected to Navy needs in image exploitation and in template-based assisted or automatic target recognition. The challenge of this accelerated capabilities initiative is to identify important applications or opportunities within the rapid retargeting sensor-to-shooter structure that can be improved or developed using these methods.