Adiabatic approximation as a tool in image estimation

Anand Rangarajan; Rama Chellappa

doi:10.1117/12.19575

1 July 1990 Adiabatic approximation as a tool in image estimation

Anand Rangarajan, Rama Chellappa

Proceedings Volume 1246, Parallel Architectures for Image Processing; (1990) https://doi.org/10.1117/12.19575
Event: Electronic Imaging: Advanced Devices and Systems, 1990, Santa Clara, CA, United States

Abstract

The problem of image estimation is posed in a Maximum A Posteriori (MAP) framework. Gibbs distributions are used for the prior and degradation models. Finding the MAP estimate then reduces to obtaining the global minimum of a non-convex energy function defined over the intensity and line processes. The latter are used to model discontinuities like edges present in any scene. When several constraints on the interactions between the line processes are removed, deterministic algorithms have been used to find "good" suboptimal solutions. These deterministic algorithms perform relaxation on the intensities alone. We have added the missing constraints on the line process interactions. Deterministic algorithms have been suggested which now perform relaxation on the intensities and the line processes. In the absence of the interaction constraints, our algorithms are shown to be equivalent to the previously suggested algorithms. This has been achieved by invoking the adiabatic approximation. The adiabatic approximation eliminates the dynamics of "fast" relaxing variables which in our case are the line processes. In demonstrating this equivalence, we describe the utility of two new processes; the gradient (GRAD) and gradient magnitude (GMAG) processes. The line process can be obtained through a monotonic transformation of the GMAG process.

Citation Download Citation

Anand Rangarajan and Rama Chellappa "Adiabatic approximation as a tool in image estimation", Proc. SPIE 1246, Parallel Architectures for Image Processing, (1 July 1990); https://doi.org/10.1117/12.19575

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