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This paper provides a capsular introduction to the theoretical framework and experimental applications of the Polar Exponential Grid (PEG) transformation, in the context of image analysis. The PEG transformation is an isomorphic (1) representation of the image intensity array that simplifies, and potentially offers new insights about, a variety of tasks in computational vision. We describe the PEG transform representation; we briefly survey its functional precursors in optical computing and image processing. We then give an example of PEG-based image analysis for rotation-and-scale variant template matching and, present the PEG transform as a motif for a class of problems in stochastic estimation of object boundaries.