30 September 1994 Approximate shift-invariance by warping shift-variant systems
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Abstract
A method is presented in which an image, degraded by a linear shift- variant imaging system, will undergo a warping such that the resulting warped image will be approximately described by a warped original image filtered by a linear shift-invariant system. The purpose of this distortion is to make the shift-variant impulse response, which can approximately be viewed as a shift-invariant impulse response which has been warped in the original image domain, vary as little as possible. In particular cases, a transformation can be found which results in no impulse response variations. For most cases, however, the impulse response will still possess some shift-variance. A measure of shift-variance is presented, and introduced into a optimization problem which seeks to minimize the shift-variance of a system. This residual variance will be ignored (this error must be small in order for this method to work well), and an 'average' impulse response in the warped domain will be assumed. This allows for shift- invariant restoration of the warped image, with all of its attendant advantage is speed and reduced complexity. An example of a smooth space-variant one-dimensional impulse response is applied to a variant of this optimization problem. The limitations of this slightly different problem are explained, and the expected properties of the stated problem are discussed.
© (1994) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Scott R. McNown, Bobby R. Hunt, "Approximate shift-invariance by warping shift-variant systems", Proc. SPIE 2302, Image Reconstruction and Restoration, (30 September 1994); doi: 10.1117/12.188037; https://doi.org/10.1117/12.188037
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