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Reverse Engineering a PDE from an Image Inpainting Algorithm

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A common practice in designing image inpainting methods is to model the image as a continuum, where the completed image may be expressed in terms of the solution to a suitable PDE . One then discretizes this PDE to obtain an algorithm that may be applied to real images, which are discrete. However, what about working in reverse? Given a discrete algorithm, can we find a PDE such that images inpainted via this algorithm converge to solutions to said PDE in the continuum limit? If so, can this help us to understand our method or improve it?

In this talk, I will share my experience working on inpainting algorithms for industry, where people may not have heard of PDEs and methods are designed based primarily on intuition. I will show how these methods may nonetheless be understood in terms of PDEs, and furthermore that this understanding can be utilized to create improved methods. Finally, I will argue that this may give you a better algorithm in the end than if you simply started from a desired PDE and and discretized it in a routine manner.

This talk is part of the Cambridge Analysts' Knowledge Exchange series.

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