Suppose that, by utilizing a gradient-domain algorithm, we alter the gradients in each of the R, G, and B color channels of an image and thereby obtain a new approximate gradient pair in the x and y directions. Let us call this new pair p and q. These fields p and q are only an approximation of a gradient, i.e. the partial derivatives of a scalar potential. As a result, it is not possible to exactly recover the image by any of the many studied methods of taking an integral of this gradient pair. However, since indeed humans can understand images but not gradients, we are faced with the problem of to reintegrate the pair p,q to go back to the image domain. Many ways have been studied for this purpose but most of the approaches involve some form of Poisson Solver. But the problem is that Poisson solvers may cause artifacts such as halos and bends. As well, the time complexity of these approaches is high. In this thesis, studying the case of image sequence data, we introduce a new approach using regression in the gradient domain for reintegration the resulting pairs back to an image form. The advantages of this approach are that, firstly, we do not use any form of Poisson solver, so that as a result we don’t generate any Poisson artifacts. Secondly, we are able to use small thumbnail-size images to compute the regression coefficients we need, and then apply those coefficients to full-size images. Hence the time complexity for reintegration is reduced substantially. We have tested this method in two ways: Firstly, we applied the method to the intrinsic-image problem; and for the second test, we used investigated its use in the night-to-day problem. Based on these two tests we can say that our approaches can give us more clear output image results that are clearer and preferred, and carry this out in a much shorter time.
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Thesis advisor: Drew, Mark S.
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