|Stochastic Systems Group|
We consider two related problems here: correcting for the bias field in magnetic resonance (MR) imaging and separating reflectance and illumination in natural images. Both problems involve separating fields that are linked multiplicatively, and both problems are inherently ill-posed. In MR, many images that are captured are corrupted by a slowly varying field known as the bias field. This field arises from the spatially inhomogeneous response of the receiving coils. This field then makes both quantitative and qualitative analysis more difficult. A common model for natural images with Lambertian reflectance is that it is composed of two multiplicative fields: the reflectance map which depends solely on the physical configuration of the scene; and the illumination map which depends on the illumination and the scene geometry. Separating these two maps is useful for classical image processing as well as higher order computer vision techniques such as estimating scene configuration. We discuss a few techniques where we use statistical variational formulations, side information, regularization, and/or simplifying assumptions to make the problems more tractable, and show some results (with varying degrees of success).
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