Colorization of Natural Images via L1 Optimization

05/18/2009

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by   Nassir Mohammad, et al.

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Natural images in the colour space YUV have been observed to have a non-Gaussian, heavy tailed distribution (called 'sparse') when the filter G(U)(r) = U(r) - sum_s ∈ N(r) w(Y)_rs U(s), is applied to the chromacity channel U (and equivalently to V), where w is a weighting function constructed from the intensity component Y [1]. In this paper we develop Bayesian analysis of the colorization problem using the filter response as a regularization term to arrive at a non-convex optimization problem. This problem is convexified using L1 optimization which often gives the same results for sparse signals [2]. It is observed that L1 optimization, in many cases, over-performs the famous colorization algorithm by Levin et al [3].