Fast and Provably Accurate Bilateral Filtering


The bilateral filter and its variants, like the joint/cross bilateral filter, are well-known edge-preserving image smoothing tools utilized in several applications. The reason of this success is its straightforward definition and the possibility of the many variations. The bilateral filter is known to be related to robust estimation. This link is lost by the spontanepous introduction of the guide image within the joint/cross bilateral filter. We tend to here propose a new method to derive the joint/cross bilateral filter as a explicit case of a additional generic filter, that we have a tendency to name the guided bilateral filter. This new filter is iterative, generic, inherits the robustness properties of the robust bilateral filter, and uses a guide image. The link with robust estimation allows us to relate the filter parameters with the statistics of input pictures. A scheme based on graduated nonconvexity is proposed, which permits converging to an interesting native minimum even when the value function is nonconvex. With this scheme, the guided bilateral filter will handle non-Gaussian noise on the image to be filtered. A complementary scheme is additionally proposed to handle non-Gaussian noise on the guide image whether or not both are strongly correlated. This allows the guided bilateral filter to handle things with additional noise than the joint/cross bilateral filter will work with and leads to high peak signal-to-noise ratio values as shown experimentally.

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