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Monte-Carlo Acceleration of Bilateral Filter and Non-Local Means

Monte-Carlo Acceleration of Bilateral Filter and Non-Local Means

Abstract:

We propose stochastic bilateral filter (SBF) and stochastic non-local means (SNLM), efficient randomized processes that agree with conventional bilateral filter (BF) and non-local means (NLM) on average, respectively. By Monte-Carlo, we repeat this process a few times with different random instantiations so that they can be averaged to attain the correct BF/NLM output. The computational bottleneck of the SBF and SNLM are constant with respect to the window size and the color dimension of the edge image, meaning the execution times for color and hyperspectral images are nearly the same as for the grayscale images. In addition, for SNLM, the complexity is constant with respect to the block size. The proposed stochastic filter implementations are considerably faster than the conventional and existing “fast” implementations for high dimensional image data.

 

Existing System:

Non-local means is a generalization of the bilateral filter that has shown advantages in case of noise removal. It is a nonlinear filter that replaces the pixel-to-pixel similarity in the range kernel with a patch-to-patch similarity measure that respects image structures such as edges better. Obviously, the expansion of the range kernel from a pixel to a patch further increases the computational complexity. The fast bilateral filter approaches of do not generalize well to NLM, in much the same way that they do not scale well with the color dimension.

Proposed System:

We propose stochastic bilateral filter (SBF)—a new fast bilateral filter implementation that processes hyperspectral edge images with nearly the same complexity as the grayscale images and with constant time with respect to the window size. We generalize this result to a stochastic non-local means (SNLM), a new fast non-local means implementation whose complexity is also invariant to the block size. At the heart of SBF and SNLM are efficient randomized convolutional processes, where they agree with the conventional bilateral filter and the conventional non-local means on average, respectively.

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