Efficient algorithms for Non-Local Filtering and applications to Cryo-Electron microscopy and biological microscopy

Jerome Darbon
Brown University

We present fast and scalable algorithms for non-local filtering
algorithms that find applications in microscopy.

First we present an algorithm to implement the celebrate Non Local
Means Denoising method introduced by Buades, Coll and Morel in
2005. It builds on the separable property of neighborhood filtering to
offer a fast parallel and vectorized implementation in contemporary
shared memory computer architectures while reducing the theoretical
computational complexity of the original filter. In practice, our
approach is much faster than a serial, non–vectorized implementation
and it scales linearly with image size. Numerical results on cryo-EM
are presented.

Then we consider the problem of detecting and modeling the essential
features present in a biological image and the construction of a
compact representation for them which is suitable for numerical
computation. The solution we propose employs a variational energy
minimization formulation to extract noise and texture, producing a
clean image containing the geometric features of interest. Such image
decomposition is essential to reduce the image complexity for further
processing. We are particularly motivated by the image registration
problem where the goal is to align matching features in a pair of
images. A combination of algorithms from combinatorial optimization
and computational geometry render fast solutions at interactive or
near interactive rates. We demonstrate our technique in microscopy
images. We are able, for example, to process large, 2048 x 2048
pixels, histology mouse brain images under a minute creating a
faithful and sparse triangulation model for it having only 1.8% of its
original pixel count.

It is based on joint with Alexandre Cunha (California Institute of
Technology and Singular Genomics Inc.), Stan Osher (UCLA) and others.

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