Recorded 15 September 2022. Jerome Darbon of Brown University presents "Efficient algorithms for Non-Local Filtering and applications to Cryo-Electron microscopy and biological microscopy" at IPAM's Computational Microscopy Tutorials. Abstract: 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. Learn more online at: http://www.ipam.ucla.edu/programs/workshops/computational-microscopy-tutorials/?tab=schedule