Computing the output distribution and selection probabilities of a stack filter from the DNF of its positive Boolean function

Many nonlinear filters used in practise are stack filters. An algorithm is presented which calculates the output distribution of an arbitrary stack filter S from the disjunctive normal form (DNF) of its underlying positive Boolean function. The so called selection probabilities can be computed along the way.Comment: This is the version published in Journal of Mathematical Imaging and Vision, online first, 1 august 201

The output distribution of important LULU-operators

Two procedures to compute the output distribution phi_S of certain stack filters S (so called erosion-dilation cascades) are given. One rests on the disjunctive normal form of S and also yields the rank selection probabilities. The other is based on inclusion-exclusion and e.g. yields phi_S for some important LULU-operators S. Properties of phi_S can be used to characterize smoothing properties of S. One of the methods discussed also allows for the calculation of the reliability polynomial of any positive Boolean function (e.g. one derived from a connected graph).Comment: 20 pages, up to trivial differences this is the final version to be published in Quaestiones Mathematicae 201

Calculating the output distribution of stack filters that are erosion-dilation cascades, in particular LULU-filters

Original article available at http://arxiv.org/ENGLISH ABSTRACT: Two procedures to compute the output distribution 0S of certain stack filters S (so called erosion-dilation cascades) are given. One rests on the disjunctive normal form of S and also yields the rank selection probabilities. The other is based on inclusion-exclusion and e.g. yields 0S for some important LULU-operators S. Properties of 0S can be used to characterize smoothing properties.Preprin

Deep Learning as a Parton Shower

We make the connection between certain deep learning architectures and the renormalisation group explicit in the context of QCD by using a deep learning network to construct a toy parton shower model. The model aims to describe proton-proton collisions at the Large Hadron Collider. A convolutional autoencoder learns a set of kernels that efficiently encode the behaviour of fully showered QCD collision events. The network is structured recursively so as to ensure self-similarity, and the number of trained network parameters is low. Randomness is introduced via a novel custom masking layer, which also preserves existing parton splittings by using layer-skipping connections. By applying a shower merging procedure, the network can be evaluated on unshowered events produced by a matrix element calculation. The trained network behaves as a parton shower that qualitatively reproduces jet-based observables.Comment: 26 pages, 13 figure

Introducing Geometry in Active Learning for Image Segmentation

We propose an Active Learning approach to training a segmentation classifier that exploits geometric priors to streamline the annotation process in 3D image volumes. To this end, we use these priors not only to select voxels most in need of annotation but to guarantee that they lie on 2D planar patch, which makes it much easier to annotate than if they were randomly distributed in the volume. A simplified version of this approach is effective in natural 2D images. We evaluated our approach on Electron Microscopy and Magnetic Resonance image volumes, as well as on natural images. Comparing our approach against several accepted baselines demonstrates a marked performance increase

Stylizing Face Images via Multiple Exemplars

We address the problem of transferring the style of a headshot photo to face images. Existing methods using a single exemplar lead to inaccurate results when the exemplar does not contain sufficient stylized facial components for a given photo. In this work, we propose an algorithm to stylize face images using multiple exemplars containing different subjects in the same style. Patch correspondences between an input photo and multiple exemplars are established using a Markov Random Field (MRF), which enables accurate local energy transfer via Laplacian stacks. As image patches from multiple exemplars are used, the boundaries of facial components on the target image are inevitably inconsistent. The artifacts are removed by a post-processing step using an edge-preserving filter. Experimental results show that the proposed algorithm consistently produces visually pleasing results.Comment: In CVIU 2017. Project Page: http://www.cs.cityu.edu.hk/~yibisong/cviu17/index.htm