Composing morphological filters

A morphological filter is an operator on a complete lattice which is increasing and idempotent. Two well-known classes of morphological filters are openings and closings. Furthermore, an interesting class of filters, the alternating sequential filters, is obtained if one composes openings and closings. This paper explains how to construct morphological filters, and derived notions such as overfilters, underfilters, inf-overfilters, and sup-underfilters by composition, the main ingredients being dilations, erosions, openings, and closings. The class of alternating sequential filters is extended by composing overfilters and underfilters. Finally, it is shown that any composition consisting of an equal number of dilations and erosions from an adjunction is a filter. The abstract approach is illustrated with some experimental results

Morphological filtering on hypergraphs

The focus of this article is to develop computationally efficient mathematical morphology operators on hypergraphs. To this aim we consider lattice structures on hypergraphs on which we build morphological operators. We develop a pair of dual adjunctions between the vertex set and the hyper edge set of a hypergraph H, by defining a vertex-hyperedge correspondence. This allows us to recover the classical notion of a dilation/erosion of a subset of vertices and to extend it to subhypergraphs of H. Afterward, we propose several new openings, closings, granulometries and alternate sequential filters acting (i) on the subsets of the vertex and hyperedge set of H and (ii) on the subhypergraphs of a hypergraph

A General-Purpose Tagger with Convolutional Neural Networks

We present a general-purpose tagger based on convolutional neural networks (CNN), used for both composing word vectors and encoding context information. The CNN tagger is robust across different tagging tasks: without task-specific tuning of hyper-parameters, it achieves state-of-the-art results in part-of-speech tagging, morphological tagging and supertagging. The CNN tagger is also robust against the out-of-vocabulary problem, it performs well on artificially unnormalized texts

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

A graph-based mathematical morphology reader

This survey paper aims at providing a "literary" anthology of mathematical morphology on graphs. It describes in the English language many ideas stemming from a large number of different papers, hence providing a unified view of an active and diverse field of research

Video object segmentation introducing depth and motion information

We present a method to estimate the relative depth between objects in scenes of video sequences. The information for the estimation of the relative depth is obtained from the overlapping produced between objects when there is relative motion as well as from motion coherence between neighbouring regions. A relaxation labelling algorithm is used to solve conflicts and assign every region to a depth level. The depth estimation is used in a segmentation scheme which uses grey level information to produce a first segmentation. Regions of this partition are merged on the basis of their depth level.Peer ReviewedPostprint (published version