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

End-to-end Structure-Aware Convolutional Networks for Knowledge Base Completion

Knowledge graph embedding has been an active research topic for knowledge base completion, with progressive improvement from the initial TransE, TransH, DistMult et al to the current state-of-the-art ConvE. ConvE uses 2D convolution over embeddings and multiple layers of nonlinear features to model knowledge graphs. The model can be efficiently trained and scalable to large knowledge graphs. However, there is no structure enforcement in the embedding space of ConvE. The recent graph convolutional network (GCN) provides another way of learning graph node embedding by successfully utilizing graph connectivity structure. In this work, we propose a novel end-to-end Structure-Aware Convolutional Network (SACN) that takes the benefit of GCN and ConvE together. SACN consists of an encoder of a weighted graph convolutional network (WGCN), and a decoder of a convolutional network called Conv-TransE. WGCN utilizes knowledge graph node structure, node attributes and edge relation types. It has learnable weights that adapt the amount of information from neighbors used in local aggregation, leading to more accurate embeddings of graph nodes. Node attributes in the graph are represented as additional nodes in the WGCN. The decoder Conv-TransE enables the state-of-the-art ConvE to be translational between entities and relations while keeps the same link prediction performance as ConvE. We demonstrate the effectiveness of the proposed SACN on standard FB15k-237 and WN18RR datasets, and it gives about 10% relative improvement over the state-of-the-art ConvE in terms of HITS@1, HITS@3 and [email protected]: The Thirty-Third AAAI Conference on Artificial Intelligence (AAAI 2019

Efficient morphological tools for astronomical image processing

Nowadays, many applications rely on a huge quantity of images at high resolution and with high quantity of information per pixel, due either to the technological improvements of the instruments or to the type of measurement observed. This thesis is focused on exploring and developing tools and new methods in the framework of Mathematical Morphology, suitable for automatic image processing of astronomical datasets. Identifying and classifying astronomical objects is a challenging task: many of the structures that astronomers are interested into to understand the evolution of galaxies and stars are faint and near to the noise level. A new method to identify astronomical objects is proposed, based on the expected statistical behaviour of the noise across the image structures. The method works by parsing a hierarchical representation of the image data, called max-tree: it allows for image filtering and object identification in an efficient way. A novel parallel algorithm to build max-tree of 2D images and 3D volumes with very high-dynamic-range values is proposed. Besides astronomy, other application fields, like medical and remote sensing image processing, would benefit from that. Effort is put also in classifying the objects found. A parallel method is developed to compute efficiently the pattern spectra. Those are matrices whose values put in relation area and shape information of selected structures in the image. Such matrices are used both to classify different types of galaxies and to identify building footprints in satellite images