This paper aims at providing an overview of the use of mathematical morphology, in its algebraic setting, in several fields of artificial intelligence (AI). Three domains of AI will be covered. In the first domain, mathematical morphology operators will be expressed in some logics (propositional, modal, description logics) to answer typical questions in knowledge representation and reasoning, such as revision, fusion, explanatory relations, satisfying usual postulates. In the second domain, spatial reasoning will benefit from spatial relations modeled using fuzzy sets and morphological operators, with applications in model-based image understanding. In the third domain, interactions between mathematical morphology and deep learning will be detailed. Morphological neural networks were introduced as an alternative to classical architectures, yielding a new geometry in decision surfaces. Deep networks were also trained to learn morphological operators and pipelines, and morphological algorithms were used as companion tools to machine learning, for pre/post processing or even regularization purposes. These ideas have known a large resurgence in the last few years and new ones are emerging.

Many approaches exist to compute the distance between two trees in pattern recognition. These trees can be structures with or without values on their nodes or edges. However, none of these distances take into account the shapes possibly associated to the nodes of the tree. For this reason, we propose in this paper a new distance between two trees of shapes based on the Hausdorff distance. This distance allows us to make inexact tree matching and to compute what we call residual trees, representing where two trees differ. We will also see that thanks to these residual trees, we can obtain good results in matter of brain tumor segmentation. This segmentation does not provide only a segmentation but also the tree of shapes corresponding to the segmentation and its depth map.

In Mathematical Morphology (MM), dynamics are used to compute markers to proceed for example to watershed-based image decomposition. At the same time, persistence is a concept coming from Persistent Homology (PH) and Morse Theory (MT) and represents the stability of the extrema of a Morse function. Since these concepts are similar on Morse functions, we studied their relationship and we found, and proved, that they are equal on 1D Morse functions. Here, we propose to extend this proof to $n$-D, $n \geq 2$, showing that this equality can be applied to $n$-D images and not only to 1D functions. This is a step further to show how much MM and MT are related.

The tree of shapes (ToS) is a famous self-dual hierarchical structure in mathematical morphology, which represents the inclusion relationship of the shapes (<i>i.e.</i> the interior of the level lines with holes filled) in a grayscale image. The ToS has already found numerous applications in image processing tasks, such as grain filtering, contour extraction, image simplification, and so on. Its structure consistency is bound to the cleanliness of the level lines, which are themselves deeply affected by the presence of noise within the image. However, according to our knowledge, no one has measured before how resistant to (additive) noise this hierarchical structure is. In this paper, we propose and compare several measures to evaluate the stability of the ToS structure to noise.

The digitization of historical maps enables the study of ancient, fragile, unique, and hardly accessible information sources. Main map features can be retrieved and tracked through the time for subsequent thematic analysis. The goal of this work is the vectorization step, i.e., the extraction of vector shapes of the objects of interest from raster images of maps. We are particularly interested in closed shape detection such as buildings, building blocks, gardens, rivers, etc. in order to monitor their temporal evolution. Historical map images present significant pattern recognition challenges. The extraction of closed shapes by using traditional Mathematical Morphology (MM) is highly challenging due to the overlapping of multiple map features and texts. Moreover, state-of-the-art Convolutional Neural Networks (CNN) are perfectly designed for content image filtering but provide no guarantee about closed shape detection. Also, the lack of textural and color information of historical maps makes it hard for CNN to detect shapes that are represented by only their boundaries. Our contribution is a pipeline that combines the strengths of CNN (efficient edge detection and filtering) and MM (guaranteed extraction of closed shapes) in order to achieve such a task. The evaluation of our approach on a public dataset shows its effectiveness for extracting the closed boundaries of objects in historical maps.

Quicklisp is a library manager working with your existing Common Lisp implementation to download and install around 2000 libraries, from a central archive. Quickref, an application itself written in Common Lisp, generates, automatically and by introspection, a technical documentation for every library in Quicklisp, and produces a website for this documentation. In this paper, we present a corpus processing and analysis pipeline for Quickref. This pipeline consists of a set of natural language processing blocks allowing us to analyze Quicklisp libraries, based on natural language contents sources such as README files, docstrings, or symbol names. The ultimate purpose of this pipeline is the generation of a keyword index for Quickref, although other applications such as word clouds or topic analysis are also envisioned.

We introduce Go2Pins, a tool that takes a program written in Go and links it with two model-checkers: LTSMin [19] and Spot [7]. Go2Pins is an effort to promote the integration of both formal verifica- tion and testing inside industrial-size projects. With this goal in mind, we introduce black-box transitions, an efficient and scalable technique for handling the Go runtime. This approach, inspired by hardware ver- ification techniques, allows easy, automatic and efficient abstractions. Go2Pins also handles basic concurrent programs through the use of a dedicated scheduler. In this paper we demonstrate the usage of Go2Pins over benchmarks inspired by industrial problems and a set of LTL formulae. Even if Go2Pins is still at the early stages of development, our results are promising and show the the benefits of using black-box transitions.

Integrating mathematical morphology operations within deep neural networks has been subject to increasing attention lately. However, replacing standard convolution layers with erosions or dilations is particularly challenging because the min and max operations are not differentiable. Relying on the asymptotic behavior of the counter-harmonic mean, p-convolutional layers were proposed as a possible workaround to this issue since they can perform pseudo-dilation or pseudo-erosion operations (depending on the value of their inner parameter p), and very promising results were reported. In this work, we present two new morphological layers based on the same principle as the p-convolutional layer while circumventing its principal drawbacks, and demonstrate their potential interest in further implementations within deep convolutional neural network architectures.

We present a simple type system inspired by that of Common Lisp. The type system is intended to be embedded into a host language and accepts certain fundamental types from that language as axiomatically given. The type calculus provided in the type system is capable of expressing union, intersection, and complement types, as well as membership, subtype, disjoint, and habitation (non-emptiness) checks. We present a theoretical foundation and two sample implementations, one in Clojure and one in Scala.

Network users usually need a third party validation to prove that they are who they claim to be. Authentication systems mostly assume the existence of a Trusted Third Party (TTP) in the form of a Certificate Authority (CA) or as an authentication server. However, relying on a TTP implies that users do not directly manage their identities, but delegate this role to a third party. This intrinsic issue can generate trust concerns (e.g., identity theft), as well as privacy concerns towards the third party. The main objective of this research is to present an autonomous and independent solution where users can store their self created credentials without depending on TTPs. To this aim, the use of an TTP autonomous and independent network is needed, where users can manage and assess their identities themselves. In this paper, we propose the framework called Three Blockchains Identity Management with Elliptic Curve Cryptography (3BI-ECC). With our proposed framework, the users’ identities are self-generated and validated by their owners. Moreover, it allows the users to customize the information they want to share with third parties.