Digital Analytical Geometry: How do I define a digital analytical object?

International audienceThis paper is meant as a short survey on analytically de-ned digital geometric objects. We will start by giving some elements on digitizations and its relations to continuous geometry. We will then explain how, from simple assumptions about properties a digital object should have, one can build mathematical sound digital objects. We will end with open problems and challenges for the future

Efficient operations on discrete paths

We present linear time and space operations on discrete paths. First, we compute the outer hull of any discrete path. As a consequence, a linear time and space algorithm is obtained for computing the convex hull. Next, we provide a linear algorithm computing the overlay graph of two simple closed paths. From this overlay graph, one can easily compute the intersection, union and difference of two Jordan polyominoes, i.e. polyominoes whose boundary is a Jordan curve. The linear complexity is obtained by using an enriched version of a data structure introduced by Brlek, Koskas and Provençal: a quadtree for representing points in the discrete plane augmented with neighborhood links, which was introduced in particular to decide in linear time if a discrete path is self-intersecting

What's in Lisbon? Art Museums, Art Dealers, and Refugees in Portugal between 1933 and 1945

This thesis focuses on the transactions of works of art that took place in Portugal during the period of the Third Reich (1933-1945), the institutions and individuals involved in these transactions, and the works of art that were the object of those transactions. Drawing on American, Austrian, British, Dutch, French, German, Portuguese, and Swiss primary sources, the thesis sets out to determine the extent of the influence of the refugee flux into the country and of the international circulation of Nazi-looted art on the Portuguese art market. It does so by identifying and studying the actions of specific groups identified as having the higher chances of benefiting from these circumstances: importers and exporters of non-contemporary works of art; national art museums in Lisbon and Porto, cities with international communications and transport networks, which hosted the highest number of refugees; public museums in seaside and spa resorts, where thousands of refugees resided during the war years; and the foreign art dealers who opened businesses in Lisbon. Conceptually, it begins with a large universe of analysis, narrowing its scope as the chapters progress, culminating in the study of the actions of one single figure, and clarifying the provenance of one single painting, in a case study that brings together various areas of research examined previously. While findings confirm the supposition that the Portuguese State and public institutions did not knowingly engage in the acquisition of Nazi-looted art during this period, they reveal that some of their acquisitions require further provenance research, and that the actions of specific individuals in bringing works of art into the country demand further scrutiny

Gaze-Based Human-Robot Interaction by the Brunswick Model

We present a new paradigm for human-robot interaction based on social signal processing, and in particular on the Brunswick model. Originally, the Brunswick model copes with face-to-face dyadic interaction, assuming that the interactants are communicating through a continuous exchange of non verbal social signals, in addition to the spoken messages. Social signals have to be interpreted, thanks to a proper recognition phase that considers visual and audio information. The Brunswick model allows to quantitatively evaluate the quality of the interaction using statistical tools which measure how effective is the recognition phase. In this paper we cast this theory when one of the interactants is a robot; in this case, the recognition phase performed by the robot and the human have to be revised w.r.t. the original model. The model is applied to Berrick, a recent open-source low-cost robotic head platform, where the gazing is the social signal to be considered

Digital Geometry from a Geometric Algebra Perspective: 18th IAPR International Conference, DGCI 2014, Siena, Italy, September 10-12, 2014. Proceedings

International audienceTo model Euclidean spaces in computerized geometric calcu- lations, the Geometric Algebra framework is becoming popular in com- puter vision, image analysis, etc. Focusing on the Conformal Geometric Algebra, the claim of the paper is that this framework is useful in digital geometry too. To illustrate this, this paper shows how the Conformal Ge- ometric Algebra allow to simplify the description of digital objects, such as k-dimensional circles in any n-dimensional discrete space. Moreover, the notion of duality is an inherent part of the Geometric Algebra. This is particularly useful since many algorithms are based on this notion in digital geometry. We illustrate this important aspect with the definition of k-dimensional spheres