Digital geometry

The notion of gap is quite important in combinatorial image analysis and it finds several useful applications in fields as CAD and computer graphics. On the other hand, dimension is a fundamental concept in General Topology and it was recently extended to digital objects. In this paper, we show that the dimension of a 2D digital object equipped with an adjacency relation A ( 2 f0; 1g) can be determinated by the number of its gaps besides some other parameters like the number of its pixel, vertices and edges.

2017

The notion of gap is quite important in combinatorial image analysis and it finds several useful applications in fields as CAD and computer graphics. On the other hand, dimension is a fundamental concept in General Topology and it was recently extended to digital objects. In this paper, we show that the dimension of a 2D digital object equipped with an adjacency relation Aα (α ∈ {0, 1}) can be determinated by the number of its gaps besides some other parameters like the number of its pixel, vertices and edges.

Computer Vision and Image Understanding, 1995

Lecture Notes in Computer Science, 1997

Computer vision, graphics, and image processing, 1985

We study 2- and 3-dimensional digital geometry in the context of almost arbitrary adjacency relations. (Previous authors have based their work on particular adjacency relations). We define a binary digital picture to be a pair whose components are a set of lattice-points and an adjacency relation on the whole lattice. We show how a wide class of digital pictures have natural “continuous analogs.” This enables us to use methods of continuous topology in studying digital pictures. We are able to prove general results on the connectivity of digital borders, which generalize results that have appeared in the literature. In the 3-dimensional case we consider the possibility of using a uniform relation on the whole lattice. (In the past authors have used different types of adjacency for “object” and “background.”)

Paris, 2019

Spreading from Lydia (western Turkey) and Aegean Sea, the coin-shaped currency made of minted precious metals arrived in Eastern Iberian Peninsula (Emporion, Rhode, Catalonia) and Southern Gaul (Massalia) during the 5th century B.C. The first southern Gallic mints rapidly appeared in the second half of the 3rd century B.C. as copies of Greek gold staters and drachma from Emporion or Rhode and specific Gallic coins appeared at the end of the 3rd century B.C. In the 2nd century B.C., the diffusion in great areas of few types of potins which weigh variability, the lack of precious metal in their alloy and the high frequency of their loss suggest that they had probably no real monetary value and not the same purpose as contemporary gold or silver coins. Yet, being an image carrier and therefore a vector of information, the potin seemed to have diverted the primary function of minted money to please another interest associated to aristocratic or religious social strata . It became an innovative cultural vector of an elitist knowledge such as the Suessiones potin (region of Soissons, France) called ‘potin au sanglier’ on which appears the first astronomical representation of the Earth-Moon system paced by lunar phases. Interestingly, this representation is still anchored in the Magdalenian tradition depicted in la Pasiega cave (Puente Viesgo, Cantabria, Spain).

Abstract. A Bombay High Court Judgement of 1934 provides surprising leads to decipher the key of Indus Script seals and inscriptions. One unique feature of the writing system is to join parts to create images. The word for such 'joining of parts' is ज ां गड jāṅgaḍa. The word also has a similar sounding word with the semantics of 'ज ां गड jāṅgaḍa invoice on entrustment basis'. Unicorn and Standard device which occur on over 2000 seals of Indus Script are joined parts, namely: 1. young bull + double-sack on shoulder + spiny, forward-thrusting horn'; 2. lathe + churning container. Reading these joined parts results in the determination of form and function of the writing system.