This paper proposes a method for recovery of projective shape and motion from multiple images by factorization of a matrix containing the images of all scene points. Compared to previous methods, this method can handle perspective views and occlusions jointly. The projective depths of image points are estimated by the method of Sturm & Triggs [5] using epipolar geometry. Occlusions are solved b...

This paper describes a novel method for recovering the perspective geometry of textured surfaces from local spectral moments. It commences by computing the Fourier power spectrum at each of a series of local neighbourhoods. We illustrate how the vanishing point of the global perspective geometry can be estimated from local spectral moments. This is a two-step process. We commence by identifying...

Convex polyhedra are among the oldest mathematical objects. Indeed the five platonic solids, which constitute the climax of Euclid’s books, were already known to the ancient people of Scotland some 4000 years ago [1]. During the Renaissance, polyhedra were once again objects of fascination while painters were discovering the rules of perspective and laying the foundations of projective geometry...

This paper tries to identify the creative processes of Generative Art that brings to the construction of dynamic procedures of transformation, generative algorithms, by departing from interpretative logics. This construction becomes possible through a dynamic approach to Geometry. In fact, overcoming the logic of the figures and related rules, this approach opens to the logic of the progressive...

We study thermodynamic state-space geometry of the black holes in string theory and M -theory. For a large number of microstates, we analyze the intrinsic state-space geometry for (i) extremal and non-extremal black branes in string theory, (ii) multi-centered black brane configurations, (iv) small black holes with fractional branes, and (v) fuzzy rings in the setup of Mathur’s fuzzballs and su...

In the Multiple Data Streams (MDS) environment, data sources generate data with no end in sight. Because of the difference of data sources, transaction numbers of MDS are not always equal to each other during a same period. Preprocessing MDS to obtain same number of samples for each stream is an essential step for lots of mining tasks. All existing preprocessing methods assume that data arrive ...

the aim of this paper is to show the importance of analytic hyperbolic geometry introduced in [9]. in [1], ungar and chen showed that the algebra of the group sl(2,c) naturally leads to the notion of gyrogroups and gyrovector spaces for dealing with the lorentz group and its underlying hyperbolic geometry. they defined the chen addition and then chen model of hyperbolic geometry. in this paper,...

Translating Euclid reports on an effort to transform geometry for students from a stylus-andclay-tablet corpus of historical theorems to a stimulating computer-supported collaborativelearning inquiry experience. The origin of geometry was a turning point in the pre-history of informatics, literacy and rational thought. Yet, this triumph of human intellect became ossified through historic layers...