Multi-point geometry: The geometry of 1 point in N images under perspective projection has been thoroughly investigated, identifying bilinear, trilinear, and quadrilinear relations between the projections of 1 point in 2, 3 and 4 frames respectively. The dual problem-the geometry of N points in 1 image-has been studied mostly in the context of object recognition , often assuming weak perspectiv...

The artist Patrick Hughes has ingeniously painted rows of stacked Brillo boxes in Forced into Reverse Perspective. The geometry is in reverse perspective, predicting only one type of illusory motion for each planar surface for moving viewers. He "broke" these surfaces into objects by painting the boxes in three types of perspective (planar, forced, and reverse). Our experiments confirmed that h...

This paper explores the use of computer graphics and computer vision techniques in the history of art. The focus is on analysing the geometry of perspective paintings to learn about the perspectival skills of artists and explore the evolution of linear perspective in history. Algorithms for a systematic analysis of the twoand three-dimensional geometry of paintings are drawn from the work on “s...

This paper addresses the recovery of structure and motion from two uncalibrated images of a scene under ful l perspective or under affine projection. Epipolar geometry, projective reconstruction, and affine reconstruction are elaborated in a way such that everyone having knowledge of linear algebra can understand the discussion without difficulty. A general expression of the fundamental matr ix...

This paper addresses the recovery of structure and motion from two uncalibrated images of a scene under full perspective or under aane projection. Epipolar geometry, projective reconstruction , and aane reconstruction are elaborated in a way such that everyone having knowledge of linear algebra can understand the discussion without diiculty. A general expression of the fundamental matrix is der...

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 at once. The projective depths of image points are estimated by the method of Sturm & Triggs [8] using epipolar geometry. Occlusions are solved b...

Gene expression control results from the combined interactions of the nearly hundred proteins forming the pre-initiation complex, thousands of transcription regulators, and genomic DNA. In the recent years, new technologies have revealed several key aspects of nuclear spatial organization that showed a fine interplay between the function of nuclear proteins, their 3D organization, and their dyn...

There are surprisingly rich properties of these holomorphic functions. The possibility of holomorphic continuation of holomorphic functions forces us to consider multi-valued holomorphic functions. The concept of Riemann Surfaces was introduced to understand such phenomena. The ideas of branch cuts and branch points immediately relate topology of these surfaces to complex variables. The possibi...

In this paper we give a survey of some models of the integer and fractional quantum Hall effect based on noncommutative geometry. We begin by recalling some classical geometry of electrons in solids and the passage to noncommutative geometry produced by the presence of a magnetic field. We recall how one can obtain this way a single electron model of the integer quantum Hall effect. While in th...

Recently, several complex network approaches to time series analysis have been developed and applied to study a wide range of model systems as well as real-world data, e.g., geophysical or financial time series. Among these techniques, recurrence-based concepts and prominently ε-recurrence networks, most faithfully represent the geometrical fine structure of the attractors underlying chaotic (a...