Multi-view Geometry is reviewed from an Algebraic Geometry perspective and multi-focal tensors are constructed as equivariant projections of the Grassmannian. A connection to the principal minor assignment problem is made by considering several flatlander cameras. The ideal of the quadrifocal variety is computed up to degree 6 using the representations of GL(3) in the polynomial ring on the spa...

The paper reviews geometrical approaches in the area of qualitative space representation by discussing formal systems of geometry based on the notion of extended regions (mereogeometries). The focus is on primitives that are cognitively motivated and that capture different notions of naive geometry. The paper then moves to consider the role of mereogeometries (and in particular of the concepts ...

Caustics are captivating light patterns created by materials bundling or diverting light by refraction or reflection. We know caustics as random side effects, appearing, for example, at the bottom of a swimming pool. In this paper we show that it is possible to control caustic patterns to form almost any desired shape by optimizing the geometry of the reflective or refractive surface generating...

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This paper provides a new perspective to the problem of reconfiguration of a rolling sphere. It is shown that the motion of a rolling sphere can be characterized by evoluteinvolute geometry. This characterization, which is a manifestation of our specific selection of Euler angle coordinates and choice of angular velocities in a rotating coordinate frame, allows us to recast the three-dimensiona...

Metric rectification method is to restore an image from a single camera-captured document image. This method construct an isometric image mesh technique by exploiting the geometry of page surface and camera. It uses a general cylindrical surface (GCS) to model the curved page shape. It introduce a paraperspective projection to approximate the nonlinear perspective projection. A set of close-for...

The generation of design parameter sensitivity derivatives is required for gradient-based optimization. Such sensitivity derivatives are elusive at best when working with geometry defined within the solid modeling context of Computer-Aided Design (CAD) systems. Solid modeling CAD systems are often proprietary and always complex, thereby necessitating ad hoc procedures to infer parameter sensiti...

Information theoretic geometry near critical points in classical and quantum systems is well understood for exactly solvable systems. Here, we show that renormalization group flow equations can be used to construct the information metric and its associated quantities near criticality for both classical and quantum systems in a universal manner. We study this metric in various cases and establis...

From algebraic geometry perspective database relations are succinctly defined as Finite Varieties. After establishing basic framework, we give analytic proof of Heath’s theorem from Database Dependency theory. Next, we leverage Algebra-Geometry dictionary and focus on algebraic counterparts of finite varieties – [polynomial] Ideals. It is well known that intersection and sum of ideals are latti...