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Linear projections from P^k to P^h appear in computer vision as models of images of dynamic or segmented scenes. Given multiple projections of the same scene, the identification of many enough correspondences between the images allows, in…
Given two elliptic curves, each of which is associated with a projection map that identifies opposite elements with respect to the natural group structure, we investigate how their corresponding projective images of torsion points…
Object Detection is the task of identifying the existence of an object class instance and locating it within an image. Difficulties in handling high intra-class variations constitute major obstacles to achieving high performance on standard…
Geophysical inversion should ideally produce geologically realistic subsurface models that explain the available data. Multiple-point statistics is a geostatistical approach to construct subsurface models that are consistent with…
The pentagram map takes a planar polygon $P$ to a polygon $P'$ whose vertices are the intersection points of consecutive shortest diagonals of $P$. This map is known to interact nicely with Poncelet polygons, i.e. polygons which are…
We propose a novel mixture-of-experts class to optimize computer vision models in accordance with data transfer limitations at test time. Our approach postulates that the minimum acceptable amount of data allowing for highly-accurate…
Most galaxies host central supermassive black holes. As two galaxies merge, the black holes also merge. The final single black hole may suffer a kick due to asymmetric gravitational radiation and may not be at the centre of the galaxy;…
The main result is a wall crossing formula for central projections defined on submanifolds of a real projective space. Our formula gives the jump of the degree of such a projection when the center of the projection varies. The fact that the…
We demonstrate necessary and sufficient conditions of the local convergence of the alternating projection algorithm to a unique solution up to a global phase factor. Additionally, for the ptychography imaging problem, we discuss phase…
A classical set of birational invariants of a variety are its spaces of pluricanonical forms and some of their canonically defined subspaces. Each of these vector spaces admits a typical metric structure which is also birationally…
Pinwheel patterns and their higher dimensional generalisations display continuous circular or spherical symmetries in spite of being perfectly ordered. The same symmetries show up in the corresponding diffraction images. Interestingly, they…
The method of alternating projections involves orthogonally projecting an element of a Hilbert space onto a collection of closed subspaces. It is known that the resulting sequence always converges in norm if the projections are taken…
Change detection is one of the most challenging issues when analyzing remotely sensed images. Comparing several multi-date images acquired through the same kind of sensor is the most common scenario. Conversely, designing robust, flexible…
This paper studies the problem of how to choose good viewpoints for taking photographs of architectures. We achieve this by learning from professional photographs of world famous landmarks that are available on the Internet. Unlike previous…
A $K$-equivalent map between two smooth projective varieties is called simple if the map is resolved in both sides by single smooth blow-ups. In this paper, we will provide a structure theorem of simple $K$-equivalent maps, which reduces…
In this paper, we prove that any two birational projective varieties with finite quotient singularities can be realized as two geometric GIT quotients of a non-singular projective variety by a reductive algebraic group. Then, by applying…
Given two subsets of R^d, when does there exist a projective transformation that maps them to two sets with a common centroid? When is this transformation unique modulo affine transformations? We study these questions for 0- and…
Cameras with rolling shutters are becoming more common as low-power, low-cost CMOS sensors are being used more frequently in cameras. The rolling shutter means that not all scanlines are exposed over the same time interval. The effects of a…
We compute the integral homology and cohomology groups of configuration spaces of two distinct points on a given real projective space. The explicit answer is related to the (known multiplicative structure in the) integral cohomology---with…
Image stitching is typically decomposed into three phases: registration, which aligns the source images with a common target image; seam finding, which determines for each target pixel the source image it should come from; and blending,…