Related papers: Images of circles, lines, balls and half-planes un…
The image and the inverse image of a polyhedron under a linear transformation are polyhedrons.
One of the most challenging problems in the domain of 2-D image or 3-D shape is to handle the non-rigid deformation. From the perspective of transformation groups, the conformal transformation is a key part of the diffeomorphism. According…
In this article the bicomplex version of Mobius transformation is defined and special attention is paid to find the fixed points of a bicomplex Mobius transformation.
The change of conformal moduli of polygonal quadrilaterals under some geometric transformations is studied. We consider the motion of one vertex when the other vertices remain fixed, the rotation of sides, polarization, symmetrization, and…
It is well known that optical media create artificial geometry for light, and curved geometry acts as an effective optical medium. This correspondence originates from the form invariance of Maxwells equations, which recently has spawned a…
A general framework is presented which unifies the treatment of wavelet-like, quasidistribution, and tomographic transforms. Explicit formulas relating the three types of transforms are obtained. The case of transforms associated to the…
The paper presents a new cross-ratio of hypercomplex numbers based on projective geometry. We discuss the essential properties of the projective cross-ratio, notably its invariance under Mobius transformations. Applications to the geometry…
In this paper we study underlying graphs corresponding to a set of halving lines. We establish many properties of such graphs. In addition, we tighten the upper bound for the number of halving lines.
Conceptual studies and numerical simulations are performed for imaging devices that transform a near-field pattern into magnified far-zone images and are based on high-order spatial transformation in cylindrical domains. A lens translating…
We study intersections of orbits in polynomial semigroup dynamics with lines on the affine plane over a number field, extending previous work of D. Ghioca, T. Tucker, M. Zieve (2008)
M\"obius transformations of the extended complex plane are at the crossroads of many interesting topics, e.g., they form a group under composition, are the simplest form of rational function, and are a path to Lie theory. Quaternionic…
The author proposes the methodology of transformation optics in orthogonal coordinates to obtain the material parameters of the transformation media from the mapping in orthogonal coordinates. Several examples are given to show the…
Modular forms are highly self-symmetric functions studied in number theory, with connections to several areas of mathematics. But they are rarely visualized. We discuss ongoing work to compute and visualize modular forms as 3D surfaces and…
For more than half a century, the Hough transform is ever-expanding for new frontiers. Thousands of research papers and numerous applications have evolved over the decades. Carrying out an all-inclusive survey is hardly possible and…
Despite high-dimensionality of images, the sets of images of 3D objects have long been hypothesized to form low-dimensional manifolds. What is the nature of such manifolds? How do they differ across objects and object classes? Answering…
We study some conformally invariant integral equations using the method of moving spheres.
Identifying when different images are of the same object despite changes caused by imaging technologies, or processes such as growth, has many applications in fields such as computer vision and biological image analysis. One approach to…
We investigate the dynamics of Q-balls in one, two and three space dimensions, using numerical simulations of the full nonlinear equations of motion. We find that the dynamics of Q-balls is extremely complex, involving processes such as…
In this work we explore the relationship between the Mobius inverse transformation of an arbitrary sequence and unrestricted partitions identities.
We give linear-time quasiconvex programming algorithms for finding a Moebius transformation of a set of spheres in a unit ball or on the surface of a unit sphere that maximizes the minimum size of a transformed sphere. We can also use…