Rotation independent hierarchical representation for Open and Closed Curves and its Applications

The algorithm used for the segmentation of an image,and scheme used for the representation of the segmentationresult are mostly selected based on the final image analysis orinterpretation objective. The boundary based imagesegmentation and representation system developed by Naborssegments and stores the result as a graph-tree hierarchicalstructure that is capable of supporting diverse applications. Thispaper shows that Nabors’ hierarchical representation of curves isnot invariant to rotation, and proposes an enhancedrepresentation which retains its structure and remains invariantunder rotation. The curve matching algorithm which matchestwo curves based on their hierarchical representation makes iteasy to determine if a curve is a section of a larger curve. Thepotential of the representation is illustrated by developing imageregistration and image stitching methods based on the newrepresentation

Joint Clustering and Registration of Functional Data

Curve registration and clustering are fundamental tools in the analysis of functional data. While several methods have been developed and explored for either task individually, limited work has been done to infer functional clusters and register curves simultaneously. We propose a hierarchical model for joint curve clustering and registration. Our proposal combines a Dirichlet process mixture model for clustering of common shapes, with a reproducing kernel representation of phase variability for registration. We show how inference can be carried out applying standard posterior simulation algorithms and compare our method to several alternatives in both engineered data and a benchmark analysis of the Berkeley growth data. We conclude our investigation with an application to time course gene expression

On Possible Implications of Self-Organization Processes through Transformation of Laws of Arithmetic into Laws of Space and Time

In the paper we present results based on the description of complex systems in terms of self-organization processes of prime integer relations. Realized through the unity of two equivalent forms, i.e., arithmetical and geometrical, the description allows to transform the laws of a complex system in terms of arithmetic into the laws of the system in terms of space and time. Possible implications of the results are discussed.Comment: 26 pages, 4 figure

Flavor Structure in F-theory Compactifications

F-theory is one of frameworks in string theory where supersymmetric grand unification is accommodated, and all the Yukawa couplings and Majorana masses of right-handed neutrinos are generated. Yukawa couplings of charged fermions are generated at codimension-3 singularities, and a contribution from a given singularity point is known to be approximately rank 1. Thus, the approximate rank of Yukawa matrices in low-energy effective theory of generic F-theory compactifications are minimum of either the number of generations N_gen = 3 or the number of singularity points of certain types. If there is a geometry with only one E_6 type point and one D_6 type point over the entire 7-brane for SU(5) gauge fields, F-theory compactified on such a geometry would reproduce approximately rank-1 Yukawa matrices in the real world. We found, however, that there is no such geometry. Thus, it is a problem how to generate hierarchical Yukawa eigenvalues in F-theory compactifications. A solution in the literature so far is to take an appropriate factorization limit. In this article, we propose an alternative solution to the hierarchical structure problem (which requires to tune some parameters) by studying how zero mode wavefunctions depend on complex structure moduli. In this solution, the N_gen x N_gen CKM matrix is predicted to have only N_gen entries of order unity without an extra tuning of parameters, and the lepton flavor anarchy is predicted for the lepton mixing matrix. We also obtained a precise description of zero mode wavefunctions near the E_6 type singularity points, where the up-type Yukawa couplings are generated.Comment: 148 page

Efficient data structures for masks on 2D grids

This article discusses various methods of representing and manipulating arbitrary coverage information in two dimensions, with a focus on space- and time-efficiency when processing such coverages, storing them on disk, and transmitting them between computers. While these considerations were originally motivated by the specific tasks of representing sky coverage and cross-matching catalogues of astronomical surveys, they can be profitably applied in many other situations as well.Comment: accepted by A&

Computing largest circles separating two sets of segments

A circle $C$ separates two planar sets if it encloses one of the sets and its open interior disk does not meet the other set. A separating circle is a largest one if it cannot be locally increased while still separating the two given sets. An Theta(n log n) optimal algorithm is proposed to find all largest circles separating two given sets of line segments when line segments are allowed to meet only at their endpoints. In the general case, when line segments may intersect $\Omega(n^2)$ times, our algorithm can be adapted to work in O(n alpha(n) log n) time and O(n \alpha(n)) space, where alpha(n) represents the extremely slowly growing inverse of the Ackermann function.Comment: 14 pages, 3 figures, abstract presented at 8th Canadian Conference on Computational Geometry, 199

Scalable scientific data

posterQuestion Hierarchial Z-Order Evaluation How can we present hundreds or thousands of gigabytes of scientific data to a user for analysis and interpretation? • The Scientific Computing and Imaging Institute is responsible for helping scientists visualize massive amounts of data. • Sources of large scientific data include medical imaging equipment (CAT, PET, MRI, etc.), fluid dynamics simulations, and genetic sequence mapping • Some of these simulations produce hundreds of gigabytes of data per simulation time step. Evaluating the speed of loading a set of random samples from an 8GB 3D image showed that: •Both Z and HZ-order significantly outperform the standard Row Major mode representation •HZ-order also outperforms Z-order for progressive requests Based on the Lebesque curve • Indexes Z-curve resolution levels in hierarchical order from coarser to finer. • Maintains the same geometric locality for each Z-curve resolution level • Beneficial for progressive resolution requests. (e.g. an "object search" application may first attempt to perform filtering on a coarser resolution

An hierarchical approach to hull form design

As ship design tools become more integrated and more advanced analysis tools are introduced, the ability to rapidly develop and modify hull forms becomes essential. Modern hull design applications give an experienced user the ability to create almost any shape of hull. However, the direct manipulation of hull surface representations is laborious and may limit the exploration of design concept to the fullest extent. Transformation of parent forms and parametric hull generation tools can provide a quick solution, but neither method is conducive for innovative design. A hull design tool is required that can integrate the separate techniques creating a fair hull form surface that can be modified easily throughout the design process. This paper explores the concept of separating the hull surface into global and local features by establishing a hierarchical definition structure and introduces some of the benefits of this approach