Area-preserving diffeomorphisms in gauge theory on a non-commutative plane: a lattice study

We consider Yang-Mills theory with the U(1) gauge group on a non-commutative plane. Perturbatively it was observed that the invariance of this theory under area-preserving diffeomorphisms (APDs) breaks down to a rigid subgroup SL(2,R). Here we present explicit results for the APD symmetry breaking at finite gauge coupling and finite non-commutativity. They are based on lattice simulations and measurements of Wilson loops with the same area but with a variety of different shapes. Our results are consistent with the expected loss of invariance under APDs. Moreover, they strongly suggest that non-perturbatively the SL(2,R) symmetry does not persist either.Comment: 28 pages, 15 figures, published versio

Object recognition using multi-view imaging

Single view imaging data has been used in most previous research in computer vision and image understanding and lots of techniques have been developed. Recently with the fast development and dropping cost of multiple cameras, it has become possible to have many more views to achieve image processing tasks. This thesis will consider how to use the obtained multiple images in the application of target object recognition. In this context, we present two algorithms for object recognition based on scale- invariant feature points. The first is single view object recognition method (SOR), which operates on single images and uses a chirality constraint to reduce the recognition errors that arise when only a small number of feature points are matched. The procedure is extended in the second multi-view object recognition algorithm (MOR) which operates on a multi-view image sequence and, by tracking feature points using a dynamic programming method in the plenoptic domain subject to the epipolar constraint, is able to fuse feature point matches from all the available images, resulting in more robust recognition. We evaluated these algorithms using a number of data sets of real images capturing both indoor and outdoor scenes. We demonstrate that MOR is better than SOR particularly for noisy and low resolution images, and it is also able to recognize objects that are partially occluded by combining it with some segmentation techniques

Detecting Similarity of Rational Plane Curves

A novel and deterministic algorithm is presented to detect whether two given rational plane curves are related by means of a similarity, which is a central question in Pattern Recognition. As a by-product it finds all such similarities, and the particular case of equal curves yields all symmetries. A complete theoretical description of the method is provided, and the method has been implemented and tested in the Sage system for curves of moderate degrees.Comment: 22 page

Object-Based Integration of Photogrammetric and LiDAR Data for Automated Generation of Complex Polyhedral Building Models

This research is concerned with a methodology for automated generation of polyhedral building models for complex structures, whose rooftops are bounded by straight lines. The process starts by utilizing LiDAR data for building hypothesis generation and derivation of individual planar patches constituting building rooftops. Initial boundaries of these patches are then refined through the integration of LiDAR and photogrammetric data and hierarchical processing of the planar patches. Building models for complex structures are finally produced using the refined boundaries. The performance of the developed methodology is evaluated through qualitative and quantitative analysis of the generated building models from real data