Behavioral analysis of anisotropic diffusion in image processing

©1996 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or distribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.DOI: 10.1109/83.541424In this paper, we analyze the behavior of the anisotropic diffusion model of Perona and Malik (1990). The main idea is to express the anisotropic diffusion equation as coming from a certain optimization problem, so its behavior can be analyzed based on the shape of the corresponding energy surface. We show that anisotropic diffusion is the steepest descent method for solving an energy minimization problem. It is demonstrated that an anisotropic diffusion is well posed when there exists a unique global minimum for the energy functional and that the ill posedness of a certain anisotropic diffusion is caused by the fact that its energy functional has an infinite number of global minima that are dense in the image space. We give a sufficient condition for an anisotropic diffusion to be well posed and a sufficient and necessary condition for it to be ill posed due to the dense global minima. The mechanism of smoothing and edge enhancement of anisotropic diffusion is illustrated through a particular orthogonal decomposition of the diffusion operator into two parts: one that diffuses tangentially to the edges and therefore acts as an anisotropic smoothing operator, and the other that flows normally to the edges and thus acts as an enhancement operator

Robustness of composite pulses to time-dependent control noise

We study the performance of composite pulses in the presence of time-varying control noise on a single qubit. These protocols, originally devised only to correct for static, systematic errors, are shown to be robust to time-dependent non-Markovian noise in the control field up to frequencies as high as ~10% of the Rabi frequency. Our study combines a generalized filter-function approach with asymptotic dc-limit calculations to give a simple analytic framework for error analysis applied to a number of composite-pulse sequences relevant to nuclear magnetic resonance as well as quantum information experiments. Results include examination of recently introduced concatenated composite pulses and dynamically corrected gates, demonstrating equivalent first-order suppression of time-dependent fluctuations in amplitude and/or detuning, as appropriate for the sequence in question. Our analytic results agree well with numerical simulations for realistic $1/f$ noise spectra with a roll-off to $1/f^2$, providing independent validation of our theoretical insights.Comment: 11 pages, 4 figures, text and figures updated to published versio

Pre-corneal tear film thickness in humans measured with a novel technique.

PurposeThe purpose of this work was to gather preliminary data in normals and dry eye subjects, using a new, non-invasive imaging platform to measure the thickness of pre-corneal tear film.MethodsHuman subjects were screened for dry eye and classified as dry or normal. Tear film thickness over the inferior paracentral cornea was measured using laser illumination and a complementary metal-oxide-semiconductor (CMOS) camera. A previously developed mathematical model was used to calculate the thickness of the tear film by applying the principle of spatial auto-correlation function (ACF).ResultsMean tear film thickness values (±SD) were 3.05 μm (0.20) and 2.48 μm (0.32) on the initial visit for normals (n=18) and dry eye subjects (n=22), respectively, and were significantly different (p<0.001, 2-sample t-test). Repeatability was good between visit 1 and 2 for normals (intraclass correlation coefficient [ICC]=0.935) and dry eye subjects (ICC=0.950). Tear film thickness increased above baseline for the dry eye subjects following viscous drop instillation and remained significantly elevated for up to approximately 32 min (n=20; p<0.05 until 32 min; general linear mixed model and Dunnett's tests).ConclusionsThis technique for imaging the ocular surface appears to provide tear thickness values in agreement with other non-invasive methods. Moreover, the technique can differentiate between normal and dry eye patient types

Community engagement as a tool to help deliver smart city innovation: a case study of Nottingham, United Kingdom

Cities are complex urban conurbations and facing many challenges. The majority of the world’s population now live in cities and consume 80% of the resources. 'Smart City' innovation is emerging as a major response to the challenges cities are facing. Much of the focus remains on technological interventions, but technology alone may not be sufficient to reach smart and sustainable city goals. Cities are made up of people who have influence and are therefore key stakeholders in the development of smart city innovation and cannot be ignored. This paper aims to explore community engagement in Nottingham to help deliver smart city innovation and the way Nottingham City Council is engaging local communities in its smart projects. The paper analyses the community engagement strategy of Nottingham developed as part of the EU funded smart city project, REMOURBAN (REgeneration MOdel for accelerating the smart URBAN transformation). The main drivers and barriers to effective community engagement are identified in the smart city context. This exploratory study adopted a case study strategy and qualitative research methods. The data was collected through thirteen semi-structured interviews with middle and senior managers in Nottingham City Council and other stakeholder organisations in the city and a focus group of five community leaders from three local community groups. The content analysis of the REMOURBAN documents related to citizen engagement and the council’s energy strategies and policies was carried out. The key results are discussed with recommendations to nurture effective community engagement as a smart city tool and conclusions are drawn

Modified Dolphin Monitoring Operator for Weight Optimization of Frame Structures

In this article, a modified dolphin monitoring (MDM) operatoris introduced and used to improve the performance of the collidingbodies optimization (CBO) algorithm for optimal designof steel structures (CBO-MDM). The performance of the CBO,enhanced colliding bodies optimization (ECBO) and CBOMDMare compared through three well-established structuralbenchmarks. The optimized designs obtained by thesealgorithms are compared, and the results show that the performanceof CBO-MDM is superior to those of the other twoalgorithms. The MDM is found to be a suitable tool to enhancethe performance of the CBO algorithm