Edge detection is the process that attempts to characterize the intensity changes in the image in terms of the physical processes that have originated them. A critical, intermediate goal of edge detection is the detection and characterization of significant intensity changes. This paper discusses this part fo the edge detection problem. To characterize the types of intensity changes derivatives of different types, and possibly different scales, are needed. Thus we consider this part of edge detection as a problem in numerical differentiation. We show that numerical differentiation of images is an ill-posed problem in the sense of Hadamard. Differentiation needs to be regularized by a regularizing filtering operation before differentiation. This shows that his part of edge detection consists of two steps, a filtering step and differentiation step.

We will briefly outline a computational theory of the first stages of human vision according to which (a) the retinal image is filtered by a set of centre-surround receptive fields (of about 5 different spatial sizes) which are approximately bandpass in spatial frequency and (b) zero-crossings are detected independently in the output of each of these channels. Zero-crossings in each channel are then a set of discrete symbols which may be used for later processing such as contour extraction and stereopsis. A formulation of Logan's zero-crossing results is proved for the case of Fourier polynomials and an extension of Logan's theorem to 2-dimentsional functions is also approved. Within this framework, we shall describe an experimental and theoretical approach (developed by one of us with M. Fahle) to the problem of visual acuity and hyperacuity of human vision. The positional accuracy achieved, for instance, in reading a vernier is astonishingly high, corresponding to a fraction of the spacing between adjacent photoreceptors in the fovea. Stroboscopic presentation of a moving object can be interpolated by our visual system into the perception of continuous motion; and this "spatio-temporal" interpolation also can be very accurate. It is suggested that the known spatiotemporal properties of the channels envisaged by the theory of visual processing outlined above implement an interpolation scheme which can explain human vernier acuity for moving targets.

Thesis (M.S.)--Montana State University--Bozeman, 2007. / Typescript. Chairperson, Graduate Committee: Sharon Eversman. Includes bibliographical references (leaves 85-89).

Clinch Dace (Chrosomus sp. cf. saylori) is a newly recognized species of minnow with a restricted distribution in southwestern Virginia. Field sampling and genetic analysis support the hypothesis that Clinch Dace populations are small and fragmented. Analysis of neutral genetic markers shows that most Clinch Dace populations have undergone past bottleneck events and are being operated upon by random genetic drift. Bayesian cluster analysis showed that three out of the seven populations found in 2017 are distinct, while the other four show signs of more recent admixture. However, Fst values among streams were high and analysis of molecular variance indicated differentiation among populations in all streams. These findings support the view that these populations are genetically isolated. Effective populations sizes were low at most sites, enhancing the likelihood of loss of alleles to genetic drift. Low M-ratios, non-zero Fis values, and high degrees of relatedness among individuals indicate that some inbreeding is taking place. Habitat analysis did not identify variables affecting distribution or abundance of Clinch Dace populations. As the collection sites were targeted near known Clinch Dace occupied sites, it is likely that habitat variables known to impact Clinch Dace, such as conductivity, were within the species' range of tolerance. Results showed that Clinch Dace seem particularly resilient to sedimentation, corroborating earlier work showing a negative relationship between Clinch Dace abundance to sediment size. That is, small sediment size does not seem to have a negative impact on Clinch Dace abundance. Of all sites where Clinch Dace were found, only one culvert at one site was clearly perched and may present a barrier to upstream migration, a possibility which is supported by the genetic differentiation found among collections above and below that culvert. While this study demonstrates that selectively neutral genetic differentiation has taken place among Clinch Dace populations, it does address any local adaptation that may be taking place which would render translocations a risk for outbreeding depression. The findings of this study can inform conservation management in identifying possible sources of individuals for translocations among populations or for augmentation following captive breeding. / Master of Science / The Clinch Dace is a small, threatened minnow in the Clinch River basin that was unknown until 1999. Since then, research has addressed the biology, life history, and distribution of this fish. This study used data from selectively neutral genetic markers to analyze the population structure and degree of differentiation of Clinch Dace populations. My study sites were targeted at road crossings near known Clinch Dace populations to assess the effect of habitat fragmentation on Clinch Dace populations and to maximize the likelihood that I would collect enough genetic material for analysis. Genetic analyses showed that while there is some admixture among certain populations of Clinch Dace, there is differentiation at neutral genetic markers. This differentiation does not necessarily indicate adaptive variation among populations which could result in outbreeding depression should populations be mixed through translocations, but it is reason to proceed with caution. Road crossings were generally not found to be a cause of further population fragmentation in Clinch Dace, as demonstrated by genetic analysis and statistical analysis. Almost all of the occupied road crossing sites in this study were either embedded, free-flowing culverts that were not perched or small bridges, and these were not deemed to be obvious barriers to fish movement. The only exception was Hart Creek 2, where the culvert is slightly perched and Fst is high between populations in the upstream and downstream reaches. The results of this study will help to inform managers as to what conservation actions can be taken to improve population viability. One potential management action from this study could be the retrofitting of culverts that have become perched and are acting as barriers to Clinch Dace movement. Another potential conservation strategy is to translocate individuals from large population to small populations. The study determined: 1) which translocations might be acceptable based on the degree of genetic differentiation among populations, and 2) identified potential donor and receiving streams for translocations.

Let X denote a reduced algebraic variety and D a Weil divisor on X. The pair (X,D) is said to be semi-simple normal crossings (semi-snc) at a in X if X is simple normal crossings at a (i.e., a simple normal crossings hypersurface, with respect to a local embedding in a smooth ambient variety), and D is induced by the restriction to X of a hypersurface that is simple normal crossings with respect to X. For a pair (X,D), over a field of characteristic zero, we construct a composition of blowings-up f:X'-->X such that the transformed pair (X',D') is everywhere semi-simple normal crossings, and f is an isomorphism over the semi-simple normal crossings locus of (X,D). The result answers a question of Kolla'r.

Let X denote a reduced algebraic variety and D a Weil divisor on X. The pair (X,D) is said to be semi-simple normal crossings (semi-snc) at a in X if X is simple normal crossings at a (i.e., a simple normal crossings hypersurface, with respect to a local embedding in a smooth ambient variety), and D is induced by the restriction to X of a hypersurface that is simple normal crossings with respect to X. For a pair (X,D), over a field of characteristic zero, we construct a composition of blowings-up f:X'-->X such that the transformed pair (X',D') is everywhere semi-simple normal crossings, and f is an isomorphism over the semi-simple normal crossings locus of (X,D). The result answers a question of Kolla'r.

We study the unique phenomena which occur in certain systems characterized by the crossing or avoided crossing of two electronic eigenvalues. First, an example problem will be investigated for a given Hamiltonian resulting in a codimension 1 crossing by implementing results by Hagedorn from 1994. Then we perturb the Hamiltonian to study the system for the corresponding avoided crossing by implementing results by Hagedorn and Joye from 1998. The results from these demonstrate the behavior which occurs at a codimension 1 crossing and avoided crossing and illustrates the differences. These solutions may also be used in further studies with Herman-Kluk propagation and more. Secondly, we study codimension 2 crossings by considering a more general type of wave packet. We focus on the case of Schrödinger equation but our methods are general enough to be adapted to other systems with the geometric conditions therein. The motivation comes from the construction of surface hopping algorithms giving an approximation of the solution of a system of Schrödinger equations coupled by a potential admitting a conical intersection, in the spirit of Herman-Kluk approximation (in close relation with frozen/thawed approximations). Our main Theorem gives explicit transition formulas for the profiles when passing through a conical crossing point, including precise computation of the transformation of the phase and its proof is based on a normal form approach. / Doctor of Philosophy / We study energies of molecular systems in which special circumstances occur. In particular, when these energies intersect, or come close to intersecting. These phenomena give rise to unique physics which allows special reactions to occur and are thus of interest to study. We study one example of a more specific type of energy level crossing and avoided crossing, and then consider another type of crossing in a more general setting. We find solutions for these systems to draw our results from.

For over a decade proposals for connecting the metropolitan areas of Austin and San Antonio, Texas via passenger rail have been studied. In the Texas Department of Transportation’s 2010 Rail Plan several ideas, including high-speed rail, regional Amtrak service, and a new passenger rail service have been proposed as a means to provide an alternate mode of transportation along the I-35 corridor. Union Pacific Railroad currently owns and operations a rail line that connects the Austin and San Antonio metropolitan areas; each of the passenger rail projects proposes sharing this corridor with Union Pacific. A literature review reveals that a key factor in negotiating with a freight railroad for shared use of a corridor is safety. One element of the safety risk analysis is the evaluation of at-grade highway-railroad crossing. This study discusses the Austin-San Antonio corridor, its current mobility challenges and the proposed passenger rail projects. It then discusses rail safety as expressed in the literature and provides background about safety at highway-railroad crossings. Crossing inventory and accident data, as maintained by the Federal Railroad Administration (FRA), is then analyzed using regression modeling in an attempt to better understand the relationship between the physical and operational characteristics of highway-railroad crossings and accidents on corridors shared by freight and passenger rail. It analyzes a five-year accident history (2005 to 2009) from of a sample of shared use highway-rail crossings throughout the US. The findings are then used to analyze the at-grade highway-railroad crossings along the Austin-San Antonio corridor. And finally, the implications of the findings are discussed. The findings of this report recommend that characteristics of the built environment such as land use, number of traffic lanes, and function classification of the roadway should be considered when assessing accident risk at highway-railroad crossings. In addition, this analysis reveals the need for a way to better measure safety risks at private highway-railroad crossings. / text

Call number: LD2668 .T4 1984 W66 / Master of Science

Level-crossings, i.e. intersections where railways and road meet in the same vertical level, constitute risk for the users of respective infrastructure system. The aim of this thesis is to examine possible regional differences between the infrastructural safety standard of level-crossings in Sweden. With the use of spatial analyses tools in a Geographical Information System, the differences between Swedish counties are outlined and mapped. By the use of a logistic regression model, the variables that increase the risk of an accident in a level-crossings are analysed. The results show that the variables concerning the level of protection, together with the location on a highway, show statistical significance of being associated with an increased accidental risk. The results of the regression model factors have been returned to the GIS in order to find the most hazardous level-crossings. Considering the train flows and amount of people living in the proximity of the crossings, the hotpots of hazards have been spatially identified. 38 level-crossings with passive or semi-active warning system meet the criteria and should be the targets for practitioners’ work towards an increased level of safety and reduced risk.