Ellipse Fitting Using the Finite Rate of Innovation Sampling Principle

Standard approaches for ellipse fitting are based on the minimization of algebraic or geometric distance between the given data and a template ellipse. When the data are noisy and come from a partial ellipse, the state-of-the-art methods tend to produce biased ellipses. We rely on the sampling structure of the underlying signal and show that the x- and y-coordinate functions of an ellipse are finite-rate-of-innovation (FRI) signals, and that their parameters are estimable from partial data. We consider both uniform and nonuniform sampling scenarios in the presence of noise and show that the data can be modeled as a sum of random amplitude-modulated complex exponentials. A low-pass filter is used to suppress noise and approximate the data as a sum of weighted complex exponentials. The annihilating filter used in FRI approaches is applied to estimate the sampling interval in the closed form. We perform experiments on simulated and real data, and assess both objective and subjective performances in comparison with the state-of-the-art ellipse fitting methods. The proposed method produces ellipses with lesser bias. Furthermore, the mean-squared error is lesser by about 2 to 10 dB. We show the applications of ellipse fitting in iris images starting from partial edge contours, and to free-hand ellipses drawn on a touch-screen tablet.

Wave-front analysis method of circular aperture sampling for collimation testing

A new type of wave-front analysis method for the collimation testing of laser beams is proposed. A concept of wave-front height is defined, and, on this basis, the wave-front analysis method of circular aperture sampling is introduced. The wave-front height of the tested noncollimated wave can be estimated from the distance between two identical fiducial diffraction planes of the sampled wave, and then the divergence is determined. The design is detailed, and the experiment is demonstrated. The principle and experiment results of the method are presented. Owing to the simplicity of the method and its low cost, it is a promising method for checking the collimation of a laser beam with a large divergence. © 2005 Optical Society of America.

Biogeographic characterization of fish communities and associated benthic habitats within the Flower Garden Banks National Marine Sanctuary: sampling design and implementation of scuba surveys on the coral caps

The Flower Garden Banks National Marine Sanctuary (FGBNMS) is located in the northwestern Gulf of Mexico approximately 180 km south of Galveston, Texas. The sanctuary’s distance from shore combined with its depth (the coral caps reach to within approximately 17 m of the surface) result in limited exposure of this coral reef ecosystem to natural and human-induced impacts compared to other coral reefs of the western Atlantic. In spite of this, the sanctuary still confronts serious impacts including hurricanes events, recent outbreaks of coral disease, an increase in the frequency of coral bleaching and the massive Diadema antillarum die-off during the mid-1980s. Anthropogenic impacts include large vessel anchoring, commercial and recreational fishing, recreational scuba diving, and oil and gas related activities. The FGBNMS was designated in 1992 to help protect against some of these impacts. Basic monitoring and research efforts have been conducted on the banks since the 1970s. Early on, these efforts focused primarily on describing the benthic communities (corals, sponges) and providing qualitative characterizations of the fish community. Subsequently, more quantitative work has been conducted; however, it has been limited in spatial scope. To complement these efforts, the current study addresses the following two goals put forth by sanctuary management: 1) to develop a sampling design for monitoring benthic fish communities across the coral caps; and 2) to obtain a spatial and quantitative characterization of those communities and their associated habitats.

Identifying appropriate sampling and modelling approaches for analysing distributional patterns of Antarctic terrestrial arthropods along the Victoria Land latitudinal gradient

Biotic communities in Antarctic terrestrial ecosystems are relatively simple and often lack higher trophic levels (e. g. predators); thus, it is often assumed that species' distributions are mainly affected by abiotic factors such as climatic conditions, which change with increasing latitude, altitude and/or distance from the coast. However, it is becoming increasingly apparent that factors other than geographical gradients affect the distribution of organisms with low dispersal capability such as the terrestrial arthropods. In Victoria Land (East Antarctica) the distribution of springtail (Collembola) and mite (Acari) species vary at scales that range from a few square centimetres to regional and continental. Different species show different scales of variation that relate to factors such as local geological and glaciological history, and biotic interactions, but only weakly with latitudinal/altitudinal gradients. Here, we review the relevant literature and outline more appropriate sampling designs as well as suitable modelling techniques (e. g. linear mixed models and eigenvector mapping), that will more adequately address and identify the range of factors responsible for the distribution of terrestrial arthropods in Antarctica.

Indexing and matching trajectories under inconsistent sampling rates

Quantifying the similarity between two trajectories is a fundamental operation in analysis of spatio-temporal databases. While a number of distance functions exist, the recent shift in the dynamics of the trajectory generation procedure violates one of their core assumptions; a consistent and uniform sampling rate. In this paper, we formulate a robust distance function called Edit Distance with Projections (EDwP) to match trajectories under inconsistent and variable sampling rates through dynamic interpolation. This is achieved by deploying the idea of projections that goes beyond matching only the sampled points while aligning trajectories. To enable efficient trajectory retrievals using EDwP, we design an index structure called TrajTree. TrajTree derives its pruning power by employing the unique combination of bounding boxes with Lipschitz embedding. Extensive experiments on real trajectory databases demonstrate EDwP to be up to 5 times more accurate than the state-of-the-art distance functions. Additionally, TrajTree increases the efficiency of trajectory retrievals by up to an order of magnitude over existing techniques.

Biased representation of disturbance rates in the roadside sampling frame in boreal forests: implications for monitoring design

The North American Breeding Bird Survey (BBS) is the principal source of data to inform researchers about the status of and trend for boreal forest birds. Unfortunately, little BBS coverage is available in the boreal forest, where increasing concern over the status of species breeding there has increased interest in northward expansion of the BBS. However, high disturbance rates in the boreal forest may complicate roadside monitoring. If the roadside sampling frame does not capture variation in disturbance rates because of either road placement or the use of roads for resource extraction, biased trend estimates might result. In this study, we examined roadside bias in the proportional representation of habitat disturbance via spatial data on forest “loss,” forest fires, and anthropogenic disturbance. In each of 455 BBS routes, the area disturbed within multiple buffers away from the road was calculated and compared against the area disturbed in degree blocks and BBS strata. We found a nonlinear relationship between bias and distance from the road, suggesting forest loss and forest fires were underrepresented below 75 and 100 m, respectively. In contrast, anthropogenic disturbance was overrepresented at distances below 500 m and underrepresented thereafter. After accounting for distance from road, BBS routes were reasonably representative of the degree blocks they were within, with only a few strata showing biased representation. In general, anthropogenic disturbance is overrepresented in southern strata, and forest fires are underrepresented in almost all strata. Similar biases exist when comparing the entire road network and the subset sampled by BBS routes against the amount of disturbance within BBS strata; however, the magnitude of biases differed. Based on our results, we recommend that spatial stratification and rotating panel designs be used to spread limited BBS and off-road sampling effort in an unbiased fashion and that new BBS routes be established where sufficient road coverage exists.

Comparing sampling needs for variograms of soil properties computed by the method of moments and residual maximum likelihood

It has been generally accepted that the method of moments (MoM) variogram, which has been widely applied in soil science, requires about 100 sites at an appropriate interval apart to describe the variation adequately. This sample size is often larger than can be afforded for soil surveys of agricultural fields or contaminated sites. Furthermore, it might be a much larger sample size than is needed where the scale of variation is large. A possible alternative in such situations is the residual maximum likelihood (REML) variogram because fewer data appear to be required. The REML method is parametric and is considered reliable where there is trend in the data because it is based on generalized increments that filter trend out and only the covariance parameters are estimated. Previous research has suggested that fewer data are needed to compute a reliable variogram using a maximum likelihood approach such as REML, however, the results can vary according to the nature of the spatial variation. There remain issues to examine: how many fewer data can be used, how should the sampling sites be distributed over the site of interest, and how do different degrees of spatial variation affect the data requirements? The soil of four field sites of different size, physiography, parent material and soil type was sampled intensively, and MoM and REML variograms were calculated for clay content. The data were then sub-sampled to give different sample sizes and distributions of sites and the variograms were computed again. The model parameters for the sets of variograms for each site were used for cross-validation. Predictions based on REML variograms were generally more accurate than those from MoM variograms with fewer than 100 sampling sites. A sample size of around 50 sites at an appropriate distance apart, possibly determined from variograms of ancillary data, appears adequate to compute REML variograms for kriging soil properties for precision agriculture and contaminated sites. (C) 2007 Elsevier B.V. All rights reserved.

Spatial variability of soil penetration resistance influenced by season of sampling

O objetivo deste trabalho foi analizar a distribuição espacial da compactação do solo e a influência da umidade do solo na resistência à penetração. Esta última variável foi descrita pelo índice de cone. O solo estudado foi Nitossolo e os dados de índice de cone foram obtidos usando um penetrômetro. A resistência do solo foi avaliada a 5 profundidades diferentes, 0-10 cm, 10-20 cm, 20-30 cm, 30-40 cm e mais de 40 cm, porém o conteúdo de umidade do solo foi medido a 0-20 cm e 20-40 cm. As condições hídricas do solo variaram nas diferentes amostragems. Os coeficientes de variação para o índice de cone foram 16,5% a 45,8% e os do conteúdo de umidade do solo variaram entre 8,96% e 21,38%. Os resultados sugeriram elevada correlação entre a resistência do solo, estimada pelo índice de cone e a profundidade do solo. Sem embargo, a relação esperada com a umidade do solo não foi apreciada. Observou-se dependência espacial em 31 de 35 séries de dados de índice de cone e umidade do solo. Esta dependência foi ajustada por modelos exponenciais com efeito pepita variável de 0 a 90% o valor do patamar. em séries de dados o comportamento foi aleatório. Portanto, a técnica das distâncias inversas foi utilizada para cartografar a distribuição das variáveis que não tiveram estrutura espacial. Na krigagem constatou-se uma suavização dos mapas comparados com esses das distâncias inversas. A krigagem indicadora foi utilizada para cartografar a variabilidade espacial do índice de cone e recomendar melhor manejo do solo.

Precision of distances and ordering of microsatellite markers in consensus linkage maps of chromosomes 1, 3 and 4 from two reciprocal chicken populations using bootstrap sampling

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Local Interstellar Medium: Six Years of Direct Sampling by IBEX

The Interstellar Boundary Explorer (IBEX) has been directly observing neutral atoms from the local interstellar medium for the last six years (2009–2014). This paper ties together the 14 studies in this Astrophysical Journal Supplement Series Special Issue, which collectively describe the IBEX interstellar neutral results from this epoch and provide a number of other relevant theoretical and observational results. Interstellar neutrals interact with each other and with the ionized portion of the interstellar population in the “pristine” interstellar medium ahead of the heliosphere. Then, in the heliosphereʼs close vicinity, the interstellar medium begins to interact with escaping heliospheric neutrals. In this study, we compare the results from two major analysis approaches led by IBEX groups in New Hampshire and Warsaw. We also directly address the question of the distance upstream to the pristine interstellar medium and adjust both sets of results to a common distance of ~1000 AU. The two analysis approaches are quite different, but yield fully consistent measurements of the interstellar He flow properties, further validating our findings. While detailed error bars are given for both approaches, we recommend that for most purposes, the community use “working values” of ~25.4 km s⁻¹, ~75°7 ecliptic inflow longitude, ~−5°1 ecliptic inflow latitude, and ~7500 K temperature at ~1000 AU upstream. Finally, we briefly address future opportunities for even better interstellar neutral observations to be provided by the Interstellar Mapping and Acceleration Probe mission, which was recommended as the next major Heliophysics mission by the NRCʼs 2013 Decadal Survey.