On the fitting of surfaces to data with covariances

Copyright © 2000 IEEEWe consider the problem of estimating parameters of a model described by an equation of special form. Specific models arise in the analysis of a wide class of computer vision problems, including conic fitting and estimation of the fundamental matrix. We assume that noisy data are accompanied by (known) covariance matrices characterizing the uncertainty of the measurements. A cost function is first obtained by considering a maximum-likelihood formulation and applying certain necessary approximations that render the problem tractable. A Newton-like iterative scheme is then generated for determining a minimizer of the cost function. Unlike alternative approaches such as Sampson's method or the renormalization technique, the new scheme has as its theoretical limit the minimizer of the cost function. Furthermore, the scheme is simply expressed, efficient, and unsurpassed as a general technique in our testing. An important feature of the method is that it can serve as a basis for conducting theoretical comparison of various estimation approaches.Wojciech Chojnacki, Michael J. Brooks, Anton van den Hengel and Darren Gawle

FNS and HEIV: relating two vision parameter estimation frameworks

©2003 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 redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.Problems requiring accurate determination of parameters from image-based quantities arise often in computer vision. Two recent, independently developed frameworks for estimating such parameters are the FNS and HEIV schemes. Here it is shown that FNS and a core version of HEIV are essentially equivalent, solving a common underlying equation via different means. The analysis is driven by the search for a non-degenerate form of a certain generalised eigen-value problem, and effectively leads to a new derivation of the relevant case of the HEIV algorithm. This work may be seen as an extension of previous efforts to rationalise and inter-relate a spectrum of estimators, including the renormalisation method of Kanatani and the normalised eight-point method of Hartley.Wojciech Chojnacki, Michael J. Brooks, Anton van den Hengel, Darren Gawle

From FNS to HEIV: A link between two vision parameter estimation methods

Copyright © 2004 IEEEProblems requiring accurate determination of parameters from imagebased quantities arise often in computer vision. Two recent, independently developed frameworks for estimating such parameters are the FNS and HEIV schemes. Here, it is shown that FNS and a core version of HEIV are essentially equivalent, solving a common underlying equation via different means. The analysis is driven by the search for a nondegenerate form of a certain generalized eigenvalue problem and effectively leads to a new derivation of the relevant case of the HEIV algorithm. This work may be seen as an extension of previous efforts to rationalize and interrelate a spectrum of estimators, including the renormalization method of Kanatani and the normalized eight-point method of Hartley.Wojciech Chojnacki, Michael J. Brooks, Anton van den Hengel, and Darren Gawle

What value covariance information in estimating vision parameters?

©2001 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 redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.Many parameter estimation methods used in computer vision are able to utilise covariance information describing the uncertainty of data measurements. This paper considers the value of this information to the estimation process when applied to measured image point locations. Covariance matrices are first described and a procedure is then outlined whereby covariances may be associated with image features located via a measurement process. An empirical study is made of the conditions under which covariance information enables generation of improved parameter estimates. Also explored is the extent to which the noise should be anisotropic and inhomogeneous if improvements are to be obtained over covariance-free methods. Critical in this is the devising of synthetic experiments under which noise conditions can be precisely controlled. Given that covariance information is, in itself, subject to estimation error tests are also undertaken to determine the impact of imprecise covariance information upon the quality of parameter estimates. Finally, an experiment is carried out to assess the value of covariances in estimating the fundamental matrix from real imagesBrooks, M.J. Chojnacki, W. Gawley, D. van den Hengel, A

Revisiting Hartley's normalized eight-point algorithm

Copyright © 2003 IEEEHartley's eight-point algorithm has maintained an important place in computer vision, notably as a means of providing an initial value of the fundamental matrix for use in iterative estimation methods. In this paper, a novel explanation is given for the improvement in performance of the eight-point algorithm that results from using normalized data. It is first established that the normalized algorithm acts to minimize a specific cost function. It is then shown that this cost function I!; statistically better founded than the cost function associated with the nonnormalized algorithm. This augments the original argument that improved performance is due to the better conditioning of a pivotal matrix. Experimental results are given that support the adopted approach. This work continues a wider effort to place a variety of estimation techniques within a coherent framework.Wojciech Chojnacki, Michael J. Brooks, Anton van den Hengel and Darren Gawle

A statistical rationalisation of Hartley's normalised eight-point algorithm

©2003 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 redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.The eight-point algorithm of Hartley occupies an important place in computer vision, notably as a means of providing an initial value of the fundamental matrix for use in iterative estimation methods. In this paper, a novel explanation is given for the improvement in performance of the eight-point algorithm that results from using normalised data. A first step is singling out a cost function that the normalised algorithm acts to minimise. The cost function is then shown to be statistically better founded than the cost function associated with the non-normalised algorithm. This augments the original argument that improved performance is due to the better conditioning of a pivotal matrix. Experimental results are given that support the adopted approach. This work continues a wider effort to place a variety of estimation techniques within a coherent framework.Wojciech Chojnacki, Michael J. Brooks, Anton van den Hengel, Darren Gawle

Are Pfiesteria species toxicogenic? Evidence against production of ichthyotoxins by Pfiesteria shumwayae

The estuarine genus Pfiesteria has received considerable attention since it was first identified and proposed to be the causative agent of fish kills along the mid-Atlantic coast in 1992. The presumption has been that the mechanism of fish death is by release of one or more toxins by the dinoflagellate. In this report, we challenge the notion that Pfiesteria species produce ichthyotoxins. Specifically, we show that (i) simple centrifugation, with and without ultrasonication, is sufficient to detoxify water of actively fish-killing cultures of Pfiesteria shumwayae, (ii) organic extracts of lyophilized cultures are not toxic to fish, (fit) degenerate primers that amplify PKS genes from several polyketide-producing dinoflagellates failed to yield a product with A shumwayae DNA or cDNA, and (iv) degenerate primers for NRPS genes failed to amplify any NRPS genes but (unexpectedly) yielded a band (among several) that corresponded to known or putative PKSs and fatty acid synthases. We conclude that P. shumwayae is able to kill fish by means other than releasing a toxin into bulk water. Alternative explanations of the effects attributed to Pfiesteria are suggested

A curvilinear effect of height on reproductive success in human males

Human male height is associated with mate choice and intra-sexual competition, and therefore potentially with reproductive success. A literature review (n = 18) on the relationship between male height and reproductive success revealed a variety of relationships ranging from negative to curvilinear to positive. Some of the variation in results may stem from methodological issues, such as low power, including men in the sample who have not yet ended their reproductive career, or not controlling for important potential confounders (e.g. education and income). We investigated the associations between height, education, income and the number of surviving children in a large longitudinal sample of men (n = 3,578; Wisconsin Longitudinal Study), who likely had ended their reproductive careers (e.g. > 64 years). There was a curvilinear association between height and number of children, with men of average height attaining the highest reproductive success. This curvilinear relationship remained after controlling for education and income, which were associated with both reproductive success and height. Average height men also married at a younger age than shorter and taller men, and the effect of height diminished after controlling for this association. Thus, average height men partly achieved higher reproductive success by marrying at a younger age. On the basis of our literature review and our data, we conclude that men of average height most likely have higher reproductive success than either short or tall men

Environmental Influences on Mate Preferences as Assessed by a Scenario Manipulation Experiment

Many evolutionary psychology studies have addressed the topic of mate preferences, focusing particularly on gender and cultural differences. However, the extent to which situational and environmental variables might affect mate preferences has been comparatively neglected. We tested 288 participants in order to investigate the perceived relative importance of six traits of an ideal partner (wealth, dominance, intelligence, height, kindness, attractiveness) under four different hypothetical scenarios (status quo/nowadays, violence/post-nuclear, poverty/resource exhaustion, prosperity/global well-being). An equal number of participants (36 women, 36 men) was allotted to each scenario; each was asked to allocate 120 points across the six traits according to their perceived value. Overall, intelligence was the trait to which participants assigned most importance, followed by kindness and attractiveness, and then by wealth, dominance and height. Men appraised attractiveness as more valuable than women. Scenario strongly influenced the relative importance attributed to traits, the main finding being that wealth and dominance were more valued in the poverty and post-nuclear scenarios, respectively, compared to the other scenarios. Scenario manipulation generally had similar effects in both sexes, but women appeared particularly prone to trade off other traits for dominance in the violence scenario, and men particularly prone to trade off other traits for wealth in the poverty scenario. Our results are in line with other correlational studies of situational variables and mate preferences, and represent strong evidence of a causal relationship of environmental factors on specific mate preferences, corroborating the notion of an evolved plasticity to current ecological conditions. A control experiment seems to suggest that our scenarios can be considered as realistic descriptions of the intended ecological conditions