Estimation Of Shape Parameter Research Articles

Directed mean Hausdorff distance of parameterized freeform shapes in 3D: a case study

Shape matching in 3D is a process underlying several applications, including engineering, medicine, and animation. Searching, recognition, and matching of shape patterns directly in 3D model-space is far from a mature technique. In this paper we report an investigation of the computation of shape similarity based on Hausdorff-like measures. We have assessed a number of properties of the directed Hausdorff distance between 3D shapes, namely accuracy, robustness, and computational complexity of the algorithms. The driving application here was the reuse of digitized shapes in geometric modeling. The shapes involved in the analysis were from sampled physical object surfaces, or they were synthetic shapes. To support the application it was necessary to extend the search space beyond rigid and affine transformation spaces; a number of deformation parameters (intrinsic shape parameters) needed to be introduced. The sensitivity of the Hausdorff distance to pose parameters and to intrinsic shape parameters was investigated. Shape parameter estimation turned out to be feasible when an appropriate fitting strategy was selected. Besides a short straight ridge, ridges developing along a 3D spine can also be successfully registered. Finally, it is demonstrated how the performance of the algorithms is improved by a 3D binning technique.

Robust estimators and probability integral transformations

This article gives a construction of a weighted mean which has good robust properties (qualitative robustness, bounded influence function, high breakdown points). The construction is based on M-functionals with smooth defining functions which are used to control weighting. This construction has the advantage of the computational speed and opens up the possibility of allowing the weighting to take the shape of the original data set into account. This method can be applied to some other statistical problems: the estimation of shape parameter at the Student- and Weibull-family, examination for sufficient statistics of Ornstein-Uhlenbeck process.

Applying knowledge to reverse engineering problems

This paper summarizes a series of recent research results made at Edinburgh University based on projects that apply domain knowledge of standard shapes and relation ships to solve or improve reverse engineering problems. The problems considered are how to enforce known relationships when data fitting, how to extract features even in very noisy data, how to get better shape parameter estimates and how to infer data about unseen features.

Efficient estimation of the weibull shape parameter based on a modified profile likelihood

The maximum likelihood estimator of the Weibull shape parameter can be very biased. An estimator based on the modified profile likelihood is proposed and its properties are studied. It is shown that the new estimator is almost unbiased with relative bias being less than 1% in most of situations, and it is much more efficient than the regular MLE. The smaller the sample or the heavier of the censoring, the more efficient is the new estimator relative to the regular MLE.

Stochastic modeling of flood peaks using the generalized extreme value distribution

The generalized extreme value (GEV) distribution is a standard tool for modeling flood peaks, both in annual maximum series (AMS) and in partial duration series (PDS). In this paper, combined maximum likelihood estimation (MLE) and L moment (LMOM) procedures are developed for estimating location, shape, and scale parameters of the GEV distribution. Particular attention is given to estimation of the shape parameter, which determines the “thickness” of the upper tail of the flood frequency distribution. Mixed MLE–LMOM methods avoid problems with both MLE (estimator variance) and LMOM (estimator bias) estimators of the shape parameter. The mixed MLE–LMOM procedure is extended to use the two largest flood peaks in a year. This extension is developed in a PDS framework. Estimation procedures are applied to flood peak observations from 104 central Appalachian basins. The estimated values of the shape parameter for the central Appalachian basins are more negative than has been considered physically reasonable, independent of the estimation procedure that is used. Twenty‐eight percent of mixed method estimators of the shape parameter have values less than −0.5, implying that the moments of order 2 and above are infinite. The estimated shape parameters for the central Appalachian basins do not depend on basin morphological parameters (such as drainage area) or land cover properties (such as percent urban, forest, or agricultural land use). Estimated values of the location and scale parameters for the central Appalachian watersheds correspond well with GEV‐based simple scaling theory. Estimated values of the shape parameter for central Appalachian watersheds are shown to differ markedly from those of southern Appalachian watersheds and the difference is shown to be linked to contrasting properties of extreme floods. To conclude the paper, analyses of mixture distribution models are presented to address the question of whether flood peaks really have extreme “heavy tail” behavior or whether the GEV distribution is not the appropriate model for flood peaks.

Assessing chronic disease progression using non-homogeneous exponential regression Markov models: an illustration using a selective breast cancer screening in Taiwan.

Previous research on estimation of the progression of chronic disease, from the normal preclinical screen-detectable phase (PCDP) to the final clinical phase, has usually assumed constant transition rates and has rarely addressed how relevant covariates affect multi-state transitions. The present study proposes two non-homogeneous models using the Weibull distribution and piecewise exponential model, together with covariate functions of the proportional hazard form, to tackle these problems. We illustrate the models by application to a selective breast cancer screening programme. The results of the Weibull model yield estimates of scale and shape parameters for annual preclinical incidence rate as 0.0000058 (SE=0.0000019) and 2.4755 (SE=0.1153), the latter being significantly higher than 1. Annual transition rate was estimated as 0.3153 (SE=0.1385). Relative risks for the effects of late age at first pregnancy (AP) and high body mass index (BMI) on preclinical incidence rate were 1.98 and 2.59, respectively. The corresponding figures on the transition from the PCDP to clinical phase were 1.56 and 1.99, respectively. Non-homogeneous Markov models proposed in this study can be easily applied to rates of progression of chronic disease with increasing or decreasing rates with time and to model the effect of relevant covariates on multi-state transition rates.

Comparison of logistic and generalized surplus-production models applied to swordfish, Xiphias gladius, in the north Atlantic Ocean

Recent assessments of swordfish, Xiphias gladius, in the north Atlantic Ocean by the International Commission for the Conservation of Atlantic Tunas (ICCAT) have included fitting a nonequilibrium logistic (Schaefer) surplus-production model. The logistic model offers simplicity, but concern has been expressed that its fixed model shape may bias estimates of quantities of management interest. Here, I compare results from the logistic estimator used by ICCAT to those from an otherwise equivalent generalized (Pella–Tomlinson) production-model estimator. Following initial estimation with nonlinear least-squares, a resistant fitting method was used to identify statistical outliers, and both models were refit with outliers removed. The estimate of model shape from the generalized model was then close to the logistic, and estimates of stock status from the two estimators were similar. A simulation study conditioned on the trimmed generalized fit suggests that any systematic estimation error caused by assuming logistic shape for this stock is small. Moreover, the generalized estimator was sensitive to outlying observations and thus less precise than the logistic estimator, and it exhibited larger median proportional unsigned error. Sensitivity to outliers and lack of precision in an estimator make it more likely to provide misleading estimates in a given analysis; therefore, if the generalized production model with estimated shape parameter is used in stock assessment, it should be applied with skepticism and in conjunction with the more robust logistic form. Unless a good external estimate of model shape is available, the logistic model appears more suitable for routine assessment use on stocks similar to swordfish.

Using simple particle shapes to model the Stokes scattering matrix of ensembles of wavelength-sized particles with complex shapes: possibilities and limitations

We investigate to what extent the full Stokes scattering matrix of an ensemble of wavelength-sized particles with complex shapes can be modeled by employing an ensemble of simple model shapes, such as spheres, spheroids, and circular cylinders. We also examine to what extent such a simple-shape particle model can be used to retrieve meaningful shape information about the complex-shaped particle ensemble. More specifically, we compute the Stokes scattering matrix for ensembles of randomly oriented particles having several polyhedral prism geometries of different sizes and shape parameters. These ensembles serve as proxies for size-shape mixtures of particles containing several different shapes of higher geometrical complexity than the simple-shaped model particles we employ. We find that the phase function of the complex-shaped particle ensemble can be accurately modeled with a size distribution of volume-equivalent spheres. The diagonal elements of the scattering matrix are accurately reproduced with a size-shape mixture of spheroids. A model based on circular cylinders accurately fits the full scattering matrix including the off-diagonal elements. However, the modeling results provide us with only a rough estimate of the effective shape parameter of the complex-shaped particle ensemble to be modeled. They do not allow us to infer detailed information about the shape distribution of the complex-shaped particle ensemble.

Generalized Maximum Likelihood Pareto‐Poisson estimators for partial duration series

This paper considers use of the generalized Pareto ∥GP) distribution with a Poisson model for arrivals to describe peaks over a threshold. This yields a three‐parameter generalized extreme value (GEV) distribution for the annual maximum series. Maximum likelihood estimates of the GP shape parameter к can result in absurd estimates in small samples. These problems are resolved by addition of a prior distribution on к yielding a generalized maximum likelihood estimator. Results show that a three‐ parameter partial duration series (PDS) analysis yields quantile estimators with the same precision as an annual maximum series (AMS) analysis when the generalized maximum likelihood (GML) GP and GEV estimators are adopted. For к ≤ 0 the GML quantile estimators with both PDS and AMS have the best performance among the quantile estimators examined (moments, L moments, and GML). The precision of flood quantiles derived from a PDS analysis is insensitive to the arrival rate λ, so that a year of PDS data is generally worth about as much as a year of AMS data when estimating the 100‐year flood.

Scaling and modeling in the analysis of dispersive relaxation of ionic materials

Problems with scaling of conductive-system experimental Mdat″(ω) and σdat′(ω) data are considered and resolved by dispersive-relaxation-model fitting and comparison. Scaling is attempted for both synthetic and experimental M″(ω) data sets. A crucial element in all experimental frequency-response data is the influence of the high-frequency-limiting dipolar-and-vibronic dielectric constant εD∞, often designated ε∞, and not related to ionic transport. It is shown that εD∞ precludes scaling of Mdat″(ω) for ionic materials when the mobile-charge concentration varies. When the effects of εD∞ are properly removed from the data, however, such scaling is viable. Only the σ′(ω) and ε″(ω) parts of immittance response are uninfluenced by εD∞. Thus, scaling is possible for experimental σ′(ω) data sets under concentration variation if the shape parameter of a well-fitting model remains constant and if any parts of the response not associated with bulk ionic transport are eliminated. Comparison between the predictions of the original-modulus-formalism (OMF) response model of 1972–1973 and a corrected version of it that takes proper account of εD∞, the corrected modulus formalism (CMF), demonstrates that the role played by εD∞ (or ε∞) in the OMF is incorrect. Detailed fitting of data for three different ionic glasses using a Kohlrausch–Williams–Watts response model, the KWW1, for OMF and CMF analysis clearly demonstrates that the OMF leads to inconsistent shape-parameter (β1) estimates and the CMF does not. The CMF KWW1 model is shown to subsume, correct, and generalize the recent disparate scaling/fitting approaches of Sidebottom, León, Roling, and Ngai.

The estimation of extreme quantiles of wind velocity using L-moments in the peaks-over-threshold approach

The paper evaluates the effectiveness of the method of L-moments for estimating parameters of the Pareto distribution model of peaks over a sufficiently high threshold, and compares its performance against a widely used method of de Haan (de Haan L. Extreme value statistics. In: Galambos J, Lechner J, Simin E, editor. Extreme value theory and applications, vol. 1. 1994. p. 93–122). Monte Carlo simulations and actual wind speed data collected at various stations in the United States have been utilized in this study. In the de Haan method, the first two moments of peaks of log-transformed data are used for the parameter estimation, whereas the L-moment method utilizes linear combinations of expectations of order statistics of peaks in the original data. Despite the procedural differences, the paper shows that the de Haan and two L-moments based estimates of the tail shape parameter are in fairly close agreement in simulated data as well as in the US wind speed data. Furthermore, higher order estimates of the shape parameter are obtained using the L-skewness of peaks data. Such estimates appear to provide a more stable upper bound, which can be useful in identifying meaningful values of design quantiles.

映像情報の検索技術と編集処理 Ｓｈａｐｅ‐ｆｒｏｍ‐ｔｅｘｔｕｒｅ手法による３次元運動推定と移動前後のテクセル間の対応付けに基づく形状復元

This paper proposes a method for estimating three-dimensional (3D) motion parameters of a rigid object, of which surface is covered with a texture, by three images from a single camera. The method estimates unit normal vectors of texels and the 3D shape of the rigid object in each image by using a Shape-from-Texture technique. The rotation parameters are obtained from average vectors of the normal vectors at the three images. The translation parameters are determined as the displacement between the centroids of successive shapes. Based on the 3D motion parameters, a correspondence between texels in successive images is established. The correspondence can provide a more exact shape of the object through stereo triangulation. The estimation of exact shape and 3D motion parameters should prove to be useful technique for the content-based image retrieval.

Compact and parametric shape representation by a tree of sigmoid functions for automatic shape modeling

A modeling method to represent an object shape by a tree of sigmoid functions, and a gradient-descent-based searching procedure to estimate shape parameters are described. The model's unique feature is that it can produce a shape parameterized with a gain parameter determining the resolution of the represented shape. With a large gain value, the model represents a detailed shape with a sharp edge, which is described by a piecewise combination of lines and curves. With a small gain value, it generates a blurred shape, which has explicit (analytic) forms of partial derivaties with respect to parameters describing the shape. Using the model's differentiable property, the gradient-descent-based searching method updates the shape parameters and the gain parameter simultaneously so that an optimal set of shape parameters which makes the model fit to a target shape is found through a coarse-to-fine search. Previous shape description techniques were either contour-based (spline, active contour, wireframe, polygon and so on) or expansion-based (wavelet, radial basis function, eigenfunction and so on). The method has a dual modal nature with its capability of dealing with sharp edges and its differentiable and resolution adjustable nature. The model's performance was evaluated by some coarse-to-fine shape modeling simulations and its efficiency and robustness were verified.

The apparent and intrinsic shape of the APM galaxy clusters

methods. The first method is based on moments of the discrete galaxy distribution while the second is based on moments of the smoothed galaxy distribution. We study the performance of both methods using Monte Carlo cluster simulations covering the range of APM cluster distances and including a random distribution of background galaxies. We find that the first method suffers from severe systematic biases, whereas the second is more reliable. After excluding clusters dominated by substructure and quantifying the systematic biases in our estimated shape parameters, we recover a corrected distribution of projected ellipticities. We use the non-parametric kernel method to estimate the smooth apparent ellipticity distribution, and numerically invert a set of integral equations to recover the corresponding distribution of intrinsic ellipticities under the assumption that the clusters are either oblate or prolate spheroids. The prolate spheroidal model fits the APM cluster data best.

Differences of tensile strength distribution between mechanically high-grade and low-grade Japanese larch lumber I: Effect of length on the strength of lumber

An experimental study was conducted to evaluate the effect of length on the parallel-to-grain tensile strength of Japanese larch (Larix kaempferi, Carriere) lumber. Six hundred pieces of mechanically graded lumber were tested at gauge lengths of 60, 100, and 180 cm. The lumber was sorted into matched groups according to the dynamic Young's modulus measured by the longitudinal vibration method before the lumber was cut to the particular length. The averages of the dynamic Young's modulus of high-grade (H) and low-grade (L) specimens were 12.8 and 7.5 GPa, respectively. Using nonparametric estimates, the estimated length effect parameters of H and L were 0.268 and 0.304 for the 50th percentile and 0.121 and 0.256 for the 5th percentile, respectively. We then concluded that the different length effect factors between H and L could be used when using the lumber for practical purposes. The parameters of L were larger than those for H, and the parameters for 5th percentiles were smaller than the parameters for 50th percentiles. When two-parameter Weibull distribution functions were fitted to the strength data, the estimated shape parameters of the Weibull distribution by the parametric method were almost identifical to the inverse of nonparametric parameters except the 5th percentiles for H. The influence of defects such as knots on the lower tail of the strength distribution in H may be different from that in L.

The analysis of 2 × 2 factorial fracture experiments with brittle materials

Experiments conducted at all combinations of the levels of two or more factors are called factorial experiments. Factorial experiments have been shown to be more efficient in exploring the effects of external factors on a response variable than non-factorial arrangements of factor levels. This paper presents a methodology for the analysis of test results obtained at all combinations of the levels of two two-level factors. The response variable is assumed to follow the two parameter Weibull distribution with a shape parameter that, although unknown, does not vary with the factor levels. The scale parameter on the other hand may vary in various ways with the levels of the factors. These assumptions well reflect the behavior of the fracture strength of glassy polymers as it is influenced by factors such as water sorption and silanation of filler. The purpose of the analysis is (1) to compute interval estimates of the common shape parameter and (2) to assess whether either factor singly or in combination with the other affects the Weibull scale parameter. The procedure is illustrated with an example using simulated data for which only one of the factors had a real effect. A further example is given using shear strength measurements made in a 22 factorial experiment conducted on a glassy polymer material used in dental restorations.

ML parameter estimation for Markov random fields with applications to Bayesian tomography

Markov random fields (MRF's) have been widely used to model images in Bayesian frameworks for image reconstruction and restoration. Typically, these MRF models have parameters that allow the prior model to be adjusted for best performance. However, optimal estimation of these parameters(sometimes referred to as hyper parameters) is difficult in practice for two reasons: i) direct parameter estimation for MRF's is known to be mathematically and numerically challenging; ii)parameters can not be directly estimated because the true image cross section is unavailable.In this paper, we propose a computationally efficient scheme to address both these difficulties for a general class of MRF models,and we derive specific methods of parameter estimation for the MRF model known as generalized Gaussian MRF (GGMRF).The first section of the paper derives methods of direct estimation of scale and shape parameters for a general continuously valued MRF. For the GGMRF case, we show that the ML estimate of the scale parameter, sigma, has a simple closed-form solution, and we present an efficient scheme for computing the ML estimate of the shape parameter, p, by an off-line numerical computation of the dependence of the partition function on p.The second section of the paper presents a fast algorithm for computing ML parameter estimates when the true image is unavailable. To do this, we use the expectation maximization(EM) algorithm. We develop a fast simulation method to replace the E-step, and a method to improve parameter estimates when the simulations are terminated prior to convergence.Experimental results indicate that our fast algorithms substantially reduce computation and result in good scale estimates for real tomographic data sets.

Longitudinal analysis of deciduous tooth emergence: II. Parametric survival analysis in Bangladeshi, Guatemalan, Japanese, and Javanese children

We present a form of parametric survival analysis that incorporates exact, interval-censored, and right-censored times to deciduous tooth emergence. The method is an extension of common cross-sectional procedures such as logit and probit analysis, so that data arising from mixed longitudinal and cross-sectional studies can be properly combined. We extended the method to incorporate and estimate a proportion of agenic teeth. While we concentrate on deciduous tooth emergence, the method is relevant to studies of permanent tooth emergence and other developmental events. Deciduous tooth emergence data were analyzed from four longitudinal studies. The samples are 1,271 rural Guatemalan children examined every three months up to age two and every six months thereafter as part of the INCAP study; 397 rural Bangladeshi children examined monthly to age one and quarterly thereafter as part of the Meheran Growth and Development Study; 468 rural Indonesian children examined monthly as part of the Ngaglik study; and 114 urban Japanese children examined monthly in studies from 1910 and 1920. Although all four studies were longitudinal, many observations from the Guatemala and Bangladesh studies were effectively cross-sectionally observed. Three different parametric forms were used to model the eruption process: a normal distribution, a lognormal distribution, and a lognormal distribution with age shifted to shortly after conception. All three distributions produced reliable estimates of central tendencies, but the shifted lognormal distribution produced the best overall estimates of shape (variance) parameters. Estimates of emergence were compared to other studies that used similar methods. Japanese children showed relatively fast emergence times for all teeth. Bangladeshi and Javanese children showed emergence times that were slower than are found in most previous studies. Estimates of agenesis were not significantly different from zero for most teeth. One or two central incisors showed significant agenesis that ranged from 0.1 to 0.8% in three of the samples; even so, failure to model the agenic proportion did not seriously bias the estimates. Am J Phys Anthropol 105:209–230, 1998. © 1998 Wiley-Liss, Inc.

Automatic segmentation of intravascular ultrasound images: A texture-based approach

Extraction of blood vessel boundaries from intravascular ultrasound images is essential in the quantitative analysis of cardiovascular functions. In this study, we are presenting a completely automated procedure for determining blood vessel borders. This approach uses textural operators to separate different tissue regions and morphological processing to refine extracted contours. The method was tested in a set of 29 intravascular ultrasound images obtained in vivo. To assess the performance of the method, we have compared the automatically processed images with the manual tracings, using three different criteria: correlation coefficient, match ratio, and relative error of computed shape parameters. In both contour detection and shape parameters estimation, the proposed method yielded consistently good results. Due to its robustness and accuracy, this approach is appropriate for clinical use, whereas computational efficiency of the method facilitates low-cost implementation.

Class-based recognition of 3D objects represented by volumetric primitives

This paper presents a novel approach to recognizing 3D complex objects that have similar geometric structure but belong to different subclasses. Test scenes are acquired by a laser striper as range images and the objects are modelled using a composite volumetric representation of superquadrics and geons. Matching is decomposed into two stages: first, an indexing scheme designed to make effective use of the symbolic keys of the representation is implemented in order to direct the search to the models containing the parts identified; second, a method is proposed where the hypotheses picked from the index are searched using an Interpretation Tree algorithm combined with a quality measure to evaluate the bindings and the final valid hypotheses based on Possibility Theory, or the Theory of Fuzzy Sets. The valid hypotheses ranked by the matching process are then passed to the pose estimation module. From the results shown here, we can conclude that shape and pose parameter estimation from range data is sufficiently accurate to allow the algorithms used here to discriminate between objects having the same general topology, but different specific shapes.