Variational Bayesian noise estimation of point sets

ABSTRACTThis paper proposes a novel method for register partially overlapped three-dimensional (3D) point sets when a complete 3D scanned model is constructed from partially scanned 3D point sets. 3D point sets are the most primitive and fundamental surface representations. 3D acquisition devices such as laser scanners and range image finders are popular sources for acquiring point clouds. With the availability of low cost and highly efficient 3D laser scanners, the popularity of such devices is increasing rapidly in various fields. Generally, a standard scanner can obtain only a partial data to build a complete 3D model of the object. These partially scanned 3D patches need to be aligned together in the same coordinate system to construct a complete 3D model, and this process is widely known as registration. A coarse-to-fine alignment technique is proposed to register two partially overlapped point sets. First, the overlapping regions using a novel sampling strategy are identified and the overlapping regions of two point sets are aligned together. Second, fine registration is carried out, in which an auxiliary pair and surface normal constraints are used to find reliable corresponding points in order to achieve higher accuracy.

Given multiple image data from a set of points in 3D, there are two fundamental questions that can be addressed: (1) What is the structure of the set of points in 3D? (2) What are the positions of the cameras relative to the points? In this paper, we show that for projective views and with structure- and position-defined modulo linear transformations, these problems are are dual in the sense that their solution arises from constraint equations where space point and camera positions occur in a reciprocal way. The problem of computing camera positions from m points in n views can be solved with the same algorithm as the problem of directly reconstructing n+4 points in m-4 views. This unifies different approaches for projective reconstruction: methods based on external calibration and direct methods exploiting constraints that exist between space and image invariants.

A comprehensive understanding of surface reconstruction was critical to developing high performance lattice oxygen oxidation mechanism (LOM) based perovskite electrocatalysts. Traditionally, the primary determining factor of the surface reconstruction process was believed to be the oxygen vacancy formation energy. Hence, most previous studies focused on optimizing composition to reduce the oxygen vacancies formation energy, which in turn facilitated the surface reconstruction process. Here, for the first time, we found that adding oxyanions (SO42-, CO32-, NO3-) into the electrolyte could effectively regulate the solid-liquid interface, significantly accelerating the surface reconstruction process and enhancingoxygen evolution reaction (OER) activities. Further studies indicated that the added oxyanions would adsorb onto the solid-liquid interface layer, disrupting the dynamic equilibrium between the adsorbed OH- ions and the OH- ions generated during surface reconstruction process. As such, the OH- ions generated during surface reconstruction process could be more readily released into the electrolyte, thereby leading to an acceleration of the surface reconstruction. Thus, it was expected that our finding would provide a new layer of understanding to the surface reconstruction process in LOM-based perovskite electrocatalysts.

This paper presents a new method that combines a medial axis and implicit surfaces in order to reconstruct a 3D solid from an unstructured set of points scattered on the object's surface. The representation produced is based on iso‐surfaces generated by skeletons, and is a particularly compact way of defining a smooth free‐form solid. The method is based on the minimisation of an energy representing a “distance” between the set of data points and the iso‐surface, resembling previous reserach19. Initialisation, however, is more robust and efficient since there is computation of the medial axis of the set of points. Instead of subdividing existing skeletons in order to refine the object's surface, a new reconstruction algorithm progressively selects skeleton‐points from the pre‐ computed medial axis using an heuristic principle based on a “local energy” criterion. This drastically speeds up the reconstruction process. Moreover, using the medial axis allows reconstruction of objects with complex topology and geometry, like objects that have holes and branches or that are composed of several connected components. This process is fully automatic. The method has been successfully applied to both synthetic and real data.

In this work we consider 3D point sets, which in a typical setting represent unorganized point clouds. Segmentation of these point sets requires first to single out structural components of the unknown surface discretely approximated by the point cloud. Structural components, in turn, are surface patches approximating unknown parts of elementary geometric structures, such as planes, ellipsoids, spheres and so on. The approach used is based on level set methods computing the moving front of the surface and tracing the interfaces between different parts of it. Level set methods are widely recognized to be one of the most efficient methods to segment both 2D images and 3D medical images. Level set methods for 3D segmentation have recently received an increasing interest. We contribute by proposing a novel approach for raw point sets. Based on the motion and distance functions of the level set we introduce four energy minimization models, which are used for segmentation, by considering an equal number of distance functions specified by geometric features. Finally we evaluate the proposed algorithm on point sets simulating unorganized point clouds.

We develop expressions for measuring the distance between 2D point sets, which are invariant to either 2D affine transformations or 2D similarity transformations of the sets, and assuming a known correspondence between the point sets. We discuss the image normalization to be applied to the images before their comparison so that the computed distance is symmetric with respect to the two images. We then give a general (metric) definition of the distance between images, which leads to the same expressions for the similarity and affine cases. This definition avoids ad hoc decisions about normalization. Moreover, it makes it possible to compute the distance between images under different conditions, including cases where the images are treated asymmetrically. We demonstrate these results with real and simulated images.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Finding a new drug which is both safe and efficient is an expensive and time-consuming endeavour. In particular, establishing the ‘dose-effect relationship’ – how beneficial a drug is at different dosages – can be challenging. Predicting this curve requires gathering experimental data by exposing and recording how cells respond to various levels of the drug. However, extreme values are often observed at low and high dosages, potentially introducing errors that are hard to correct in the prediction process. Yet, these extreme observations are sometimes genuine so researchers cannot just ignore them. To improve dose-effect estimation, Zhou, Liu, Fang et al. developed a new general-purpose approach. It uses advanced statistical modelling to account for extremes in lab data. This strategy outperformed other methods when dealing with these observations while also providing higher efficiency in data analysis with more uniform data in experiments. To facilitate implementation, Zhou, Liu, Fang et al. set up a user-friendly tool baptized ‘REAP’; this free online resource allows scientists without advanced statistical experience to harness the new approach and to perform dose-effect analysis more easily and accurately. This could boost research across many different disciplines that examine the effects of chemicals on cells.

The aim of this study is the determination of the best fit ellipsoid to given points by quaternions. The problem of the fitting ellipsoid is frequently encountered in image processing, computer games, medicine, engineering and science applications, geodesy, etc. The ellipsoid fitting problem is the process of determining the ellipsoid that best fits a given set of points in 3D. In the fitting process, it is generally done over two models. The first of these is the algebraic method and the second one is orthogonal (geometric) method. In this study, we tried to solve the problem of algebraic and orthogonal ellipsoid fitting based on Euler angles for the first time over quaternions. The superiority of quaternions over Euler rotation angles is well known. In addition, the variance–covariance matrix of the parameters of the fitted ellipsoid will also be calculated. Numerical applications show that the proposed method can be used successfully.

Our goal is the registration of multiple 3D point clouds obtained from LIDAR scans of underground mines. Such a capability is crucial to the surveying and planning operations in mining. Often, the point clouds only partially overlap and initial alignment is unavailable. Here, we propose an interactive user-assisted point cloud registration system. Guided by the system, the user's role is simply to identify and search for overlapping regions across the point clouds. Specifically, given two point sets, the user clicks on a point in one set, then simply hovers the mouse on the other set to find a matching point. Each mouse position gives rise to a translation, and our system instantly optimises the rotation that aligns the point clouds. Assuming that each individual point set is horizontally levelled with the ground by the level compensator on the LIDAR device, given a candidate 3D translation only one angular parameter needs to be estimated to rotationally align two 3D point sets. We propose a fast rotation search algorithm that delivers globally optimal results in real time. Our method conducts branch-and-bound optimisation with a novel bounding function whose evaluation amounts to simple sorted array operations. This provides smooth and accurate feedback to the user's search for overlapping regions. Our system is intuitive and helps to accelerate the registration of multiple scans.

The purpose of this paper is to develop parameter transformation strategies that improve the accuracy of the Variational Bayes (VB) approximation. The idea is to find a transformed metric in which coupling between parameters is reduced. Parameter orthogonalization methods from the statistical literature provide a starting point, but these are extended in the paper to yield transformed distributions more amenable to the independence approximation imposed by VB. Among other contexts, the Transformed VB approximation is applied successfully to (i) the normal inverse-gamma distribution central to Bayesian inference for (auto)regressive models, and (ii) the nonlinear context of sinusoidal frequency inference, where promising performance enhancements are reported.

Invariance against rotation of 3D objects is one of the essential properties for 3D shape analysis. Recently proposed algorithms have achieved rotationally invariant 3D point set analysis by using inherently rotation-invariant 3D shape features, i.e., distances and angles among 3D points, as input to Deep Neural Networks (DNNs). The DNNs capture spatial hierarchy and context among the geometric features to produce accurate analytical results. In this article, we delve further into the DNN-based approach to rotation-invariant and highly accurate 3D point set analysis. In particular, we focus our attention on segmentation of 3D point sets, which is one of the most challenging among 3D point set analysis tasks. We propose a novel DNN for 3D point set segmentation called Rotation-invariant and Multi-scale feature Graph convolutional neural network, or RMGnet. Our RMGnet is more flexible than the previous methods as it accepts as input any handcrafted 3D shape features having rotation invariance. In addition, to accurately segment 3D point sets composed of parts having various sizes, we randomize scales at which handcrafted features are extracted and perform multi-resolution analysis of the features by using the DNN. Experimental evaluation demonstrates high segmentation accuracy as well as rotation invariance of the proposed RMGnet.

Variational Bayesian Approximation (VBA) methods are recent tools for effective Bayesian computations. In this paper, these tools are used for inverse problems where the prior models include hidden variables and where where the estimation of the hyper parameters has also to be addressed. In particular two specific prior models (Student-t and mixture of Gaussian models) are considered and details of the algorithms are given.

Latent growth models (LGMs) are an application of structural equation modeling and frequently used in developmental and clinical research to analyze change over time in longitudinal outcomes. Maximum likelihood (ML), the most common approach for estimating LGMs, can fail to converge or may produce biased estimates in complex LGMs especially in studies with modest samples. Bayesian estimation is a logical alternative to ML for LGMs, but there is a lack of research providing guidance on when Bayesian estimation may be preferable to ML or vice versa. This study compared the performance of Bayesian versus ML estimators for LGMs by evaluating their accuracy via Monte Carlo (MC) simulations. For the MC study, longitudinal data sets were generated and estimated using LGM via both ML and Bayesian estimation with three different priors, and parameter recovery across the two estimators was evaluated to determine their relative performance. The findings suggest that ML estimation is a reasonable choice for most LGMs, unless it fails to converge, which can occur with limiting data situations (i.e., just a few time points, no covariate or outcome, modest sample sizes). When models do not converge using ML, we recommend Bayesian estimation with one caveat that the influence of the priors on estimation may have to be carefully examined, per recent recommendations on Bayesian modeling for applied researchers.

The pairwise comparisons or post-hoc methods are used for determining the source of the difference of group means in one-way ANOVA. These methods are mostly depend on normality assumption. However, nonnormal distributions are more prevalent than normal distribution. Therefore, robust estimation methods become very important tools in statistical analysis. In this paper, we assume that the distribution of the error terms is Azzalini's skew $t$ and obtain the robust estimators in order to make post-hoc tests in one-way ANOVA. We use maximum likelihood (ML) methodology and compare this methodology with some of robust estimators like M estimator, Wave estimator, trimmed mean and modified maximum likelihood (MML) methodology with Monte Carlo simulation study. Simulation results show that the proposed methodology is more preferable. We also compare power values of the test statistics and conclude that the test statistics based on the ML estimators are more powerful than the test statistics based on other methods.

This paper addresses the problem of segmenting an unstructured set of 3D points sampled from a physical model. Given such a set of points the first problem is that of creating a polyhedral approximation of the model. For that we introduce an algorithm which extends Boissonnat's work and generates a triangular surface approximation. The proposed method allows the reconstruction of objects with arbitrary genus and proposes an automatic termination procedure. The next step in the process concerns the segmentation of the data points into regions for which each may be fitted by a single surface. Here we summarize our experiences with a region growing technique based on angle between normals criteria. Using just first order derivative estimations it is shown that the method is able to classify segments into predefined second order surface classes.