Colored Point Cloud Registration by Depth Filtering

In the last stage of colored point cloud registration, depth measurement errors hinder the achievement of accurate and visually plausible alignments. Recently, an algorithm has been proposed to extend the Iterative Closest Point (ICP) algorithm to refine the measured depth values instead of the pose between point clouds. However, the algorithm suffers from numerical instability, so a postprocessing step is needed to restrict erroneous output depth values. In this paper, we present a new algorithm with improved numerical stability. Unlike the previous algorithm heavily relying on point-to-plane distances, our algorithm constructs a cost function based on an adaptive combination of two different projected distances to prevent numerical instability. We address the problem of registering a source point cloud to the union of the source and reference point clouds. This extension allows all source points to be processed in a unified filtering framework, irrespective of the existence of their corresponding points in the reference point cloud. The extension also improves the numerical stability of using the point-to-plane distances. The experiments show that the proposed algorithm improves the registration accuracy and provides high-quality alignments of colored point clouds.

The Stability of Linear Diffusion Acceleration Relative to CMFD

Coarse Mesh Finite Difference (CMFD) is a widely-used iterative acceleration method for neutron transport problems in which nonlinear terms are introduced in the derivation of the low-order CMFD diffusion equation. These terms, including the homogenized diffusion coefficient, the current coupling coefficients, and the multiplicative prolongation constant, are subject to numerical instability when a scalar flux estimate becomes sufficiently small or negative. In this paper, we use a suite of contrived problems to demonstrate the susceptibility of CMFD to failure for each of the vulnerable quantities of interest. Our results show that if a scalar flux estimate becomes negative in any portion of phase space, for any iterate, numerical instability can occur. Specifically, the number of outer iterations required for convergence of the CMFD-accelerated transport problem can increase dramatically, or worse, the iteration scheme can diverge. An alternative Linear Diffusion Acceleration (LDA) scheme addresses these issues by explicitly avoiding local nonlinearities. Our numerical results show that the rapid convergence of LDA is unaffected by the very small or negative scalar flux estimates that can adversely affect the performance of CMFD. Therefore, our results demonstrate that LDA is a robust alternative to CMFD for certain sensitive problems in which CMFD can exhibit reduced effectiveness or failure.

About the Solution of the Numerical Instability for Topological Solitons with Long Range Interaction

The computations of solutions of the field equations in the Model of Topological Particles, formulated with a scalar SU(2)-field, have shown instabilities leading to discrepancies between the numerical and analytical solutions. We identify the origin of these deviations in misalignments of the rotational axes corresponding to the SU(2) elements. The system of a single soliton we use as an example to show that a constraint suppressing the wave-like disturbances is able to lead to excellent agreement between the result of the numerical minimisation procedure and the analytical solution.

Stable Identification of Sources Located on Interface of Nonhomogeneous Media

This paper presents a stable method for the identification of sources located on the separation interface of two homogeneous media (where one of them is contained by the other one), from measurement yielded by those sources on the exterior boundary of the media. This is an ill-posed problem because numerical instability is presented, i.e., minimal errors in the measurement can result in significant changes in the solution. To obtain the proposed stable method the identification problem is categorized into three subproblems, two of which present numerical instability and regularization methods must be applied to obtain their solution in a stable form. To manage the numerical instability due to the ill-posedness of these subproblems, the Tikhonov regularization and sequential smoothing methods are used. We illustrate this methodology in a circular and irregular region to demonstrate the feasibility of the proposed method, which yields convergent and stable solutions for input data with and without noise.

InChI version 1.06: now more than 99.99% reliable

The software for the IUPAC Chemical Identifier, InChI, is extraordinarily reliable. It has been tested on large databases around the world, and has proved itself to be an essential tool in the handling and integration of large chemical databases. InChI version 1.05 was released in January 2017 and version 1.06 in December 2020. In this paper, we report on the current state of the InChI Software, the details of the improvements in the v1.06 release, and the results of a test of the InChI run on PubChem, a database of more than a hundred million molecules. The upgrade introduces significant new features, including support for pseudo-element atoms and an improved description of polymers. We expect that few, if any, applications using the standard InChI will need to change as a result of the changes in version 1.06. Numerical instability was discovered for 0.002% of this database, and a small number of other molecules were discovered for which the algorithm did not run smoothly. On the basis of PubChem data, we can demonstrate that InChI version 1.05 was 99.996% accurate, and InChI version 1.06 represents a step closer to perfection. Finally, we look forward to future releases and extensions for the InChI Chemical identifier.