A convenient look-up-table based method for the compensation of non-linear error in digital fringe projection

Although the structured light system that uses digital fringe projection has been widely implemented in three-dimensional surface profile measurement, the measurement system is susceptible to non-linear error. In this work, we propose a convenient look-up-table-based （LUT-based） method to compensate for the non-linear error in captured fringe patterns. Without extra calibration, this LUT-based method completely utilizes the captured fringe pattern by recording the full-field differences. Then, a phase compensation map is established to revise the measured phase. Experimental results demonstrate that this method works effectively.

A class of fully third-order accurate projection methods for solving the incompressible Navier-Stokes equations

In this paper, a fully third-order accurate projection method for solving the incompressible Navier-Stokes equations is proposed. To construct the scheme, a continuous projection procedure is firstly presented. We then derive a sufficient condition for the continuous projection equations to be temporally third-order accurate approximations of the original Navier-Stokes equations by means of the localtruncation-error-analysis technique. The continuous projection equations are discretized temporally and spatially to third-order accuracy on the staggered grids, resulting in a fully third-order discrete projection scheme. The possibility to design higher-order projection methods is thus demonstrated in the present paper. A heuristic stability analysis is performed on this projection method showing the probability of its being stable. The stability of the present scheme is further verified through numerical tests. The third-order accuracy of the present projection method is validated by several numerical test cases.

Exploring visual quality of multidimensional time series projections

Dimensionality reduction is often used to project time series data from multidimensional to two-dimensional space to generate visual representations of the temporal evolution.In this context,we address the problem of multidimensional time series visualization by presenting a new method to show and handle projection errors introduced by dimensionality reduction techniques on multidimensional temporal data.For visualization,subsequent time instances are rendered as dots that are connected by lines or curves to indicate the temporal dependencies.However,inevitable projection artifacts may lead to poor visualization quality and misinterpretation of the temporal information.Wrongly projected data points,inaccurate variations in the distances between projected time instances,and intersections of connecting lines could lead to wrong assumptions about the original data.We adapt local and global quality metrics to measure the visual quality along the projected time series,and we introduce a model to assess the projection error at intersecting lines.These serve as a basis for our new uncertainty visualization techniques that use different visual encodings and interactions to indicate,communicate,and work with the visualization uncertainty from projection errors and artifacts along the timeline of data points,their connections,and intersections.Our approach is agnostic to the projection method and works for linear and non-linear dimensionality reduction methods alike.

Seven possible states of geospatial data with respect to map projection and definition: a novel pedagogical device for GIS education

Conceptually,the theory and implementation of“map projection”in geographic information system(GIS)technology is difficult to comprehend for most introductory students and novice users.Compounding this difficulty is the concept of a“map projection file”that defines map projection parameters of geo-spatial data.The problem of the“missing projection file”appears ubiquitous for all users,especially in practice where data is widely shared.Another common problem is inadvertent misapplication of the“Define Projection”tool that can result in a GIS dataset with an incorrectly defined map projection file.GIS education should provide more guidance in differentiating the concepts of map projection versus projection files by increasing understanding and minimizing common errors.A novel pedagogical device is introduced in this paper:the seven possible states of GIS data with respect to map projection and definition.The seven possible states are:(1)a projected coordinate system(PCS)that is correctly defined,(2)a PCS that is incorrectly defined,(3)a PCS that is undefined,(4)a geographic coordinate system(GCS)that is correctly defined,(5)a GCS that is incorrectly defined,(6)a GCS that is undefined,and(7)a non-GCS.Recently created automated troubleshooting tools to determine a missing map projection file are discussed.