Iterative Refinement Algorithm Research Articles

Visualizing Geographic Classifications Using Color

This paper presents the cartographic elements of a system for classifying and visualizing high-dimensional geographic datasets. The system has been developed as part of the Land Ocean Interactions in the Coastal Zone (LOICZ) project. The goal of the system is to develop regional and global typologies of coastal zones using large multi-variable datasets. Our implementation bring together statistical clustering algorithms with visualization capabilities to allow easy analysis and comprehension of the result. The two main tasks of the visualization are to allow for discrimination of multiple classes and to show relationships between those classes. These are accomplished in two different visual presentations. In both cases, the system selects colors appropriate to the purpose. In the latter case — showing relationships — the system uses a novel iterative refinement algorithm to select the colors. The result show that the system is successful at both generation the classes and visualizing the relationships between them.

General Object Reconstruction Based on Simplex Meshes

In this paper, we propose a general tridimensional reconstruction algorithm of range and volumetric images, based on deformable simplex meshes. Simplex meshes are topologically dual of triangulations and have the advantage of permitting smooth deformations in a simple and efficient manner. Our reconstruction algorithm can handle surfaces without any restriction on their shape or topology. The different tasks performed during the reconstruction include the segmentation of given objects in the scene, the extrapolation of missing data, and the control of smoothness, density, and geometric quality of the reconstructed meshes. The reconstruction takes place in two stages. First, the initialization stage creates a simplex mesh in the vicinity of the data model either manually or using an automatic procedure. Then, after a few iterations, the mesh topology can be modified by creating holes or by increasing its genus. Finally, an iterative refinement algorithm decreases the distance of the mesh from the data while preserving high geometric and topological quality. Several reconstruction examples are provided with quantitative and qualitative results.

Modeling Train Delays in Urban Networks

The reliability of urban passenger trains is a critical performance measure for passenger satisfaction and ultimately market share. A delay to one train in a peak period can have a severe effect on the schedule adherence of other trains. This paper presents an analytically based model to quantify the expected positive delay for individual passenger trains and track links in an urban rail network. The model specifically addresses direct delay to trains, knock-on delays to other trains, and delays at scheduled connections. A solution to the resultant system of equations is found using an iterative refinement algorithm. Model validation, which is carried out using a real-life suburban train network consisting of 157 trains, shows the model estimates to be on average within 8% of those obtained from a large scale simulation. Also discussed, is the application of the model to assess the consequences of increased scheduled slack time as well as investment strategies designed to reduce delay.

Iterative refinement of parameter estimates and residuals from a regression model fitted using QR decomposition methods

Algorithms for iteratively refining the parameter estimates and residuals from the fitting of a regression model using QR decomposition methods are described. It is shown that if square root free algorithms for performing the QR decomposition are used the related iterative refinement algorithms can also be square root free. Testing of the algorithms is carried out and comments made about accuracies of parameter estimates.

Active Shape Models-Their Training and Application

Model-based vision is firmly established as a robust approach to recognizing and locating known rigid objects in the presence of noise, clutter, and occlusion. It is more problematic to apply model-based methods to images of objects whose appearance can vary, though a number of approaches based on the use of flexible templates have been proposed. The problem with existing methods is that they sacrifice model specificity in order to accommodate variability, thereby compromising robustness during image interpretation. We argue that a model should only be able to deform in ways characteristic of the class of objects it represents. We describe a method for building models by learning patterns of variability from a training set of correctly annotated images. These models can be used for image search in an iterative refinement algorithm analogous to that employed by Active Contour Models (Snakes). The key difference is that our Active Shape Models can only deform to fit the data in ways consistent with the training set. We show several practical examples where we have built such models and used them to locate partially occluded objects in noisy, cluttered images.

Iterative refinement for constrained and weighted linear least squares

We present an algorithm for mixed precision iterative refinement on the constrained and weighted linear least squares problem, the CWLSQ problem. The approximate solution is obtained by solving the CWLSQ problem with the weightedQR factorization [6]. With backward errors for the weightedQR decomposition together with perturbation bounds for the CWLSQ problem we analyze the convergence behaviour of the iterative refinement procedure.

Schwarz alternating and iterative refinement methods for mixed formulations of elliptic problems, part II: Convergence theory

In this paper we discuss bounds for the convergence rates of several domain decomposition algorithms to solve symmetric, indefinite linear systems arising from mixed finite element discretizations of elliptic problems. The algorithms include Schwarz methods and iterative refinement methods on locally refined grids. The implementation of Schwarz and iterative refinement algorithms have been discussed in part I. A discussion on the stability of mixed discretizations on locally refined grids is included and quantiative estimates for the convergence rates of some iterative refinement algorithms are also derived.