Progressive Structure from Motion by Iteratively Prioritizing and Refining Match Pairs

Structure from motion (SfM) has been treated as a mature technique to carry out the task of image orientation and 3D reconstruction. However, it is an ongoing challenge to obtain correct reconstruction results from image sets consisting of problematic match pairs. This paper investigated two types of problematic match pairs, stemming from repetitive structures and very short baselines. We built a weighted view-graph based on all potential match pairs and propose a progressive SfM method (PRMP-PSfM) that iteratively prioritizes and refines its match pairs (or edges). The method has two main steps: initialization and expansion. Initialization is developed for reliable seed reconstruction. Specifically, we prioritize a subset of match pairs by the union of multiple independent minimum spanning trees and refine them by the idea of cycle consistency inference (CCI), which aims to infer incorrect edges by analyzing the geometric consistency over cycles of the view-graph. The seed reconstruction is progressively expanded by iteratively adding new minimum spanning trees and refining the corresponding match pairs, and the expansion terminates when a certain completeness of the block is achieved. Results from evaluations on several public datasets demonstrate that PRMP-PSfM can successfully accomplish the image orientation task for datasets with repetitive structures and very short baselines and can obtain better or similar accuracy of reconstruction results compared to several state-of-the-art incremental and hierarchical SfM methods.

Overview of Network-based Methods for Analyzing Financial Markets

Network based methods are suitable for the analysis of a large number of financial time series and a better understanding of their interdependencies. Known approaches to reveal the underlying information about the complex structure of these interdependencies include network-wise and vertex-wise measures of the topology, as well as filtering techniques relying on minimum spanning trees, planar graphs, or spectral analysis. The aim of this study is to review relevant graph theoretical and statistical models and techniques for generating and examining the properties of financial networks, obtained by computing time series correlations or causality relationships. In particular, this study reviews literature discussing the time evolution of the observed phenomena from a network perspective, as well as applications in economy and finance, ranging from risk and diversification, through policy making and better understanding crisis impact, to forecasting. The information synthesized in this paper can be useful to gain further insights into this relatively new research area.