Cluster-Wise Ratio Tests for Fast Camera Localization

Feature point matching for camera localization suffers from scalability problems. Even when feature descriptors associated with 3D scene points are locally unique, as coverage grows, similar or repeated features become increasingly common. As a result, the standard distance ratio-test used to identify reliable image feature points is overly restrictive and rejects many good candidate matches. We propose a simple coarse-to-fine strategy that uses conservative approximations to robust local ratio-tests that can be computed efficiently using global approximate k-nearest neighbor search. We treat these forward matches as votes in camera pose space and use them to prioritize back-matching within candidate camera pose clusters, exploiting feature co-visibility captured by clustering the 3D model camera pose graph. This approach achieves state-of-the-art camera localization results on a variety of popular benchmarks, outperforming several methods that use more complicated data structures and that make more restrictive assumptions on camera pose. We also carry out diagnostic analyses on a difficult test dataset containing globally repetitive structure that suggest our approach successfully adapts to the challenges of large-scale image localization

Characterization and Reduction of Noise in Manifold Representations of Hyperspectral Imagery

A new workflow to produce dimensionality reduced manifold coordinates based on the improvements of landmark Isometric Mapping (ISOMAP) algorithms using local spectral models is proposed. Manifold space from nonlinear dimensionality reduction better addresses the nonlinearity of the hyperspectral data and often has better per- formance comparing to the results of linear methods such as Minimum Noise Fraction (MNF). The dissertation mainly focuses on using adaptive local spectral models to fur- ther improve the performance of ISOMAP algorithms by addressing local noise issues and perform guided landmark selection and nearest neighborhood construction in local spectral subsets. This work could benefit the performance of common hyperspectral image analysis tasks, such as classification, target detection, etc., but also keep the computational burden low. This work is based on and improves the previous ENH- ISOMAP algorithm in various ways. The workflow is based on a unified local spectral subsetting framework. Embedding spaces in local spectral subsets as local noise models are first proposed and used to perform noise estimation, MNF regression and guided landmark selection in a local sense. Passive and active methods are proposed and ver- ified to select landmarks deliberately to ensure local geometric structure coverage and local noise avoidance. Then, a novel local spectral adaptive method is used to construct the k-nearest neighbor graph. Finally, a global MNF transformation in the manifold space is also introduced to further compress the signal dimensions. The workflow is implemented using C++ with multiple implementation optimizations, including using heterogeneous computing platforms that are available in personal computers. The re- sults are presented and evaluated by Jeffries-Matsushita separability metric, as well as the classification accuracy of supervised classifiers. The proposed workflow shows sig- nificant and stable improvements over the dimensionality reduction performance from traditional MNF and ENH-ISOMAP on various hyperspectral datasets. The computa- tional speed of the proposed implementation is also improved

Low-Rank Isomap Algorithm

The Isomap is a well-known nonlinear dimensionality reduction method that highly suffers from computational complexity. Its computational complexity mainly arises from two stages; a) embedding a full graph on the data in the ambient space, and b) a complete eigenvalue decomposition. Although the reduction of the computational complexity of the graphing stage has been investigated, yet the eigenvalue decomposition stage remains a bottleneck in the problem. In this paper, we propose the Low-Rank Isomap algorithm by introducing a projection operator on the embedded graph from the ambient space to a low-rank latent space to facilitate applying the partial eigenvalue decomposition. This approach leads to reducing the complexity of Isomap to a linear order while preserving the structural information during the dimensionality reduction process. The superiority of the Low-Rank Isomap algorithm compared to some state-of-art algorithms is experimentally verified on facial image clustering in terms of speed and accuracy