Exact Covers via Determinants

Given a k-uniform hypergraph on n vertices, partitioned in k equal parts such that every hyperedge includes one vertex from each part, the k-dimensional matching problem asks whether there is a disjoint collection of the hyperedges which covers all vertices. We show it can be solved by a randomized polynomial space algorithm in time O*(2^(n(k-2)/k)). The O*() notation hides factors polynomial in n and k. When we drop the partition constraint and permit arbitrary hyperedges of cardinality k, we obtain the exact cover by k-sets problem. We show it can be solved by a randomized polynomial space algorithm in time O*(c_k^n), where c_3=1.496, c_4=1.642, c_5=1.721, and provide a general bound for larger k. Both results substantially improve on the previous best algorithms for these problems, especially for small k, and follow from the new observation that Lovasz' perfect matching detection via determinants (1979) admits an embedding in the recently proposed inclusion-exclusion counting scheme for set covers, despite its inability to count the perfect matchings

Structured Light-Based 3D Reconstruction System for Plants.

Camera-based 3D reconstruction of physical objects is one of the most popular computer vision trends in recent years. Many systems have been built to model different real-world subjects, but there is lack of a completely robust system for plants. This paper presents a full 3D reconstruction system that incorporates both hardware structures (including the proposed structured light system to enhance textures on object surfaces) and software algorithms (including the proposed 3D point cloud registration and plant feature measurement). This paper demonstrates the ability to produce 3D models of whole plants created from multiple pairs of stereo images taken at different viewing angles, without the need to destructively cut away any parts of a plant. The ability to accurately predict phenotyping features, such as the number of leaves, plant height, leaf size and internode distances, is also demonstrated. Experimental results show that, for plants having a range of leaf sizes and a distance between leaves appropriate for the hardware design, the algorithms successfully predict phenotyping features in the target crops, with a recall of 0.97 and a precision of 0.89 for leaf detection and less than a 13-mm error for plant size, leaf size and internode distance

Higher-order Projected Power Iterations for Scalable Multi-Matching

The matching of multiple objects (e.g. shapes or images) is a fundamental problem in vision and graphics. In order to robustly handle ambiguities, noise and repetitive patterns in challenging real-world settings, it is essential to take geometric consistency between points into account. Computationally, the multi-matching problem is difficult. It can be phrased as simultaneously solving multiple (NP-hard) quadratic assignment problems (QAPs) that are coupled via cycle-consistency constraints. The main limitations of existing multi-matching methods are that they either ignore geometric consistency and thus have limited robustness, or they are restricted to small-scale problems due to their (relatively) high computational cost. We address these shortcomings by introducing a Higher-order Projected Power Iteration method, which is (i) efficient and scales to tens of thousands of points, (ii) straightforward to implement, (iii) able to incorporate geometric consistency, (iv) guarantees cycle-consistent multi-matchings, and (iv) comes with theoretical convergence guarantees. Experimentally we show that our approach is superior to existing methods

Keyframe-based monocular SLAM: design, survey, and future directions

Extensive research in the field of monocular SLAM for the past fifteen years has yielded workable systems that found their way into various applications in robotics and augmented reality. Although filter-based monocular SLAM systems were common at some time, the more efficient keyframe-based solutions are becoming the de facto methodology for building a monocular SLAM system. The objective of this paper is threefold: first, the paper serves as a guideline for people seeking to design their own monocular SLAM according to specific environmental constraints. Second, it presents a survey that covers the various keyframe-based monocular SLAM systems in the literature, detailing the components of their implementation, and critically assessing the specific strategies made in each proposed solution. Third, the paper provides insight into the direction of future research in this field, to address the major limitations still facing monocular SLAM; namely, in the issues of illumination changes, initialization, highly dynamic motion, poorly textured scenes, repetitive textures, map maintenance, and failure recovery

Multi-Image Semantic Matching by Mining Consistent Features

This work proposes a multi-image matching method to estimate semantic correspondences across multiple images. In contrast to the previous methods that optimize all pairwise correspondences, the proposed method identifies and matches only a sparse set of reliable features in the image collection. In this way, the proposed method is able to prune nonrepeatable features and also highly scalable to handle thousands of images. We additionally propose a low-rank constraint to ensure the geometric consistency of feature correspondences over the whole image collection. Besides the competitive performance on multi-graph matching and semantic flow benchmarks, we also demonstrate the applicability of the proposed method for reconstructing object-class models and discovering object-class landmarks from images without using any annotation.Comment: CVPR 201

FLAT2D: Fast localization from approximate transformation into 2D

Many autonomous vehicles require precise localization into a prior map in order to support planning and to leverage semantic information within those maps (e.g. that the right lane is a turn-only lane.) A popular approach in automotive systems is to use infrared intensity maps of the ground surface to localize, making them susceptible to failures when the surface is obscured by snow or when the road is repainted. An emerging alternative is to localize based on the 3D structure around the vehicle; these methods are robust to these types of changes, but the maps are costly both in terms of storage and the computational cost of matching. In this paper, we propose a fast method for localizing based on 3D structure around the vehicle using a 2D representation. This representation retains many of the advantages of "full" matching in 3D, but comes with dramatically lower space and computational requirements. We also introduce a variation of Graph-SLAM tailored to support localization, allowing us to make use of graph-based error-recovery techniques in our localization estimate. Finally, we present real-world localization results for both an indoor mobile robotic platform and an autonomous golf cart, demonstrating that autonomous vehicles do not need full 3D matching to accurately localize in the environment