arXiv subjects

Huu Le

Publications and source records attributed to Huu Le.

21 records · Page 2Linked to original sources

arXiv2018

A Binary Optimization Approach for Constrained K-Means Clustering

K-Means clustering still plays an important role in many computer vision problems. While the conventional Lloyd method, which alternates between centroid update and cluster assignment, is primarily used in practice, it may converge to a solution with empty clusters. Furthermore, some applications may require the clusters to satisfy a specific set of constraints, e.g., cluster sizes, must-link/cannot-link. Several methods have been introduced to solve constrained K-Means clustering. Due to the non-convex nature of K-Means, however, existing approaches may result in sub-optimal solutions that poorly approximate the true clusters. In this work, we provide a new perspective to tackle this problem. Particularly, we reconsider constrained K-Means as a Binary Optimization Problem and propose a novel optimization scheme to search for feasible solutions in the binary domain. This approach allows us to solve constrained K-Means where multiple types of constraints can be simultaneously enforced. Experimental results on synthetic and real datasets show that our method provides better clustering accuracy with faster runtime compared to several commonly used techniques.

cs.CV↗

arXiv2018

Deterministic Approximate Methods for Maximum Consensus Robust Fitting

Maximum consensus estimation plays a critically important role in robust fitting problems in computer vision. Currently, the most prevalent algorithms for consensus maximization draw from the class of randomized hypothesize-and-verify algorithms, which are cheap but can usually deliver only rough approximate solutions. On the other extreme, there are exact algorithms which are exhaustive search in nature and can be costly for practical-sized inputs. This paper fills the gap between the two extremes by proposing deterministic algorithms to approximately optimize the maximum consensus criterion. Our work begins by reformulating consensus maximization with linear complementarity constraints. Then, we develop two novel algorithms: one based on non-smooth penalty method with a Frank-Wolfe style optimization scheme, the other based on the Alternating Direction Method of Multipliers (ADMM). Both algorithms solve convex subproblems to efficiently perform the optimization. We demonstrate the capability of our algorithms to greatly improve a rough initial estimate, such as those obtained using least squares or a randomized algorithm. Compared to the exact algorithms, our approach is much more practical on realistic input sizes. Further, our approach is naturally applicable to estimation problems with geometric residuals

cs.CV↗

arXiv2018

Large scale visual place recognition with sub-linear storage growth

Robotic and animal mapping systems share many of the same objectives and challenges, but differ in one key aspect: where much of the research in robotic mapping has focused on solving the data association problem, the grid cell neurons underlying maps in the mammalian brain appear to intentionally break data association by encoding many locations with a single grid cell neuron. One potential benefit of this intentional aliasing is both sub-linear map storage and computational requirements growth with environment size, which we demonstrated in a previous proof-of-concept study that detected and encoded mutually complementary co-prime pattern frequencies in the visual map data. In this research, we solve several of the key theoretical and practical limitations of that prototype model and achieve significantly better sub-linear storage growth, a factor reduction in storage requirements per map location, scalability to large datasets on standard compute equipment and improved robustness to environments with visually challenging appearance change. These improvements are achieved through several innovations including a flexible user-driven choice mechanism for the periodic patterns underlying the new encoding method, a parallelized chunking technique that splits the map into sub-sections processed in parallel and a novel feature selection approach that selects only the image information most relevant to the encoded temporal patterns. We evaluate our techniques on two large benchmark datasets with the comparison to the previous state-of-the-art system, as well as providing a detailed analysis of system performance with respect to parameters such as required precision performance and the number of cyclic patterns encoded.

cs.CV↗