The complexity of detecting taut angle structures on triangulations

There are many fundamental algorithmic problems on triangulated 3-manifolds whose complexities are unknown. Here we study the problem of finding a taut angle structure on a 3-manifold triangulation, whose existence has implications for both the geometry and combinatorics of the triangulation. We prove that detecting taut angle structures is NP-complete, but also fixed-parameter tractable in the treewidth of the face pairing graph of the triangulation. These results have deeper implications: the core techniques can serve as a launching point for approaching decision problems such as unknot recognition and prime decomposition of 3-manifolds.Comment: 22 pages, 10 figures, 3 tables; v2: minor updates. To appear in SODA 2013: Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithm

Extension of Sparse Randomized Kaczmarz Algorithm for Multiple Measurement Vectors

The Kaczmarz algorithm is popular for iteratively solving an overdetermined system of linear equations. The traditional Kaczmarz algorithm can approximate the solution in few sweeps through the equations but a randomized version of the Kaczmarz algorithm was shown to converge exponentially and independent of number of equations. Recently an algorithm for finding sparse solution to a linear system of equations has been proposed based on weighted randomized Kaczmarz algorithm. These algorithms solves single measurement vector problem; however there are applications were multiple-measurements are available. In this work, the objective is to solve a multiple measurement vector problem with common sparse support by modifying the randomized Kaczmarz algorithm. We have also modeled the problem of face recognition from video as the multiple measurement vector problem and solved using our proposed technique. We have compared the proposed algorithm with state-of-art spectral projected gradient algorithm for multiple measurement vectors on both real and synthetic datasets. The Monte Carlo simulations confirms that our proposed algorithm have better recovery and convergence rate than the MMV version of spectral projected gradient algorithm under fairness constraints

A bank of unscented Kalman filters for multimodal human perception with mobile service robots

A new generation of mobile service robots could be ready soon to operate in human environments if they can robustly estimate position and identity of surrounding people. Researchers in this field face a number of challenging problems, among which sensor uncertainties and real-time constraints. In this paper, we propose a novel and efficient solution for simultaneous tracking and recognition of people within the observation range of a mobile robot. Multisensor techniques for legs and face detection are fused in a robust probabilistic framework to height, clothes and face recognition algorithms. The system is based on an efficient bank of Unscented Kalman Filters that keeps a multi-hypothesis estimate of the person being tracked, including the case where the latter is unknown to the robot. Several experiments with real mobile robots are presented to validate the proposed approach. They show that our solutions can improve the robot's perception and recognition of humans, providing a useful contribution for the future application of service robotics

Finding Faces in Cluttered Scenes using Random Labeled Graph Matching

An algorithm for locating quasi-frontal views of human faces in cluttered scenes is presented. The algorithm works by coupling a set of local feature detectors with a statistical model of the mutual distances between facial features it is invariant with respect to translation, rotation (in the plane), and scale and can handle partial occlusions of the face. On a challenging database with complicated and varied backgrounds, the algorithm achieved a correct localization rate of 95% in images where the face appeared quasi-frontally

Facial Point Detection using Boosted Regression and Graph Models

Finding fiducial facial points in any frame of a video showing rich naturalistic facial behaviour is an unsolved problem. Yet this is a crucial step for geometric-featurebased facial expression analysis, and methods that use appearance-based features extracted at fiducial facial point locations. In this paper we present a method based on a combination of Support Vector Regression and Markov Random Fields to drastically reduce the time needed to search for a point’s location and increase the accuracy and robustness of the algorithm. Using Markov Random Fields allows us to constrain the search space by exploiting the constellations that facial points can form. The regressors on the other hand learn a mapping between the appearance of the area surrounding a point and the positions of these points, which makes detection of the points very fast and can make the algorithm robust to variations of appearance due to facial expression and moderate changes in head pose. The proposed point detection algorithm was tested on 1855 images, the results of which showed we outperform current state of the art point detectors