Motion-capture-based hand gesture recognition for computing and control

This dissertation focuses on the study and development of algorithms that enable the analysis and recognition of hand gestures in a motion capture environment. Central to this work is the study of unlabeled point sets in a more abstract sense. Evaluations of proposed methods focus on examining their generalization to users not encountered during system training. In an initial exploratory study, we compare various classification algorithms based upon multiple interpretations and feature transformations of point sets, including those based upon aggregate features (e.g. mean) and a pseudo-rasterization of the capture space. We find aggregate feature classifiers to be balanced across multiple users but relatively limited in maximum achievable accuracy. Certain classifiers based upon the pseudo-rasterization performed best among tested classification algorithms. We follow this study with targeted examinations of certain subproblems. For the first subproblem, we introduce the a fortiori expectation-maximization (AFEM) algorithm for computing the parameters of a distribution from which un­ labeled, correlated point sets are presumed to be generated. Each unlabeled point is assumed to correspond to a target with independent probability of appearance but correlated positions. We propose replacing the expectation phase of the algo­ rithm with a Kalman filter modified within a Bayesian framework to account for the unknown point labels which manifest as uncertain measurement matrices. We also propose a mechanism to reorder the measurements in order to improve parameter estimates. In addition, we use a state-of-the-art Markov chain Monte Carlo sampler to efficiently sample measurement matrices. In the process, we indirectly propose a constrained /c-means clustering algorithm. Simulations verify the utility of AFEM against a traditional expectation-maximization algorithm in a variety of scenarios. In the second subproblem, we consider the application of positive definite kernels and the earth mover’s distance (EMD) to our work. Positive definite kernels are an important tool in machine learning that enable efficient solutions to otherwise difficult or intractable problems by implicitly linearizing the problem geometry. We develop a set-theoretic interpretation of EMD and propose earth mover’s intersection (EMI), a positive definite analog to EMD. We offer proof of EMD’s negative definiteness and provide necessary and sufficient conditions for EMD to be conditionally negative definite, including approximations that guarantee negative definiteness. In particular, we show that EMD is related to various min-like kernels. We also present a positive definite preserving transformation that can be applied to any kernel and can be used to derive positive definite EMD-based kernels, and we show that the Jaccard index is simply the result of this transformation applied to set intersection. Finally, we evaluate kernels based on EMI and the proposed transformation versus EMD in various computer vision tasks and show that EMD is generally inferior even with indefinite kernel techniques. Finally, we apply deep learning to our problem. We propose neural network architectures for hand posture and gesture recognition from unlabeled marker sets in a coordinate system local to the hand. As a means of ensuring data integrity, we also