Capturing Hands in Action using Discriminative Salient Points and Physics Simulation

Hand motion capture is a popular research field, recently gaining more attention due to the ubiquity of RGB-D sensors. However, even most recent approaches focus on the case of a single isolated hand. In this work, we focus on hands that interact with other hands or objects and present a framework that successfully captures motion in such interaction scenarios for both rigid and articulated objects. Our framework combines a generative model with discriminatively trained salient points to achieve a low tracking error and with collision detection and physics simulation to achieve physically plausible estimates even in case of occlusions and missing visual data. Since all components are unified in a single objective function which is almost everywhere differentiable, it can be optimized with standard optimization techniques. Our approach works for monocular RGB-D sequences as well as setups with multiple synchronized RGB cameras. For a qualitative and quantitative evaluation, we captured 29 sequences with a large variety of interactions and up to 150 degrees of freedom.Comment: Accepted for publication by the International Journal of Computer Vision (IJCV) on 16.02.2016 (submitted on 17.10.14). A combination into a single framework of an ECCV'12 multicamera-RGB and a monocular-RGBD GCPR'14 hand tracking paper with several extensions, additional experiments and detail

Causal Dependence Tree Approximations of Joint Distributions for Multiple Random Processes

We investigate approximating joint distributions of random processes with causal dependence tree distributions. Such distributions are particularly useful in providing parsimonious representation when there exists causal dynamics among processes. By extending the results by Chow and Liu on dependence tree approximations, we show that the best causal dependence tree approximation is the one which maximizes the sum of directed informations on its edges, where best is defined in terms of minimizing the KL-divergence between the original and the approximate distribution. Moreover, we describe a low-complexity algorithm to efficiently pick this approximate distribution.Comment: 9 pages, 15 figure

Generalized discrete Fourier transform with non-linear phase : theory and design

Constant modulus transforms like discrete Fourier transform (DFT), Walsh transform, and Gold codes have been successfully used over several decades in various engineering applications, including discrete multi-tone (DMT), orthogonal frequency division multiplexing (OFDM) and code division multiple access (CDMA) communications systems. Among these popular transforms, DFT is a linear phase transform and widely used in multicarrier communications due to its performance and fast algorithms. In this thesis, a theoretical framework for Generalized DFT (GDFT) with nonlinear phase exploiting the phase space is developed. It is shown that GDFT offers sizable correlation improvements over DFT, Walsh, and Gold codes. Brute force search algorithm is employed to obtain orthogonal GDFT code sets with improved correlations. Design examples and simulation results on several channel types presented in the thesis show that the proposed GDFT codes, with better auto and cross-correlation properties than DFT, lead to better bit-error-rate performance in all multi-carrier and multi-user communications scenarios investigated. It is also highlighted how known constant modulus code families such as Walsh, Walsh-like and other codes are special solutions of the GDFT framework. In addition to theoretical framework, practical design methods with computationally efficient implementations of GDFT as enhancements to DFT are presented in the thesis. The main advantage of the proposed method is its ability to design a wide selection of constant modulus orthogonal code sets based on the desired performance metrics mimicking the engineering .specs of interest. Orthogonal Frequency Division Multiplexing (OFDM) is a leading candidate to be adopted for high speed 4G wireless communications standards due to its high spectral efficiency, strong resistance to multipath fading and ease of implementation with Fast Fourier Transform (FFT) algorithms. However, the main disadvantage of an OFDM based communications technique is of its high PAPR at the RF stage of a transmitter. PAPR dominates the power (battery) efficiency of the radio transceiver. Among the PAPR reduction methods proposed in the literature, Selected Mapping (SLM) method has been successfully used in OFDM communications. In this thesis, an SLM method employing GDFT with closed form phase functions rather than fixed DFT for PAPR reduction is introduced. The performance improvements of GDFT based SLM PAPR reduction for various OFDM communications scenarios including the WiMAX standard based system are evaluated by simulations. Moreover, an efficient implementation of GDFT based SLM method reducing computational cost of multiple transform operations is forwarded. Performance simulation results show that power efficiency of non-linear RF amplifier in an OFDM system employing proposed method significantly improved

Composite CDMA - A statistical mechanics analysis

Code Division Multiple Access (CDMA) in which the spreading code assignment to users contains a random element has recently become a cornerstone of CDMA research. The random element in the construction is particular attractive as it provides robustness and flexibility in utilising multi-access channels, whilst not making significant sacrifices in terms of transmission power. Random codes are generated from some ensemble, here we consider the possibility of combining two standard paradigms, sparsely and densely spread codes, in a single composite code ensemble. The composite code analysis includes a replica symmetric calculation of performance in the large system limit, and investigation of finite systems through a composite belief propagation algorithm. A variety of codes are examined with a focus on the high multi-access interference regime. In both the large size limit and finite systems we demonstrate scenarios in which the composite code has typical performance exceeding sparse and dense codes at equivalent signal to noise ratio.Comment: 23 pages, 11 figures, Sigma Phi 2008 conference submission - submitted to J.Stat.Mec

Abstract Hidden Markov Models: a monadic account of quantitative information flow

Hidden Markov Models, HMM's, are mathematical models of Markov processes with state that is hidden, but from which information can leak. They are typically represented as 3-way joint-probability distributions. We use HMM's as denotations of probabilistic hidden-state sequential programs: for that, we recast them as `abstract' HMM's, computations in the Giry monad $\mathbb{D}$, and we equip them with a partial order of increasing security. However to encode the monadic type with hiding over some state $\mathcal{X}$ we use $\mathbb{D}\mathcal{X}\to \mathbb{D}^2\mathcal{X}$ rather than the conventional $\mathcal{X}{\to}\mathbb{D}\mathcal{X}$ that suffices for Markov models whose state is not hidden. We illustrate the $\mathbb{D}\mathcal{X}\to \mathbb{D}^2\mathcal{X}$ construction with a small Haskell prototype. We then present uncertainty measures as a generalisation of the extant diversity of probabilistic entropies, with characteristic analytic properties for them, and show how the new entropies interact with the order of increasing security. Furthermore, we give a `backwards' uncertainty-transformer semantics for HMM's that is dual to the `forwards' abstract HMM's - it is an analogue of the duality between forwards, relational semantics and backwards, predicate-transformer semantics for imperative programs with demonic choice. Finally, we argue that, from this new denotational-semantic viewpoint, one can see that the Dalenius desideratum for statistical databases is actually an issue in compositionality. We propose a means for taking it into account