Search results for "Hankel matrix"
showing 7 items of 7 documents
Gesture Modeling by Hanklet-Based Hidden Markov Model
2015
In this paper we propose a novel approach for gesture modeling. We aim at decomposing a gesture into sub-trajectories that are the output of a sequence of atomic linear time invariant (LTI) systems, and we use a Hidden Markov Model to model the transitions from the LTI system to another. For this purpose, we represent the human body motion in a temporal window as a set of body joint trajectories that we assume are the output of an LTI system. We describe the set of trajectories in a temporal window by the corresponding Hankel matrix (Hanklet), which embeds the observability matrix of the LTI system that produced it. We train a set of HMMs (one for each gesture class) with a discriminative a…
Hilbert-Schmidt Hankel operators on the Segal-Bargmann space
2004
This paper considers Hankel operators on the Segal-Bargmann space of holomorphic functions onCn\mathbb {C}^nthat are square integrable with respect to the Gaussian measure. It is shown that in the case of a bounded symbolg∈L∞(Cn)g \in L^{\infty }(\mathbb {C}^n)the Hankel operatorHgH_gis of the Hilbert-Schmidt class if and only ifHg¯H_{\bar {g}}is Hilbert-Schmidt. In the case where the symbol is square integrable with respect to the Lebesgue measure it is known that the Hilbert-Schmidt norms of the Hankel operatorsHgH_gandHg¯H_{\bar {g}}coincide. But, in general, if we deal with bounded symbols, only the inequality‖Hg‖HS≤2‖Hg¯‖HS\|H_g\|_{HS}\leq 2\|H_{\bar {g}}\|_{HS}can be proved. The resul…
Ensemble of Hankel Matrices for Face Emotion Recognition
2015
In this paper, a face emotion is considered as the result of the composition of multiple concurrent signals, each corresponding to the movements of a specific facial muscle. These concurrent signals are represented by means of a set of multi-scale appearance features that might be correlated with one or more concurrent signals. The extraction of these appearance features from a sequence of face images yields to a set of time series. This paper proposes to use the dynamics regulating each appearance feature time series to recognize among different face emotions. To this purpose, an ensemble of Hankel matrices corresponding to the extracted time series is used for emotion classification withi…
Hankelet-based dynamical systems modeling for 3D action recognition
2015
This paper proposes to model an action as the output of a sequence of atomic Linear Time Invariant (LTI) systems. The sequence of LTI systems generating the action is modeled as a Markov chain, where a Hidden Markov Model (HMM) is used to model the transition from one atomic LTI system to another. In turn, the LTI systems are represented in terms of their Hankel matrices. For classification purposes, the parameters of a set of HMMs (one for each action class) are learned via a discriminative approach. This work proposes a novel method to learn the atomic LTI systems from training data, and analyzes in detail the action representation in terms of a sequence of Hankel matrices. Extensive eval…
Boosting Hankel matrices for face emotion recognition and pain detection
2017
HighligthsDynamics of face expression descriptors are modeled for emotion recognition.A set of Hankel matrices is built upon several multi-scale face representations.Boosting and random subspace projection are used for dynamics selection.Dynamics of Haar-like features and Gabor Energies are compared.Fine-grained dynamics of subtle expressions can be modeled at small spatial scales. Studies in psychology have shown that the dynamics of emotional expressions play an important role in face emotion recognition in humans. Motivated by these studies, in this paper the dynamics of face expressions are modeled and used for automatic emotion recognition and pain detection.Given a temporal sequence o…
Using Hankel matrices for dynamics-based facial emotion recognition and pain detection
2015
This paper proposes a new approach to model the temporal dynamics of a sequence of facial expressions. To this purpose, a sequence of Face Image Descriptors (FID) is regarded as the output of a Linear Time Invariant (LTI) system. The temporal dynamics of such sequence of descriptors are represented by means of a Hankel matrix. The paper presents different strategies to compute dynamics-based representation of a sequence of FID, and reports classification accuracy values of the proposed representations within different standard classification frameworks. The representations have been validated in two very challenging application domains: emotion recognition and pain detection. Experiments on…
Hankelet-based action classification for motor intention recognition
2017
Powered lower-limb prostheses require a natural, and an easy-to-use, interface for communicating amputee’s motor intention in order to select the appropriate motor program in any given context, or simply to commute from active (powered) to passive mode of functioning. To be widely accepted, such an interface should not put additional cognitive load at the end-user, it should be reliable and minimally invasive. In this paper we present a one such interface based on a robust method for detecting and recognizing motor actions from a low-cost wearable sensor network mounted on a sound leg providing inertial (accelerometer, gyrometer and magnetometer) data in real-time. We assume that the sensor…