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In this article, we primarily propose a novel Bayesian characterization of stationary and nonstationary stochastic processes. In practice, this theory aims to distinguish between global stationarity and nonstationarity for both parametric…
Classifications of $\rm{SL}(n)$ covariant function-valued valuations are established with some assumptions of continuity. New valuations, for example, weighted moment functions, are introduced and our classifications give unified…
Affect (emotion) recognition has gained significant attention from researchers in the past decade. Emotion-aware computer systems and devices have many applications ranging from interactive robots, intelligent online tutor to emotion based…
We give a new heuristic for all of the main terms in the integral moments of various families of primitive L-functions. The results agree with previous conjectures for the leading order terms. Our conjectures also have an almost identical…
Head-pose estimation has many applications, such as social event analysis, human-robot and human-computer interaction, driving assistance, and so forth. Head-pose estimation is challenging because it must cope with changing illumination…
An unbiased estimator for the ellipticity of an object in a noisy image is given in terms of the image moments. Three assumptions are made: i) the pixel noise is normally distributed, although with arbitrary covariance matrix, ii) the image…
The performance of modern deep learning-based systems dramatically depends on the quality of input objects. For example, face recognition quality would be lower for blurry or corrupted inputs. However, it is hard to predict the influence of…
Real-time magnetic resonance imaging (MRI) methods generally shorten the measuring time by acquiring less data than needed according to the sampling theorem. In order to obtain a proper image from such undersampled data, the reconstruction…
In this work, a method for obtaining pixel-wise error bounds in Bayesian regularization of inverse imaging problems is introduced. The proposed method employs estimates of the posterior variance together with techniques from conformal…
Using the large deviation principle (LDP) for a re-scaled fractional Brownian motion $B^H_t$ where the rate function is defined via the reproducing kernel Hilbert space, we compute small-time asymptotics for a correlated fractional…
Facial expression recognition has been an active research area over the past few decades, and it is still challenging due to the high intra-class variation. Traditional approaches for this problem rely on hand-crafted features such as SIFT,…
Computer Vision techniques represent a class of algorithms that are highly computation and data intensive in nature. Generally, performance of these algorithms in terms of execution speed on desktop computers is far from real-time. Since…
Fractional moments have been investigated by many authors to represent the density of univariate and bivariate random variables in different contexts. Fractional moments are indeed important when the density of the random variable has…
Real-world time series data are often generated from several sources of variation. Learning representations that capture the factors contributing to this variability enables a better understanding of the data via its underlying generative…
This work introduces a novel deep-learning approach for estimating age from a single facial image by refining an initial age estimate. The refinement leverages a reference face database of individuals with similar ages and appearances. We…
In this paper we address smoothing-that is, optimisation-based-estimation techniques for localisation problems in the case where motion sensors are very accurate. Our mathematical analysis focuses on the difficult limit case where motion…
This paper focuses on visual motion-based invariants that result in a representation of 3D points in which the stationary environment remains invariant, ensuring shape constancy. This is achieved even as the images undergo constant change…
Classifying facial expressions into different categories requires capturing regional distortions of facial landmarks. We believe that second-order statistics such as covariance is better able to capture such distortions in regional facial…
We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to…
Function registration, also referred to as alignment, has been one of the fundamental problems in the field of functional data analysis. Classical registration methods such as the Fisher-Rao alignment focus on estimating optimal time…