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The paper concerns the investigation of nonconvex and nondifferentiable integral functionals on general Banach spaces, which may not be reflexive and/or separable. Considering two major subdifferentials of variational analysis, we derive…

The principle of translation equivariance (if an input image is translated an output image should be translated by the same amount), led to the development of convolutional neural networks that revolutionized machine vision. Other…

Method of moment estimators exhibit appealing statistical properties, such as asymptotic unbiasedness, for nonconvex problems. However, they typically require a large number of samples and are extremely sensitive to model misspecification.…

We introduce a new variational estimator for the intensity function of an inhomogeneous spatial point process with points in the $d$-dimensional Euclidean space and observed within a bounded region. The variational estimator applies in a…

Recent work by Cohen \emph{et al.} has achieved state-of-the-art results for learning spherical images in a rotation invariant way by using ideas from group representation theory and noncommutative harmonic analysis. In this paper we…

Rotation-invariant face detection, i.e. detecting faces with arbitrary rotation-in-plane (RIP) angles, is widely required in unconstrained applications but still remains as a challenging task, due to the large variations of face…

This paper develops a unified and computationally efficient method for change-point estimation along the time dimension in a non-stationary spatio-temporal process. By modeling a non-stationary spatio-temporal process as a piecewise…

In this paper, modulating functions-based method is proposed for estimating space-time dependent unknowns in one-dimensional partial differential equations. The proposed method simplified the problem into a system of algebraic equations…

The recent development of spectral method has been praised for its high-order convergence in simulating complex physical problems. The combination of embedded boundary method and spectral method becomes a mainstream way to tackle…

Human face analysis is an important task in computer vision. According to cognitive-psychological studies, facial dynamics could provide crucial cues for face analysis. The motion of a facial local region in facial expression is related to…

Concern regarding the wide-spread use of fraudulent images/videos in social media necessitates precise detection of such fraud. The importance of facial expressions in communication is widely known, and adversarial attacks often focus on…

Convolutional neural networks have shown great success on feature extraction from raw input data such as images. Although convolutional neural networks are invariant to translations on the inputs, they are not invariant to other…

Emotion recognition from facial videos enables non-contact inference of human emotional states. Although facial expressions are widely used cues, they cannot fully reflect intrinsic affective states. Remote photoplethysmography (rPPG)…

Deep convolutional neural networks have led to breakthrough results in numerous practical machine learning tasks such as classification of images in the ImageNet data set, control-policy-learning to play Atari games or the board game Go,…

This paper introduces a couple of new time-frequency transforms, designed to adapt their scale to specific features of the analyzed function. Such an adaptation is implemented via so-called focus functions, which control the window scale as…

Visual repetition is ubiquitous in our world. It appears in human activity (sports, cooking), animal behavior (a bee's waggle dance), natural phenomena (leaves in the wind) and in urban environments (flashing lights). Estimating visual…

All elementary Hamiltonians in nature are expected to be invariant under rotation. Despite this restriction, we usually assume that any arbitrary measurement or unitary time evolution can be implemented on a physical system, an assumption…

This paper introduces a novel method for human face detection with its orientation by using wavelet, principle component analysis (PCA) and redial basis networks. The input image is analyzed by two-dimensional wavelet and a two-dimensional…

Viewpoint change invariance and action temporal consistency are critical aspects for the effective deployment of human action detection of untrimmed videos. Existing appearance-based video detection methods often struggle with limited…

Context: Occultation experiments represent unique opportunities for probing remotely physical properties of atmospheres. The data processing requires one to properly account for refractivity while modeling the time/frequency transfers of an…