Harmonic-Counting Measures and Spectral Theory of Lens Spaces

In this article, associated with each lattice $T\subseteq \mathbb{Z}^n$ the concept of a harmonic-counting measure $\nu_T$ on a sphere $S^{n-1}$ is introduced and it is applied to determine the asymptotic behavior of the eigenfunctions of the Laplace-Beltrami operator on a lens space. In fact, the asymptotic behavior of the cardinality of the set of independent eigenfunctions associated with the elements of $T$ which lie in a cone is determined when $T$ is the lattice of a lens space

Recombinator Networks: Learning Coarse-to-Fine Feature Aggregation

Deep neural networks with alternating convolutional, max-pooling and decimation layers are widely used in state of the art architectures for computer vision. Max-pooling purposefully discards precise spatial information in order to create features that are more robust, and typically organized as lower resolution spatial feature maps. On some tasks, such as whole-image classification, max-pooling derived features are well suited; however, for tasks requiring precise localization, such as pixel level prediction and segmentation, max-pooling destroys exactly the information required to perform well. Precise localization may be preserved by shallow convnets without pooling but at the expense of robustness. Can we have our max-pooled multi-layered cake and eat it too? Several papers have proposed summation and concatenation based methods for combining upsampled coarse, abstract features with finer features to produce robust pixel level predictions. Here we introduce another model --- dubbed Recombinator Networks --- where coarse features inform finer features early in their formation such that finer features can make use of several layers of computation in deciding how to use coarse features. The model is trained once, end-to-end and performs better than summation-based architectures, reducing the error from the previous state of the art on two facial keypoint datasets, AFW and AFLW, by 30\% and beating the current state-of-the-art on 300W without using extra data. We improve performance even further by adding a denoising prediction model based on a novel convnet formulation.Comment: accepted in CVPR 201

Improving Facial Analysis and Performance Driven Animation through Disentangling Identity and Expression

We present techniques for improving performance driven facial animation, emotion recognition, and facial key-point or landmark prediction using learned identity invariant representations. Established approaches to these problems can work well if sufficient examples and labels for a particular identity are available and factors of variation are highly controlled. However, labeled examples of facial expressions, emotions and key-points for new individuals are difficult and costly to obtain. In this paper we improve the ability of techniques to generalize to new and unseen individuals by explicitly modeling previously seen variations related to identity and expression. We use a weakly-supervised approach in which identity labels are used to learn the different factors of variation linked to identity separately from factors related to expression. We show how probabilistic modeling of these sources of variation allows one to learn identity-invariant representations for expressions which can then be used to identity-normalize various procedures for facial expression analysis and animation control. We also show how to extend the widely used techniques of active appearance models and constrained local models through replacing the underlying point distribution models which are typically constructed using principal component analysis with identity-expression factorized representations. We present a wide variety of experiments in which we consistently improve performance on emotion recognition, markerless performance-driven facial animation and facial key-point tracking.Comment: to appear in Image and Vision Computing Journal (IMAVIS

Sport tourism development: Cultural, economic and political perspectives

Sport tourism is a new concept in the world having the most growth in tourism industry. Many of countries enjoy an appropriate status with respect to sport tourism and,accordingly,contribute directly to their nation`s economic prosperity. Hence, the goal of this research is comparison and survey of tourism managers, interest managers and tourisms' ideas about creation of sport tourism-induced employment and income in Mazandaran-Iran. The tool of this research is a researcher-made five scale likert questionnaire. The questionnaire reliability and the coefficient validity were confirmed by experienced professors and with (α = 0.82),respectively. Finally, The data analysis carried out using the SPSS software and χ2 statistic test.The results show that job creation (χ ‗ 4.360, p‗ 0.35) and income production (χ2 ‗1.633, p‗ 0.80) were previously at a minimum However, the role of tourism industry development is believed to create jobs (χ2 ‗ 9.740 ,p‗ 0.04)and income(χ2 ‗ 5.224,0.51). Compared with other studies ,the present research indicates that future sport tourism industry influences job and income production in the regions hosting the sport events provided that the sport tourism industry and its respective infrastructures are well-developed

Learning to Find Eye Region Landmarks for Remote Gaze Estimation in Unconstrained Settings

Conventional feature-based and model-based gaze estimation methods have proven to perform well in settings with controlled illumination and specialized cameras. In unconstrained real-world settings, however, such methods are surpassed by recent appearance-based methods due to difficulties in modeling factors such as illumination changes and other visual artifacts. We present a novel learning-based method for eye region landmark localization that enables conventional methods to be competitive to latest appearance-based methods. Despite having been trained exclusively on synthetic data, our method exceeds the state of the art for iris localization and eye shape registration on real-world imagery. We then use the detected landmarks as input to iterative model-fitting and lightweight learning-based gaze estimation methods. Our approach outperforms existing model-fitting and appearance-based methods in the context of person-independent and personalized gaze estimation