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The transportation $mathrm{L}^p$ distance, denoted $mathrm{TL}^p$, has been proposed as a generalisation of Wasserstein $mathrm{W}^p$ distances motivated by the property that it can be applied directly to colour or multi-channelled images, as well as multivariate time-series without normalisation or mass constraints. These distances, as with $mathrm{W}^p$, are powerful tools in modelling data with spatial or temporal perturbations. However, their computational cost can make them infeasible to apply to even moderate pattern recognition tasks. We propose line
We prove that functions of locally bounded deformation on $mathbb{R}^n$ are $mathrm{L}^{n/(n-1)}$-differentiable almost everywhere. More generally, we show that this critical $mathrm{L}^p$-differentiability result holds for functions of locally bound
Many problems in science and engineering can be formulated in terms of geometric patterns in high-dimensional spaces. We present high-dimensional convolutional networks (ConvNets) for pattern recognition problems that arise in the context of geometri
We study a class of mathematical and statistical algorithms with the aim of establishing a computer-based framework for fast and reliable automatic abnormality detection on landmark represented image templates. Under this framework, we apply a landma
Contour tracking in adverse environments is a challenging problem due to cluttered background, illumination variation, occlusion, and noise, among others. This paper presents a robust contour tracking method by contributing to some of the key issues
As a unique and promising biometric, video-based gait recognition has broad applications. The key step of this methodology is to learn the walking pattern of individuals, which, however, often suffers challenges to extract the behavioral feature from