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This is the first book to present a complete characterization of Stein-Tomas type Fourier restriction estimates for large classes of smooth hypersurfaces in three dimensions, including all real-analytic hypersurfaces. The range of Lebesgue spaces for which these estimates are valid is described in terms of Newton polyhedra associated to the given surface.Isroil Ikromov and Detlef Müller begin with Elias M. Stein's concept of Fourier restriction and some relations between the decay of the Fourier transform of the surface measure and Stein-Tomas type restriction estimates. Varchenko's ideas relating Fourier decay to associated Newton polyhedra are briefly explained, particularly the concept of adapted coordinates and the notion of height. It turns out that these classical tools essentially suffice already to treat the case where there exist linear adapted coordinates, and thus Ikromov and Müller concentrate on the remaining case. Here the notion of r-height is introduced, which proves to be the right new concept. They then describe decomposition techniques and related stopping time algorithms that allow to partition the given surface into various pieces, which can eventually be handled by means of oscillatory integral estimates. Different interpolation techniques are presented and used, from complex to more recent real methods by Bak and Seeger.Fourier restriction plays an important role in several fields, in particular in real and harmonic analysis, number theory, and PDEs. This book will interest graduate students and researchers working in such fields.

Hypersurfaces. --- Polyhedra. --- Surfaces, Algebraic. --- Fourier analysis. --- Analysis, Fourier --- Mathematical analysis --- Polyhedral figures --- Polyhedrons --- Geometry, Solid --- Shapes --- Algebraic surfaces --- Geometry, Algebraic --- Hyperspace --- Surfaces --- Airy cone. --- Airy-type analysis. --- Airy-type decompositions. --- Fourier decay. --- Fourier integral. --- Fourier restriction estimate. --- Fourier restriction problem. --- Fourier restriction theorem. --- Fourier restriction. --- Fourier transform. --- Greenleaf's restriction. --- Lebesgue spaces. --- LittlewoodАaley decomposition. --- LittlewoodАaley theory. --- Newton polyhedra. --- Newton polyhedral. --- Newton polyhedron. --- SteinДomas-type Fourier restriction. --- auxiliary results. --- complex interpolation. --- dyadic decomposition. --- dyadic decompositions. --- dyadic domain decompositions. --- endpoint estimates. --- endpoint result. --- improved estimates. --- interpolation arguments. --- interpolation theorem. --- invariant description. --- linear coordinates. --- linearly adapted coordinates. --- normalized measures. --- normalized rescale measures. --- one-dimensional oscillatory integrals. --- open cases. --- operator norms. --- phase functions. --- preparatory results. --- principal root jet. --- propositions. --- r-height. --- real interpolation. --- real-analytic hypersurface. --- refined Airy-type analysis. --- restriction estimates. --- restriction. --- smooth hypersurface. --- smooth hypersurfaces. --- spectral localization. --- stopping-time algorithm. --- sublevel type. --- thin sets. --- three dimensions. --- transition domains. --- uniform bounds. --- van der Corput-type estimates.

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The recent revolution in deep learning has enabled considerable development in the fields of object and activity detection. Visual object detection tries to find objects of target classes with precise localisation in an image and assign each object instance a corresponding class label. At the same time, activity recognition aims to determine the actions or activities of an agent or group of agents based on sensor or video observation data. It is a very important and challenging problem to detect, identify, track, and understand the behaviour of objects through images and videos taken by various cameras. Together, objects and their activity recognition in imaging data captured by remote sensing platforms is a highly dynamic and challenging research topic. During the last decade, there has been significant growth in the number of publications in the field of object and activity recognition. In particular, many researchers have proposed application domains to identify objects and their specific behaviours from air and spaceborne imagery. This Special Issue includes papers that explore novel and challenging topics for object and activity detection in remote sensing images and videos acquired by diverse platforms.

Technology: general issues --- History of engineering & technology --- multi-camera system --- space alignment --- UAV-assisted calibration --- cross-view matching --- spatiotemporal feature map --- view-invariant description --- air-to-ground synchronization --- tidal flat water --- YOLOv3 --- similarity algorithm for water extraction --- arbitrary-oriented object detection in satellite optical imagery --- adaptive dynamic refined single-stage transformer detector --- feature pyramid transformer --- dynamic feature refinement --- synthetic aperture radar (SAR) --- ship detection --- convolutional neural network (CNN) --- deep learning (DL) --- feature pyramid network (FPN) --- quad feature pyramid network (Quad-FPN) --- crowd estimation --- 3D simulation --- unmanned aerial vehicle --- synthetic crowd data --- invasive species --- thermal imaging --- habitat identification --- deep learning --- drone --- multiview semantic vegetation index --- urban forestry --- green view index (GVI) --- semantic segmentation --- urban vegetation --- RGB vegetation index