Related papers: Spatial Perspective Transform Estimation from Four…
This paper determines how to define a discretely implemented Fourier transform when analysing an observed spatial point process. To develop this transform we answer four questions; first what is the natural definition of a Fourier…
When observing the surface patterns of objects delimited by smooth surfaces, the projections of the surface patterns to the image domain will be subject to substantial variabilities, as induced by variabilities in the geometric viewing…
Recent developments in machine learning and signal processing have resulted in many new techniques that are able to effectively capture the intrinsic yet complex properties of hyperspectral imagery. Tasks ranging from anomaly detection to…
Spatial variables can be observed in many different forms, such as regularly sampled random fields (lattice data), point processes, and randomly sampled spatial processes. Joint analysis of such collections of observations is clearly…
We present an approach to computing spatial information based on Fourier coefficient distributions. The Fourier transform (FT) of an image contains a complete description of the image, and the values of the FT coefficients are uniquely…
We represent three-dimensional Fourier transform light scattering, a method to reconstruct angle-resolved light scattering (ARLS) with extended angle-range from individual spherical objects. To overcome the angle limitation determined by…
6D pose estimation is a central problem in robot vision. Compared with pose estimation based on point correspondences or its robust versions, correspondence-free methods are often more flexible. However, existing correspondence-free methods…
Urban form has been empirically demonstrated to be of scaling invariance and can be described with fractal geometry. However, the rational range of fractal dimension value and the relationships between various fractal indicators of cities…
Affine transformations have been recently used for stereo vision. They can be exploited in various computer vision application, e.g., when estimating surface normals, homographies, fundamental and essential matrices. Even full 3D…
As a new type of series expansion, the so-called one-dimensional adaptive Fourier decomposition (AFD) and its variations (1D-AFDs) have effective applications in signal analysis and system identification. The 1D-AFDs have considerable…
The Fourier inversion of phased coherent diffraction patterns offers images without the resolution and depth-of-focus limitations of lens-based tomographic systems. We report on our recent experimental images inverted using recent…
Accurate and fast 3D imaging of specular surfaces still poses major challenges for state-of-the-art optical measurement principles. Frequently used methods, such as phase-measuring deflectometry (PMD) or shape-from-polarization (SfP), rely…
Fourier transform is applied to annular beams of simplified flat two-level geometry: bright outer ring with a darker core. The pattern of focal beam profile (i.e. far field) is calculated and characterized with respect of its intensity…
We propose a new recursive method for simultaneous estimation of both the pose and the shape of a three-dimensional extended object. The key idea of the presented method is to represent the shape of the object using spherical harmonics,…
Reliable image correspondences form the foundation of vision-based spatial perception, enabling recovery of 3D structure and camera poses. However, unconstrained feature matching across domains such as aerial, indoor, and outdoor scenes…
We tackle the problem of object-centric learning on point clouds, which is crucial for high-level relational reasoning and scalable machine intelligence. In particular, we introduce a framework, SPAIR3D, to factorize a 3D point cloud into a…
We give a simple proof of the sharp decay of the Fourier-transform of surface-carried measures of two-dimensional generic surfaces. The estimates are applied to prove Strichartz and resolvent estimates for elliptic operators whose…
In this work, we present a theoretical and experimental study about the spatial correlations of paired photons generated by type-II spontaneous parametric down-conversion. In particular, we show how these correlations can be positive or…
In this work, we derive a model for the covariance of the visual residuals in multi-view SfM, odometry and SLAM setups. The core of our approach is the formulation of the residual covariances as a combination of geometric and photometric…
Existing convolutional neural networks widely adopt spatial down-/up-sampling for multi-scale modeling. However, spatial up-sampling operators (\emph{e.g.}, interpolation, transposed convolution, and un-pooling) heavily depend on local…