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Automatic colourisation of grey-scale images is an ill-posed multi-modal problem. Where full-reference images exist, objective performance measures rely on pixel-difference techniques such as MSE and PSNR. These measures penalise any…
Mode-sorting is a procedure that decomposes a light field into a basis of transverse modes, directing each mode into a separate spatial location, allowing the constituent mode intensities to be measured simultaneously. We demonstrate a…
We present a technique for the approximation of a class of Hilbert space-valued maps which arise within the framework of Model Order Reduction for parametric partial differential equations, whose solution map has a meromorphic structure.…
Size uniformity is one of the main criteria of superpixel methods. But size uniformity rarely conforms to the varying content of an image. The chosen size of the superpixels therefore represents a compromise - how to obtain the fewest…
A solid object's geometry, density, and elastic moduli completely determine its spectrum of normal modes. Solving the inverse problem - determining a material's elastic moduli given a set of resonance frequencies and sample geometry -…
Zernike polynomials are widely used to describe the wavefront phase as they are well suited to the circular geometry of various optical apertures. Non-conventional optical systems, such as future large optical telescopes with highly…
Modern Integrated-Circuit(IC) manufacturing introduces diverse, fine-grained defects that depress yield and reliability. Most industrial defect segmentation compares a test image against an external normal set, a strategy that is brittle…
In this work, we tackle the challenging problem of category-level object pose and size estimation from a single depth image. Although previous fully-supervised works have demonstrated promising performance, collecting ground-truth pose…
One-shot image semantic segmentation poses a challenging task of recognizing the object regions from unseen categories with only one annotated example as supervision. In this paper, we propose a simple yet effective Similarity Guidance…
In this paper, we investigate the approximation properties of two types of multiscale finite element methods with oversampling as proposed in [Hou \& Wu, {\textit{J. Comput. Phys.}}, 1997] and [Efendiev, Hou \& Wu, \textit{SIAM J. Numer.…
We compare the long-time error bounds and spatial resolution of finite difference methods with different spatial discretizations for the Dirac equation with small electromagnetic potentials characterized by $\varepsilon \in (0, 1]$ a…
In this work we show how to decompose a linear code relatively to any given poset metric. We prove that the complexity of syndrome decoding is determined by a maximal (primary) such decomposition and then show that a refinement of a partial…
The error on a real quantity Y due to the graduation of the measuring instrument may be represented, when the graduation is regular and fines down, by a Dirichlet form on R whose square field operator do not depend on the probability law of…
Wide-area synchrophasor ambient measurements provide a valuable data source for real-time oscillation mode monitoring and analysis. This paper introduces a novel method for identifying inter-area oscillation modes using wide-area ambient…
The symplectic geometry mode decomposition (SGMD) is a powerful method for decomposing time series, which is based on the diagonal averaging principle (DAP) inherited from the singular spectrum analysis (SSA). Although the authors of SGMD…
Parameter estimation in linear errors-in-variables models typically requires that the measurement error distribution be known (or estimable from replicate data). A generalized method of moments approach can be used to estimate model…
Recently, several single-pixel imaging (SPI) schemes have emerged for imaging fast-moving objects and have shown dramatic results. However, fast image reconstruction of a moving object with high quality is still challenging for SPI, thereby…
Category-level object pose estimation aims to determine the pose and size of novel objects in specific categories. Existing correspondence-based approaches typically adopt point-based representations to establish the correspondences between…
Entanglement-assisted quantum error-correcting (EAQEC) codes are a subclass of quantum error-correcting codes which use entanglement as a resource. These codes can provide error correction capability higher than the codes derived from the…
A pattern of interpolation nodes on the disk is studied, for which the interpolation problem is theoretically unisolvent, and which renders a minimal numerical condition for the collocation matrix when the standard basis of Zernike…