相关论文: Measure Functions for Frames

A finite-dimensional Hilbert space is usually described in terms of an orthonormal basis, but in certain approaches or applications a description in terms of a finite overcomplete system of vectors, called a finite tight frame, may offer…

The series of papers is devoted to the study of convergence for pairs of surfaces and smooth functions thereon. We model such pairs with varifolds and multiple-valued functions to capture their limits. In the present paper, we study Young…

In this position paper we suggest a possible metric approach to shape comparison that is based on a mathematical formalization of the concept of observer, seen as a collection of suitable operators acting on a metric space of functions.…

The ability to quantify distinctness of a cluster structure is fundamental for certain simulation studies, in particular for those comparing performance of different classification algorithms. The intrinsic integral measure based on the…

Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…

The most prevalent routine for camera calibration is based on the detection of well-defined feature points on a purpose-made calibration artifact. These could be checkerboard saddle points, circles, rings or triangles, often printed on a…

Frames are redundant system which are useful in the reconstruction of certain classes of spaces. Duffin and Schaeffer introduced frames for Hilbert spaces, while addressing some deep problems in non harmonic Fourier series. The dual of a…

In this letter, we show that a perfect lens can be employed to make multiple objects appear like only one in the far field, leading to a new concept of illusion optics. Numerical simulations are performed to verify the functionalities for…

Successive divisions of compact metric spaces appear in many different areas of mathematics such as the construction of self-similar sets, Markov partitions associated with hyperbolic dynamical systems, dyadic cubes associated with a…

We propose measurement modeling from the quantitative social sciences as a framework for understanding fairness in computational systems. Computational systems often involve unobservable theoretical constructs, such as socioeconomic status,…

We introduce a framework for benchmarking optimizers according to multiple criteria over various test functions. Based on a recently introduced union-free generic depth function for partial orders/rankings, it fully exploits the ordinal…

In the context of formal verification in general and model checking in particular, parity games serve as a mighty vehicle: many problems are encoded as parity games, which are then solved by the seminal algorithm by Jurdzinski. In this…

Deep functional map frameworks are widely employed for 3D shape matching. However, most existing deep functional map methods cannot adaptively capture important frequency information for functional map estimation in specific matching…

Depth estimation is a fundamental task in computer vision with diverse applications. Recent advancements in deep learning have led to powerful depth foundation models (DFMs), yet their evaluation remains challenging due to inconsistencies…

In ultrasound nondestructive testing, a widespread approach is to take synthetic aperture measurements from the surface of a specimen to detect and locate defects within it. Based on these measurements, imaging is usually performed using…

This is a tutorial introduction to the functional analysis mathematics needed in many physical problems, such as in waves in continuous media. Functional analysis takes us beyond finite matrices, allowing us to work with infinite sets of…

Protective measurement, which was proposed as a method of observing the wavefunction of a single system, is extended to the observation of the density matrix of a single system. d'Espagnat's definition of `proper mixture' is shown to be…

A new classification of real functions and other related real objects defined within a compact interval is proposed. The scope of the classification includes normal real functions and distributions in the sense of Schwartz, referred to…

A measurable map between measure spaces is shown to have bounded compression if and only if its image via the measure-algebra functor is Lipschitz-continuous w.r.t. the measure-algebra distances. This provides a natural interpretation of…

Research on video frame interpolation has made significant progress in recent years. However, existing methods mostly use off-the-shelf metrics to measure the quality of interpolation results with the exception of a few methods that employ…