Related papers: A precise method for visualizing dispersive featur…
This paper deals with the concept of curvature of framed space curves, their higher-order derivatives, variations, and co-rotational derivatives. We realize that parametrizing rotation tensor using the Gibbs vector is effective in deriving…
Bump hunting deals with finding in sample spaces meaningful data subsets known as bumps. These have traditionally been conceived as modal or concave regions in the graph of the underlying density function. We define an abstract bump…
We introduce an estimator for the curvature of curves and surfaces by using finite sample points drawn from sampling a probability distribution that has support on the curve or surface. First we give an algorithm for estimation of the…
Two methods for the determination of extrema timings and their uncertainties appropriate for the analysis of time series of variable stars using matrix calculus are presented. The method I is suitable for determination of times of extrema…
We introduce a new intrinsic measure of local curvature on point-cloud data called diffusion curvature. Our measure uses the framework of diffusion maps, including the data diffusion operator, to structure point cloud data and define local…
Human has an incredible ability to effortlessly perceive the viewpoint difference between two images containing the same object, even when the viewpoint change is astonishingly vast with no co-visible regions in the images. This remarkable…
We present a novel visualization-driven illumination model for density plots, a new technique to enhance density plots by effectively revealing the detailed structures in high- and medium-density regions and outliers in low-density regions,…
Starting from a variational formulation, we present a model for image segmentation that employs both region statistics and edge information. This combination allows for improved flexibility, making the proposed model suitable to process a…
The novel concept of spectral diffusivity is introduced to analyse the dissipative properties of continua. The dissipative components of a linear system of evolution equations are separated into noninteracting parts. This separation is…
The curvature regularities are well-known for providing strong priors in the continuity of edges, which have been applied to a wide range of applications in image processing and computer vision. However, these models are usually non-convex,…
Calculus and geometry are ubiquitous in the theoretical modelling of scientific phenomena, but have historically been very challenging to apply directly to real data as statistics. Diffusion geometry is a new theory that reformulates…
As an important method of handling potential uncertainties in numerical simulations, ensemble simulation has been widely applied in many disciplines. Visualization is a promising and powerful ensemble simulation analysis method. However,…
We introduce a theoretical framework for differentiable surface evolution that allows discrete topology changes through the use of topological derivatives for variational optimization of image functionals. While prior methods for inverse…
Planetary atmospheres are inherently 3D objects that can have strong gradients in latitude, longitude, and altitude. Secondary eclipse mapping is a powerful way to map the 3D distribution of the atmosphere, but the data can have large…
In this paper, we focus on statistical region-based active contour models where image features (e.g. intensity) are random variables whose distribution belongs to some parametric family (e.g. exponential) rather than confining ourselves to…
End-to-end optimization, which simultaneously optimizes optics and algorithms, has emerged as a powerful data-driven method for computational imaging system design. This method achieves joint optimization through backpropagation by…
In the multivariate setting, estimates of extremal risk measures are important in many contexts, such as environmental planning and structural engineering. In this paper, we propose new estimation methods for extremal bivariate return…
Scientists, engineers, biologists, and technology specialists universally leverage image segmentation to extract shape ensembles containing many thousands of curves representing patterns in observations and measurements. These large curve…
How does one generalize differential geometric constructs such as curvature of a manifold to the discrete world of graphs and other combinatorial structures? This problem carries significant importance for analyzing models of discrete…
We show that dispersive propagation of light followed by phase detection has properties that can be exploited for extracting features from the waveforms. This discovery is spearheading development of a new class of physics-inspired…