Related papers: Jacobi Set Driven Search for Flexible Fiber Surfac…
Jacobi sets are an important tool to study the relationship between functions. Defined as the set of all points where the function's gradients are linearly dependent, Jacobi sets extend the notion of critical point to multifields. In…
This work considers gradient-based mesh optimization, where we iteratively optimize for a 3D surface mesh by representing it as the isosurface of a scalar field, an increasingly common paradigm in applications including photogrammetry,…
The Jacobi set of a bivariate scalar field is the set of points where the gradients of the two constituent scalar fields align with each other. It captures the regions of topological changes in the bivariate field. The Jacobi set is a…
Extracting high-fidelity mesh surfaces from Signed Distance Fields has become a fundamental operation in geometry processing. Despite significant progress over the past decades, key challenges remain namely, how to automatically capture the…
Extracting level sets from scalar data is a fundamental operation in visualization with many applications. Recently, the concept of level set extraction has been extended to bivariate scalar fields. Prior work on vector field equivalence,…
There are various methods for extracting iso-surfaces from volumetric data. Marching cubes or tetrahedra or raytracing methods are mostly used. There are many specific techniques to increase speed of computation and decrease memory…
Let $f: \mathbb{R}^3 \rightarrow \mathbb{R}$ be a scalar field. An isosurface is a piecewise linear approximation of a level set $f^{-1}(\sigma)$ for some $\sigma \in \mathbb{R}$ built from some regular grid sampling of $f$. Isosurfaces…
Topological simplification of scalar and vector fields is well-established as an effective method for analysing and visualising complex data sets. For multi-field data, topological analysis requires simultaneous advances both mathematically…
This paper deals with a study of the rational elliptic surfaces whose $J$-invariant functions are of degree one. Almost all of these elliptic surfaces have four singular fibers, while the remaining surfaces have only three singular fibers.…
As constituent parts of image objects, superpixels can improve several higher-level operations. However, image segmentation methods might have their accuracy seriously compromised for reduced numbers of superpixels. We have investigated a…
Marching surfaces is a method for isosurface extraction and approximation based on a $G^1$ multi-sided patch interpolation scheme. Given a 3D grid of scalar values, an underlying curve network is formed using second order information and…
In this paper four fundamental methods for an iso-surface extraction are compared, based on cell decomposition to tetrahedra. The methods are compared both on mathematically generated data sets as well as on real data sets. The comparison…
The Reeb space is a fundamental data structure in computational topology that represents the fiber topology of a multi-field (or multiple scalar fields), extending the level set topology of a scalar field. Efficient algorithms have been…
Iso-surface extraction from an implicit field is a fundamental process in various applications of computer vision and graphics. When dealing with geometric shapes with complicated geometric details, many existing algorithms suffer from high…
We theoretically study the problem of detecting dipole radiation in an optical system of high numerical aperture in which the detector is sensitive to \textit{field amplitude}. In particular, we model the phase sensitive detector as a…
With the ever growing popularity of integral field unit (IFU) spectroscopy, countless observations are being performed over multiple object systems such as blank fields and galaxy clusters. With this, an increasing amount of time is being…
In this paper, we propose a new method, called DoubleCoverUDF, for extracting the zero level-set from unsigned distance fields (UDFs). DoubleCoverUDF takes a learned UDF and a user-specified parameter $r$ (a small positive real number) as…
Integration of scalar and vector visualization has been an interesting topic. This paper presents a technique to appropriately select and display multiple streamlines while overlaying with isosurfaces, aiming an integrated scalar and vector…
We study Jacobi matrices on trees whose coefficients are generated by multiple orthogonal polynomials. Hilbert space decomposition into an orthogonal sum of cyclic subspaces is obtained. For each subspace, we find generators and the…
Superpixel segmentation has become an important research problem in image processing. In this paper, we propose an Iterative Spanning Forest (ISF) framework, based on sequences of Image Foresting Transforms, where one can choose i) a seed…