Related papers: Critical Contours: An Invariant Linking Image Flow…
Shape inference is classically ill-posed, because it involves a map from the (2D) image domain to the (3D) world. Standard approaches regularize this problem by either assuming a prior on lighting and rendering or restricting the domain,…
Invariants underlying shape inference are elusive: a variety of shapes can give rise to the same image, and a variety of images can be rendered from the same shape. The occluding contour is a rare exception: it has both image salience, in…
Motivated by a M\"obius invariant subdivision scheme for polygons, we study a curvature notion for discrete curves where the cross-ratio plays an important role in all our key definitions. Using a particular M\"obius invariant…
Morse complexes are gradient-based topological descriptors with close connections to Morse theory. They are widely applicable in scientific visualization as they serve as important abstractions for gaining insights into the topology of…
We investigate the geometry of holomorphic curves and complex surfaces from the perspective of singularity theory. We show that, with a suitable choice of a complex bilinear symmetric form, the families of functions and mappings that…
The complexity of condensed matter arises from emergent behaviors that cannot be understood by analyzing individual constituents in isolation. While traditional condensed-matter approaches-developed primarily for ideal crystalline…
On a smooth manifold, we associate to any closed differential form a mapping cone complex. The cohomology of this mapping cone complex can vary with the de Rham cohomology class of the closed form. We present a novel Morse theoretical…
This paper brings together three distinct theories with the goal of quantifying shape textures with complex morphologies. Distance fields are central objects in shape representation, while topological data analysis uses algebraic topology…
We make a systematic study of the focal surface of a congruence of lines in the projective space. Using differential techniques together with techniques from intersection theory, we reobtain in particular all the invariants of the focal…
We develop a framework for extracting a concise representation of the shape information available from diffuse shading in a small image patch. This produces a mid-level scene descriptor, comprised of local shape distributions that are…
A convolution model which accounts for neural activity dynamics in the primary visual cortex is derived and used to detect visually salient contours in images. Image inputs to the model are modulated by long-range horizontal connections,…
As an alternative way of describing the cosmological velocity field, we discuss the evolution of rotational invariants constructed from the velocity gradient tensor. Compared with the traditional divergence-vorticity decomposition, these…
The computer vision community has witnessed recent advances in scene categorization from images, with the state-of-the art systems now achieving impressive recognition rates on challenging benchmarks such as the Places365 dataset. Such…
Invariant representations are core to representation learning, yet a central challenge remains: uncovering invariants that are stable and transferable without suppressing task-relevant signals. This raises fundamental questions, requiring…
We present a robust method to find region-level correspondences between shapes, which are invariant to changes in geometry and applicable across multiple shape representations. We generate simplified shape graphs by jointly decomposing the…
The classical approach to the study of dynamical systems consists in representing the dynamics of the system in the form of a "source-sink", that means identifying an attractor-repeller pair, which are attractor-repellent sets for all other…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…
A fundamental problem faced by object recognition systems is that objects and their features can appear in different locations, scales and orientations. Current deep learning methods attempt to achieve invariance to local translations via…
We take the fundamental group of the complement of the branch curve of a generic projection induced from canonical embedding of a surface. This group is stable on connected components of moduli spaces of surfaces. Since for many classes of…
Edges, boundaries and contours are important subjects of study in both computer graphics and computer vision. On one hand, they are the 2D elements that convey 3D shapes, on the other hand, they are indicative of occlusion events and thus…