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A two-dimensional tomographic problem is studied. The target is assumed to be a homogeneous object bounded by a smooth curve. A Non Uniform Rational Basis Splines (NURBS) curve is used as computational representation of the boundary. This…
Out-of-equilibrium systems, inherently complex and challenging to understand, are prevalent across various disciplines, including physics where they arise in contexts such as fluid dynamics. In particular, critical out-of-equilibrium…
Studies from neuroscience show that part-mapping computations are employed by human visual system in the process of object recognition. In this work, we present an approach for analyzing semantic-part characteristics of object category…
Many surface cues support three-dimensional shape perception, but people can sometimes still see shape when these features are missing -- in extreme cases, even when an object is completely occluded, as when covered with a draped cloth. We…
We propose a new set of rotationally and translationally invariant features for image or pattern recognition and classification. The new features are cubic polynomials in the pixel intensities and provide a richer representation of the…
Convolutional neural networks (CNNs) have been tremendously successful in solving imaging inverse problems. To understand their success, an effective strategy is to construct simpler and mathematically more tractable convolutional sparse…
In this paper we study embeddings of oriented connected closed surfaces in $\mathbb S^3$. We define a complete invariant, the fundamental span, for such embeddings, generalizing the notion of the peripheral system of a knot group. From the…
From the perspective of Morse theory, it is natural to investigate gradient flow trajectories between critical points. In this short note, we explore the minimal hypersurface analogue of this phenomenon and present examples that suggest…
Valuations constitute a class of functionals on convex bodies which include the Euler-characteristic, the surface area, the Lebesgue-measure, and many more classical functionals. Curvature measures may be regarded as "localised`` versions…
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…
Core-periphery structure is a common property of complex networks, which is a composition of tightly connected groups of core vertices and sparsely connected periphery vertices. This structure frequently emerges in traffic systems, biology,…
The nonlinear spaces of shapes (unparameterized immersed curves or submanifolds) are of interest for many applications in image analysis, such as the identification of shapes that are similar modulo the action of some group. In this paper…
In two parts, we present a bigness criterion for the cotangent bundle of resolutions of orbifold surfaces of general type. As a corollary, we obtain the \textit{canonical model singularities} (CMS) criterion that can be applied to determine…
Matter density is formally infinite at the location of caustic surfaces, where dark matter sheet folds in phase-space. The caustics separate regions with different number of streams and the volume elements change the parity by turning…
Co-Salient Object Detection (CoSOD) aims at simulating the human visual system to discover the common and salient objects from a group of relevant images. Recent methods typically develop sophisticated deep learning based models have…
In this thesis, we present various contributions to the study of free boundary minimal surfaces. After introducing some basic tools and discussing some delicate aspects related to the definition of Morse index when allowing for a contact…
In this paper, we construct cochain complexes generated by the cohomology of critical manifolds in the abstract setup of flow categories for Morse-Bott theories under minimum transversality assumptions. We discuss the relations between…
State-of-the-art diffusion models can generate highly realistic images based on various conditioning like text, segmentation, and depth. However, an essential aspect often overlooked is the specific camera geometry used during image…
Contour shape alignment is a fundamental but challenging problem in computer vision, especially when the observations are partial, noisy, and largely misaligned. Recent ConvNet-based architectures that were proposed to align image…
Graph invariants provide a powerful analytical tool for investigation of abstract structures of graphs. They, combined in convenient relations, carry global and general information about a graph and its various substructures such as cycle…