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Gaussian Splatting (GS) has emerged as a crucial technique for representing discrete volumetric radiance fields. It leverages unique parametrization to mitigate computational demands in scene optimization. This work introduces…

The growth of a rough and porous thin surface by deposition of randomly shaped clusters with different sizes over an initially flat linear substrate is simulated, using Monte Carlo technique. Unlike the ordinary Random Deposition, our…

Inspired by the seminal result that a graph and an associated rotation system uniquely determine the topology of a closed manifold, we propose a combinatorial method for reconstruction of surfaces from points. Our method constructs a…

We propose a fast and accurate surface reconstruction algorithm for unorganized point clouds using an implicit representation. Recent learning methods are either single-object representations with small neural models that allow for high…

The optimal use of resources has motivated the engineering community to employ controlled distribution of material within their structural designs, often relying on cellular and lattice porous structures. In this research work, a…

We propose a functorial framework for persistent homology based on finite topological spaces and their associated posets. Starting from a finite metric space, we associate a filtration of finite topologies whose structure maps are…

Point cloud compression (PCC) is a key enabler for various 3-D applications, owing to the universality of the point cloud format. Ideally, 3D point clouds endeavor to depict object/scene surfaces that are continuous. Practically, as a set…

This paper proposes a method for computing the visible occluding contours of subdivision surfaces. The paper first introduces new theory for contour visibility of smooth surfaces. Necessary and sufficient conditions are introduced for when…

We describe here the design and fabrication of a rewritable and reprintable paper as an alternative to conventional papers which are generally used for writing and printing purposes. This paper is prepared by casting a crosslinkable…

We study the grokking phenomenon through the lens of topology. Using persistent homology on point clouds derived from the embedding matrices of a range of models trained on modular arithmetic with varying primes, we identify a clear and…

Phase separation mechanisms can produce a variety of complicated and intricate microstructures, which often can be difficult to characterize in a quantitative way. In recent years, a number of novel topological metrics for microstructures…

In this study, we present a concept of morphing structure -- featuring an arch mounted on a compliant base -- that can be reconfigured via snap-through buckling and leverages bistability to retain its morphed shape. We show that…

Persistent homology is an effective method for extracting topological information, represented as persistent diagrams, of spatial structure data. Hence it is well-suited for the study of protein structures. Attempts to incorporate…

Existing networks directly learn feature representations on 3D point clouds for shape analysis. We argue that 3D point clouds are highly redundant and hold irregular (permutation-invariant) structure, which makes it difficult to achieve…

Representing shapes as level sets of neural networks has been recently proved to be useful for different shape analysis and reconstruction tasks. So far, such representations were computed using either: (i) pre-computed implicit shape…

In healthcare, accurately classifying medical images is vital, but conventional methods often hinge on medical data with a consistent grid structure, which may restrict their overall performance. Recent medical research has been focused on…

A topology preserving skeleton is a synthetic representation of an object that retains its topology and many of its significant morphological properties. The process of obtaining the skeleton, referred to as skeletonization or thinning, is…

Shells, when confined, can deform in a broad assortment of shapes and patterns, often quite dissimilar to what is produced by their flat counterparts (plates). In this work we discuss the morphological landscape of shells deposited on a…

Man-made objects usually exhibit descriptive curved features (i.e., curve networks). The curve network of an object conveys its high-level geometric and topological structure. We present a framework for extracting feature curve networks…

Learning structures of 3D shapes is a fundamental problem in the field of computer graphics and geometry processing. We present a simple yet interpretable unsupervised method for learning a new structural representation in the form of 3D…