Digital Image Processing Techniques

Neueste Paper

• A solution to the Erd\H{o}s Problem #1040

  Ioannis Tzachristas · 9. September 2026

  For a compact set $K\subset\mathbb{C}$, let $\vartheta(K)$ be the infimum of the planar areas of the unit lemniscates of all monic polynomials with zeros in $K$, allowing arbitrary degree and repeated zeros. We prove that $\vartheta(K)=0$ whenever $\operatorname{cap}(K)=1$, with no regularity assump…

• From Ordered Bernoulli Levels to Critical-Line Geometry: Integer Quantization, Bernoulli Residual Phase, and Prime-Power Spectra

  Y. Kenan Y{\i}lmaz · 4. September 2026

  We study the ordered Bernoulli-word kernel f(p,n,k)=p^k(1-p)^(n-k) and the geometry generated by its inverse-integer level sets. The binary level 2^(-n) selects p=1/2 as the unique real split-independent anchor. Under complement-preserving complex continuation, the pair becomes z=1/2+iu and 1-z=1/2-…

• Rendering 3D Gaussians on a Graph Processor

  Nicholas Fry, Ignacio Alzugaray, Mark Pupilli, Paul H. J. Kelly, Andrew J. Davison · 20. Juli 2026

  We present the first implementation of a 3D Gaussian renderer on an Intelligence Processing Unit (IPU), comprising 1,472 independent tiles with only on-chip SRAM; constraints that approximate properties of efficient sensor-processor architectures. Our input scenes are 3D Gaussian maps from real-worl…

• A Partition-Based Generating Function for Row-Convex Polyominoes

  Vincenzo M. Scarrica · 6. Mai 2026

  An alternative generating function is proposed to enumerate row-convex polyominoes without internal holes on a discrete grid. The approach is based on integer partitions of the total area, where each partition corresponds to a sequence of row lengths, and the product of all permutations of the parts…

• Multiprojective Geometry of Compatible Triples of Fundamental and Essential Matrices

  Timothy Duff, Viktor Korotynskiy, Anton Leykin, Tomas Pajdla · 2. März 2026

  We characterize the variety of compatible fundamental matrix triples by computing its multidegree and multihomogeneous vanishing ideal. This answers the first interesting case of a question recently posed by Bråtelund and Rydell. Our result improves upon previously discovered sets of algebraic const…

• Minimisation of Quasar-Convex Functions Using Random Zeroth-Order Oracles

  Amir Ali Farzin, Yuen-Man Pun, Philipp Braun, Iman Shames · 3. Februar 2026

  This paper explores the performance of a random Gaussian smoothing zeroth-order (ZO) scheme for minimising quasar-convex (QC) and strongly quasar-convex (SQC) functions in both unconstrained and constrained settings. For the unconstrained problem, we establish the ZO algorithm's convergence to a glo…

• Three-dimensional visualization of X-ray micro-CT with large-scale datasets: Efficiency and accuracy for real-time interaction

  Yipeng Yin, Rao Yao, Qingying Li, Dazhong Wang, Hong Zhou, Zhijun Fang, Jianing Chen, Longjie Qian, Mingyue Wu · 22. Januar 2026

  As Micro-CT technology continues to refine its characterization of material microstructures, industrial CT ultra-precision inspection is generating increasingly large datasets, necessitating solutions to the trade-off between accuracy and efficiency in the 3D characterization of defects during ultra…

• GaussianTrimmer: Online Trimming Boundaries for 3DGS Segmentation

  Liwei Liao, Ronggang Wang · 20. Januar 2026

  With the widespread application of 3D Gaussians in 3D scene representation, 3D scene segmentation methods based on 3D Gaussians have also gradually emerged. However, existing 3D Gaussian segmentation methods basically segment on the basis of Gaussian primitives. Due to the large variation range of t…

• Jordan-Segmentable Masks: A Topology-Aware definition for characterizing Binary Image Segmentation

  Serena Grazia De Benedictis, Amedeo Altavilla, Nicoletta Del Buono · 16. Januar 2026

  Image segmentation plays a central role in computer vision. However, widely used evaluation metrics, whether pixel-wise, region-based, or boundary-focused, often struggle to capture the structural and topological coherence of a segmentation. In many practical scenarios, such as medical imaging or ob…

• Kolmogorov--Arnold stability

  Sviatoslav V. Dzhenzher, Michael H. Freedman · 14. Januar 2026

  Regarding the representation theorem of Kolmogorov and Arnold (KA) as an algorithm for representing or <<expressing>> functions, we test its robustness by analyzing its stability to withstand re-parameterizations of the hidden space. One may think of such re-parameterizations as the work of an adver…

• Spontaneous Kolmogorov-Arnold Geometry in Shallow MLPs

  Michael H. Freedman, Michael Mulligan · 3. Dezember 2025

  The Kolmogorov-Arnold (KA) representation theorem constructs universal, but highly non-smooth inner functions (the first layer map) in a single (non-linear) hidden layer neural network. Such universal functions have a distinctive local geometry, a "texture," which can be characterized by the inner f…