About

Gabriel Taubin is a Professor of Engineering and Computer Science at Brown University. His research interests include computer vision, computer graphics, geometric modeling, mesh signal processing, geometry compression, smart cameras, smart sensor networks, and embedded systems. He is recognized for his contributions to these fields and has been acknowledged as one of the top two percent of scientists worldwide. His work has been featured in notable publications, including a paper included in a celebration of a computer graphics book. Taubin's expertise and research have established him as a prominent figure in engineering and computer science at Brown University.

Research topics

• Computer science
• Artificial intelligence
• Computer vision
• Computer graphics (images)
• Mathematics

Selected publications

• Lower Bounds for the Minimum Spanning Tree Cycle Intersection Problem

  arXiv (Cornell University) · 2024-04-26

  preprintOpen accessSenior author

  Minimum spanning trees are important tools in the analysis and design of networks. Many practical applications require their computation, ranging from biology and linguistics to economy and telecommunications. The set of cycles of a network has a vector space structure. Given a spanning tree, the set of non-tree edges defines cycles that determine a basis. The intersection of two such cycles is the number of edges they have in common and the intersection number -- denoted $\cap(G)$ -- is the number of non-empty pairwise intersections of the cycles of the basis. The Minimum Spanning Tree Cycle Intersection problem consists in finding a spanning tree such that the intersection number is minimum. This problem is relevant in order to integrate discrete differential forms. In this paper, we present two lower bounds of the intersection number of an arbitrary connected graph $G=(V,E)$. In the first part, we prove the following statement: $$\frac{1}{2}\left(\frac{ν^2}{n-1} - ν\right) \leq \cap(G),$$ where $n = |V|$ and $ν$ is the \emph{cyclomatic number} of $G$. In the second part, based on some experimental results and a new observation, we conjecture the following improved tight lower bound: $$(n-1) \binom{q}{2} + q \ r\leq \cap(G),$$ where $2 ν= q (n-1) + r$ is the integer division of $2 ν$ and $n-1$. This is the first result in a general context, that is for an arbitrary connected graph.

  PublisherOA PDFDOI

• Lower Bounds for the Minimum Spanning Tree Cycle Intersection Problem

  SSRN Electronic Journal · 2024-01-01

  preprintOpen accessSenior author
  PublisherDOI

• Method and system for unsynchronized structured lighting

  OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 2023-03-31

  articleOpen access1st authorCorresponding

  A system and method to capture the surface geometry a three-dimensional object in a scene using unsynchronized structured lighting is disclosed. The method and system includes a pattern projector configured and arranged to project a sequence of image patterns onto the scene at a pattern frame rate, a camera configured and arranged to capture a sequence of unsynchronized image patterns of the scene at an image capture rate, and a processor configured and arranged to synthesize a sequence of synchronized image frames from the unsynchronized image patterns of the scene. Each of the synchronized image frames corresponds to one image pattern of the sequence of image patterns.

  Publisher

• Three Aspects of the Mstci Problem

  SSRN Electronic Journal · 2023-01-01

  preprintOpen accessSenior author
  PublisherDOI

• Three aspects of the MSTCI problem

  arXiv (Cornell University) · 2023-01-18

  preprintOpen accessSenior author

  Consider a connected graph $G$ and let $T$ be a spanning tree of $G$. Every edge $e \in G-T$ induces a cycle in $T \cup \{e\}$. The intersection of two distinct such cycles is the set of edges of $T$ that belong to both cycles. The MSTCI problem consists in finding a spanning tree that has the least number of such non-empty intersections and the instersection number is the number of non-empty intersections of a solution. In this article we consider three aspects of the problem in a general context (i.e. for arbitrary connected graphs). The first presents two lower bounds of the intersection number. The second compares the intersection number of graphs that differ in one edge. The last is an attempt to generalize a recent result for graphs with a universal vertex.

  PublisherOA PDFDOI

• A Signal Processing Approach To Fair Surface Design

  ACM eBooks · 2023-08-01 · 26 citations

  book-chapter1st authorCorresponding

  In this paper we describe a new tool for interactive free-form fair surface design. By generalizing classical discrete Fourier analysis to two-dimensional discrete surface signals - functions defined on polyhedral surfaces of arbitrary topology -, we reduce the problem of surface smoothing, or fairing, to low-pass filtering. We describe a very simple surface signal low-pass filter algorithm that applies to surfaces of arbitrary topology. As opposed to other existing optimization-based fairing methods,which are computationally more expensive, this is a linear time and space complexity algorithm. With this algorithm, fairing very large surfaces, such as those obtained from volumetric medical data, becomes affordable. By combining this algorithm with surface subdivision methods we obtain a very effective fair surface design technique. We then extend the analysis, and modify the algorithm accordingly, to accommodate different types of constraints. Some constraints can be imposed without any modification of the algorithm, while others require the solution of a small associated linear system of equations. In particular, vertex location constraints, vertex normal constraints, and surface normal discontinuities across curves embedded in the surface, can be imposed with this technique.

  PublisherDOI

• Minimum Spanning Tree Cycle Intersection problem

  Discrete Applied Mathematics · 2021-02-20 · 6 citations

  articleOpen accessSenior author
  PublisherOA PDFDOI

• tinygarden — A java package for testing properties of spanning trees

  Software Impacts · 2021-05-18

  articleOpen accessSenior author

  Spanning trees are fundamental objects in graph theory. The spanning tree set size of an arbitrary graph can be very large. This limitation discourages its analysis. However interesting patterns can emerge in small cases. In this article we introduce tinygarden, a java package for validating hypothesis, testing properties and discovering patterns from the spanning tree set of an arbitrary graph.

  PublisherOA PDFDOI

• GCSR: Gray Code Super-Resolution 3D Scanning

  2021 International Conference on 3D Vision (3DV) · 2021-12-01

  articleSenior author

  Digital pattern projectors used in structured light 3D scanners cannot project infinitesimally thin columns of light – the projector pixel columns have a finite thickness. Current methods incorrectly model these columns of light as planes, which contributes to reconstruction errors. We propose a method to increase the resolution of structured light 3D scanners based on time-multiplexed discrete patterns by taking multiple acquisitions of the scene with different projector poses, and by modeling the light projected by each pixel column as a volume in space instead of as a plane, which results in upper and lower bounds on the resulting depth map. Furthermore, by analyzing multiple acquisitions in different projector poses, these upper and lower depth bounds can be tightened. We refer to this tightening as super-resolution, because it corresponds to an increase in the confidence in the location of the object’s surface. We describe our first implementation of such a system, and demonstrate its performance on a variety of objects.

  PublisherDOI

• Laplacian Coordinates: Theory and Methods for Seeded Image Segmentation

  IEEE Transactions on Pattern Analysis and Machine Intelligence · 2020-02-17 · 20 citations

  articleOpen access

  Seeded segmentation methods have gained a lot of attention due to their good performance in fragmenting complex images, easy usability and synergism with graph-based representations. These methods usually rely on sophisticated computational tools whose performance strongly depends on how good the training data reflect a sought image pattern. Moreover, poor adherence to the image contours, lack of unique solution, and high computational cost are other common issues present in most seeded segmentation methods. In this work we introduce Laplacian Coordinates, a quadratic energy minimization framework that tackles the issues above in an effective and mathematically sound manner. The proposed formulation builds upon graph Laplacian operators, quadratic energy functions, and fast minimization schemes to produce highly accurate segmentations. Moreover, the presented energy functions are not prone to local minima, i.e., the solution is guaranteed to be globally optimal, a trait not present in most image segmentation methods. Another key property is that the minimization procedure leads to a constrained sparse linear system of equations, enabling the segmentation of high-resolution images at interactive rates. The effectiveness of Laplacian Coordinates is attested by a comprehensive set of comparisons involving nine state-of-the-art methods and several benchmarks extensively used in the image segmentation literature.

  PublisherOA PDFDOI

Recent grants

• PFI:AIR - TT: Low Cost High Resolution 3D Scanning Technologies for 3D Printing

  NSF · $215k · 2015–2017

• Computing Shape From Depth Discontinuities

  NSF · $260k · 2007–2011

• RI: Small: Low Cost Technologies to Improve the Quality of 3D Scanning

  NSF · $450k · 2017–2022

• AF: Small: Fundamental Geometry Processing

  NSF · $250k · 2009–2013

Frequent coauthors

• Nigel Davies

  Lancaster University

  57 shared

• Michael Rabinovich

  57 shared

• Forrest Shull

  Fraunhofer USA Center Mid-Atlantic CMA

  57 shared

• Paolo Montuschi

  57 shared

• George K. Thiruvathukal

  57 shared

• Daniel Zeng

  Chinese Academy of Sciences

  57 shared

• Ron Vetter

  University of North Carolina Wilmington

  57 shared

• Lawrence Pfleeger

  A.S. Watson (Netherlands)

  48 shared

Education

• PhD, Engineering

  Brown University

  1991

• Licenciado en Ciencias Matemáticas, Matematicas

  Universidad de Buenos Aires

  1981