tinygarden - A java package for testing properties of spanning trees

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.Fil: Dubinsky, Manuel. Universidad Nacional de Avellaneda; ArgentinaFil: Massri, Cesar Dario. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Taubin, Gabriel. University Brown; Estados Unido

CrowdCam: Instantaneous Navigation of Crowd Images Using Angled Graph

We present a near real-time algorithm for interactively exploring a collectively captured moment without explicit 3D reconstruction. Our system favors immediacy and local coherency to global consistency. It is common to represent photos as vertices of a weighted graph, where edge weights measure similarity or distance between pairs of photos. We introduce Angled Graphs as a new data structure to organize collections of photos in a way that enables the construction of visually smooth paths. Weighted angled graphs extend weighted graphs with angles and angle weights which penalize turning along paths. As a result, locally straight paths can be computed by specifying a photo and a direction. The weighted angled graphs of photos used in this paper can be regarded as the result of discretizing the Riemannian geometry of the high dimensional manifold of all possible photos. Ultimately, our system enables everyday people to take advantage of each others' perspectives in order to create on-the-spot spatiotemporal visual experiences similar to the popular bullet-time sequence. We believe that this type of application will greatly enhance shared human experiences spanning from events as personal as parents watching their children's football game to highly publicized red carpet galas.Swiss National Science FoundationEuropean Commission (ERC grant #210806 4DVideo, 7th Framework Programme (FP7/2007- 2013)

One-shot scanning using de bruijn spaced grids.

Abstract In this paper we present a new "one-shot" method to reconstruct the shape of dynamic 3D objects and scenes based on active illumination. In common with other related prior-art methods, a static grid pattern is projected onto the scene, a video sequence of the illuminated scene is captured, a shape estimate is produced independently for each video frame, and the one-shot property is realized at the expense of space resolution. The main challenge in grid-based one-shot methods is to engineer the pattern and algorithms so that the correspondence between pattern grid points and their images can be established very fast and without uncertainty. We present an efficient one-shot method which exploits simple geometric constraints to solve the correspondence problem. We also introduce De Bruijn spaced grids, a novel grid pattern, and show with strong empirical data that the resulting scheme is much more robust compared to those based on uniform spaced grids

Laplacian coordinates for seeded image segmentation

Seed-based image segmentation methods have gained\ud much attention lately, mainly due to their good performance\ud in segmenting complex images with little user interaction.\ud Such popularity leveraged the development of many new\ud variations of seed-based image segmentation techniques,\ud which vary greatly regarding mathematical formulation and\ud complexity. Most existing methods in fact rely on complex\ud mathematical formulations that typically do not guarantee\ud unique solution for the segmentation problem while still being\ud prone to be trapped in local minima. In this work we\ud present a novel framework for seed-based image segmentation\ud that is mathematically simple, easy to implement, and\ud guaranteed to produce a unique solution. Moreover, the formulation\ud holds an anisotropic behavior, that is, pixels sharing\ud similar attributes are kept closer to each other while\ud big jumps are naturally imposed on the boundary between\ud image regions, thus ensuring better fitting on object boundaries.\ud We show that the proposed framework outperform\ud state-of-the-art techniques in terms of quantitative quality\ud metrics as well as qualitative visual resultsFAPESP (processos nos. 2009/17801-0 e 2011/22749-8 e 2012/14021-7)CNPq (processo no. 302643/2013-3)NSF (subvenções IIS-0808718 e 0915661-CCF

Is this a quadrisect mesh

This report has been submitted for publication outside of IBM and will probably be copyrighted is accepted for publication. It has been issued as a Research Report for early dissemination of its contents. In view of the transfer of copyright to the outside publisher, its distribution outside of IBM prior to publication should be limited to peer communications and specific requests. After outside publication, requests should be filled only by reprints or legally obtained copies of the article (e.g., payment of royalties). Some reports are available at http://domino.watson.ibm.com/library/CyberDig.nsf/home. Copies may requested from IBM T.J. Watson Researc

An Accurate Algorithm for Rasterizing Algebraic Curves

In this paper we introduce a new algorithm for rasterizing algebraic curves, and we discuss applications to surface and surface-surface intersection rendering and visualization. By rustm”zing an algebraic curve we mean to determine which cells, or pixels, from a square mesh of cells in the plane, are cut by a curve represented as the set of zeros of a polynomial in two variables. By using a recursive space subdivision scheme, the problem is be reduced to testing whether the curve cuts a square or not. Other mwearchers have followed this approach, but their tests are either computationally expensive, or apply just to special cases. Curves with singularities are particularly difficult to deal with, and most know algorithms fail to nmder these curves correctly

A Signal Processing Approach To Fair Surface Design

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. CR Categories and Subject Descriptors: I.3.3 [Computer Graphics]: Picture/image generation - display algorithms; I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling - curve, surface, solid, and object representations;J.6[Com- puter Applications]: Computer-Aided Engineering - computeraided design General Terms: Algorithms, Graphics.

Real-Time Massive 3D Data Capture and Geometry Processing

In Geometry Processing, a field which has developed during the last ten years, concepts from applied mathematics, computer science, and engineering are used to design efficient algorithms for the acquisition, manipulation, animation and transmission of complex 3D models. A number of methods have been proposed to smooth, denoise, edit, compress, transmit, re-parameterize, and animate very large polygon meshes, based on topological and combinatorial methods, signal processing techniques, constrained energy minimization, and the solution of partial differential equations. In particular, polygon models, which are used in most graphics applications, require considerable amounts of storage, even when they only approximate precise shapes with limited accuracy, and must be compressed by several orders of magnitude for fast network access. In this talk I will present some of our early contributions to the field, and some related ongoing research projects. I will also describe the state of our work towards the apparently unrelated goal of building Visual Sensor Networks with 1000s of cameras for real time capture and processing of 3D data