Point set stratification and minimum weight structures

Three different concepts of depth in a point set are considered and compared: Convex depth, location depth and Delaunay depth. As a notion of weight is naturally associated to each depth definition, we also present results on minimum weight structures (like spanning trees, poligonizations and triangulations) with respect to the three variations.DURSYMinisterio de Ciencia y Tecnologí

Approaching minimum area polygonization

The problem of fi nding a minimum area polygonization for a given set of points in the plane, Minimum Area Polygonization (MAP) is NP-hard. Due to the complexity of the problem we aim at the development of algorithms to obtain approximate solutions. In this work, we suggest di feerent strategies in order to minimize the polygonization area.We propose algorithms to search for approximate solutions for MAP problem. We present an experimental study for a set of instances for MAP problem.Presentado en el XII Workshop Agentes y Sistemas Inteligentes (WASI)Red de Universidades con Carreras en Informática (RedUNCI

Simple Kinesthetic Haptics for Object Recognition

Object recognition is an essential capability when performing various tasks. Humans naturally use either or both visual and tactile perception to extract object class and properties. Typical approaches for robots, however, require complex visual systems or multiple high-density tactile sensors which can be highly expensive. In addition, they usually require actual collection of a large dataset from real objects through direct interaction. In this paper, we propose a kinesthetic-based object recognition method that can be performed with any multi-fingered robotic hand in which the kinematics is known. The method does not require tactile sensors and is based on observing grasps of the objects. We utilize a unique and frame invariant parameterization of grasps to learn instances of object shapes. To train a classifier, training data is generated rapidly and solely in a computational process without interaction with real objects. We then propose and compare between two iterative algorithms that can integrate any trained classifier. The classifiers and algorithms are independent of any particular robot hand and, therefore, can be exerted on various ones. We show in experiments, that with few grasps, the algorithms acquire accurate classification. Furthermore, we show that the object recognition approach is scalable to objects of various sizes. Similarly, a global classifier is trained to identify general geometries (e.g., an ellipsoid or a box) rather than particular ones and demonstrated on a large set of objects. Full scale experiments and analysis are provided to show the performance of the method

StrokeStyles: Stroke-based Segmentation and Stylization of Fonts

We develop a method to automatically segment a font’s glyphs into a set of overlapping and intersecting strokes with the aim of generating artistic stylizations. The segmentation method relies on a geometric analysis of the glyph’s outline, its interior, and the surrounding areas and is grounded in perceptually informed principles and measures. Our method does not require training data or templates and applies to glyphs in a large variety of input languages, writing systems, and styles. It uses the medial axis, curvilinear shape features that specify convex and concave outline parts, links that connect concavities, and seven junction types. We show that the resulting decomposition in strokes can be used to create variations, stylizations, and animations in different artistic or design-oriented styles while remaining recognizably similar to the input font

Signal Processing on Textured Meshes

In this thesis we extend signal processing techniques originally formulated in the context of image processing to techniques that can be applied to signals on arbitrary triangles meshes. We develop methods for the two most common representations of signals on triangle meshes: signals sampled at the vertices of a finely tessellated mesh, and signals mapped to a coarsely tessellated mesh through texture maps. Our first contribution is the combination of Lagrangian Integration and the Finite Elements Method in the formulation of two signal processing tasks: Shock Filters for texture and geometry sharpening, and Optical Flow for texture registration. Our second contribution is the formulation of Gradient-Domain processing within the texture atlas. We define a function space that handles chart discontinuities, and linear operators that capture the metric distortion introduced by the parameterization. Our third contribution is the construction of a spatiotemporal atlas parameterization for evolving meshes. Our method introduces localized remeshing operations and a compact parameterization that improves geometry and texture video compression. We show temporally coherent signal processing using partial correspondences

Erosion, Self-Organization, and Procedural Modeling

Procedural modeling of natural objects such as coastlines and terrains in combination with their characteristic erosion features involves integration of appropriate physical models with the procedural approach and culminates in the development of physically-based simulations. I have invented a modeling paradigm for designing this type of simulations in a way that generalizes formation of complex relationships between erosion features, such as the tributary relationship. My generalization uses self-organization to define where erosion occurs and how it propagates rather than emphasizing the exact mechanism of erosion and the details of what happens during each erosion event. Propagation of state changes due to self-organization can also lead to emergence of fractal character, which is essential for modeling of natural objects, without explicit fractal synthesis. I successfully apply my methodology to procedural modeling of dunes, coastlines, terrains that undergo hydraulic erosion due to channel networks, and 3D channel networks that form underground

LIPIcs, Volume 258, SoCG 2023, Complete Volume

LIPIcs, Volume 258, SoCG 2023, Complete Volum