Luiz Velho

4-8 Subdivision

In this paper we introduce 4-8 subdivision, a new scheme that generalizes the four-directional box spline of class C^4 to surfaces of arbitrary topological type. The crucial advantage of the proposed scheme is that it uses bisection refinement as an elementary refinement operation, rather than more commonly used face or vertex splits. In the uniform case, bisection refinement results in doubling, rather than quadrupling of the number of faces in a mesh. Adaptive bisection refinement automatically generates conforming variable-resolution meshes in contrast to face and vertex split methods which require a postprocessing step to make an adaptively refined mesh conforming. The fact that the size of faces decreases more gradually with refinement allows one to have greater control over the resolution of a refined mesh. It also makes it possible to achieve higher smoothness while using small stencils (the size of the stencils used by our scheme is similar to Loop subdivision). We show that the subdivision surfaces produced by the 4-8 scheme are C^4 continuous almost everywhere, except at extraordinary vertices where they are is C^1-continuous.Most commonly used subdivision schemes are of primal type, i.e., they split faces. Examples include the schemes of Catmull-Clark (quadrilaterals) and Loop (triangles). In contrast, dual subdivision schemes such as Doo-Sabin, are based on vertex splits. Triangle based subdivision does not admit primal and dual schemes as the latter are based on hexagons. Quadrilateral schemes on the other hand come in both primal and dual varieties allowing for the possibility of a unified treatment and common implementation. In this paper we consider the construction of an increasing sequence of alternating primal/dual quadrilateral subdivision schemes based on a simple averaging approach. Beginning with a vertex split step we successively construct variants of Doo-Sabin and Catmull-Clark schemes followed by novel schemes generalizing B-splines of bi-degree up to nine. We prove the schemes to be C at extraordinary points, and analyze the behavior of the schemes as the number of averaging steps increases. We discuss a number of implementation issues common to all quadrilateral schemes; in particular we describe a simple algorithm for adaptive subdivision of dual schemes. Because of the unified construction framework and common algorithmic treatment of primal and dual quadrilateral subdivision schemes it is straightforward to support multiple schemes in the same application. This is useful for more flexible geometric modeling as well as in p-versions of the Subdivision Element Method.

Digital halftoning with space filling curves

This paper introduces a new digital halftoning technique that uses space filling curves to generate aperiodic patterns of clustered dots. This method allows the parameterization of the size of pixel clusters, which can vary in one pixel steps. The algorithm unifies, in this way, the dispersed and clustered-dot dithering techniques.

Kinect and RGBD Images: Challenges and Applications

Kinect is a device introduced in November 2010 as an accessory of Xbox 360. The acquired data has different and complementary natures, combining geometry with visual attributes. For this reason, Kinect is a flexible tool that can be used in applications from several areas such as: Computer Graphics, Image Processing, Computer Vision and Human-Machine Interaction. In this way, the Kinect is a widely used device in industry (games, robotics, theater performers, natural interfaces, etc.) and in research. We will initially present some concepts about the device: the architecture and the sensor. We then will discuss about the data acquisition process: capturing, representation and filtering. Capturing process consists of obtaining a colored image (RGB) and performing a depth measurement (D), with structured light technique. This data is represented by a structure called RGBD Image. We will also talk about the main tools available for developing applications on various platforms. Furthermore, we will discuss some recent projects based on RGBD Images. In particular, those related to Object Recognition, 3D Reconstruction, Augmented Reality, Image Processing, Robotic, and Interaction. In this survey, we will show some research developed by the academic community and some projects developed for the industry. We intend to show the basic principles to begin developing applications using Kinect, and present some projects developed at the VISGRAF Lab. And finally, we intend to discuss the new possibilities, challenges and trends raised by Kinect.

A hierarchical segmentation of articulated bodies

This paper presents a novel segmentation method to assist the rigging of articulated bodies. The method computes a coarse‐to‐fine hierarchy of segments ordered by the level of detail. The results are invariant to deformations, and numerically robust to noise, irregular tessellations, and topological short‐circuits. The segmentation is based on two key ideas. First, it exploits the multiscale properties of the diffusion distance on surfaces, and then it introduces a new definition of medial structures, composing a bijection between medial structures and segments. Our method computes this bijection through a simple and fast iterative approach, and applies it to triangulated meshes.

Variable Resolution 4-k Meshes: Concepts and Applications

In this paper we introduce variable resolution 4‐k meshes, a powerful structure for the representation of geometric objects at multiple levels of detail. It combines most properties of other related descriptions with several advantages, such as more flexibility and greater expressive power. The main unique feature of the 4‐k mesh structure lies in its variable resolution capability, which is crucial for adaptive computation. We also give an overview of the different methods for constructing the 4‐k mesh representation, as well as the basic algorithms necessary to incorporate it in modeling and graphics applications.

Surface reconstruction from noisy point clouds

We show that a simple modification of the power crust algorithm for surface reconstruction produces correct outputs in presence of noise. This is proved using a fairly realistic noise model. Our theoretical results are related to the problem of computing a stable subset of the medial axis. We demostrate the effectiveness of our algorithm with a number of experimental results.

Automatic 3d facial expression analysis in videos

We introduce a novel framework for automatic 3D facial expression analysis in videos. Preliminary results demonstrate editing facial expression with facial expression recognition. We first build a 3D expression database to learn the expression space of a human face. The real-time 3D video data were captured by a camera/projector scanning system. From this database, we extract the geometry deformation independent of pose and illumination changes. All possible facial deformations of an individual make a nonlinear manifold embedded in a high dimensional space. To combine the manifolds of different subjects that vary significantly and are usually hard to align, we transfer the facial deformations in all training videos to one standard model. Lipschitz embedding embeds the normalized deformation of the standard model in a low dimensional generalized manifold. We learn a probabilistic expression model on the generalized manifold. To edit a facial expression of a new subject in 3D videos, the system searches over this generalized manifold for optimal replacement with the ‘target’ expression, which will be blended with the deformation in the previous frames to synthesize images of the new expression with the current head pose. Experimental results show that our method works effectively.

Computing geodesics on triangular meshes

We present a new algorithm to compute a geodesic path over a triangulated surface. Based on Sethians Fast Marching Method and Polthiers straightest geodesics theory, we are able to generate an iterative process to obtain a good discrete geodesic approximation. It can handle both convex and non-convex surfaces.

Color image quantization by pairwise clustering

This paper presents a new quantization method for color images. It uses a local error optimization strategy to generate near optimal quantization levels. The algorithm is simple to implement and produces results that are superior than those of other popular image quantization algorithms.

Simple and efficient polygonization of implicit surfaces

This paper describes a simple and efficient polygonization algorithm that gives a practical way to construct adapted piecewise linear representations of implicit surfaces. The method starts with a coarse uniform polygonal approximation of the surface and subdivides each polygon recursively according to local curvature. In this way, the inherent complexity of the problem is tamed by separating structuring from sampling and reducing part of the full three-dimensional search to two dimensions.