Abstract
This paper presents a framework for symmetry-guided texture synthesis and processing. It is motivated by the long-standing problem of how to optimize, transfer, and control the spatial patterns in textures.
The key idea is that symmetry representations that measure autocorrelations with respect to all transformations of a group are a natural way to describe spatial patterns in many real-world textures.
To leverage this idea, we provide methods to transfer symmetry representations from one texture to another, process the symmetries of a texture, and optimize textures with respect to
properties of their symmetry representations. These methods are automatic and robust, as they don't require explicit detection of
discrete symmetries. Applications are investigated for optimizing, processing and transferring symmetries and textures.
Abstract
Conformal mappings preserve angles, the angle structure on a surface is called the conformal structure. Conformal geometry studies the invariants under conformal transformation group. Conformal structure is more rigid than topological structure and more flexible than Riemannian metric structure, therefore it plays important roles in engineering fields.
The fundamental tasks in computational conformal geometry include:
1. Given a Riemannian metric on a surface with an arbitrary topology, determine the corresponding conformal structure.
2. Compute the complete conformal invariants (conformal modules), which are the coordinates of the surface in the Teichmuller shape space.
3. Verify whether there exists a conformal mapping between two metric surfaces. If yes, construct the mapping; otherwise, find the best mapping that is cloest to the conformal mapping.
3. Fix the conformal structure, find the simplest Riemannian metric among all possible Riemannian metrics
4. Given desired Gaussian curvature, compute the corresponding Riemannian metric.
5. Given the distortion between two conformal structures, compute the quasi-conformal mapping.
The methods to tackle these tasks will be introduced. Applications in graphics, vision, medical imaging, geometric modeling and network will be briefly explained.
Abstract
Stylized rendering methods, which aim at depicting 3D scenes with 2D
marks such as pigments or strokes, are often faced with temporal
coherence issues when applied to dynamic scenes. These issues arise
from the difficulty of having to satisfy two contrary goals: ensuring
that the style marks follow 3D motions while preserving their 2D
appearance. In this paper we describe a new texture based method for
real-time temporally coherent stylization called dynamic textures. A
dynamic texture is a standard texture mapped on the object and
enriched with an infinite zoom mechanism. This simple and fast
mechanism maintains quasi-constant size and density of texture
elements in screen space for any distance from the camera. We show
that these dynamic textures can be used in many stylization
techniques, enforcing the 2D appearance of the style marks while
preserving the accurate 3D motion of the depicted objects.
Although our infinite zoom technique can be used with both 2D or 3D
textures, we focus in this paper on the 3D case (dynamic solid
textures) which avoids the need for complex parameterizations of 3D
surfaces. This makes dynamic textures easy to integrate in existing
rendering pipelines with almost no loss in performance, as
demonstrated by our implementation in a game rendering engine. Bio
INRIA, Grenoble. Visiting student at Princeton.
| 
