John Chaussard

Robust skeletonization using the discrete λ-medial axis

Medial axes and skeletons are notoriously sensitive to contour irregularities. This lack of stability is a serious problem for applications in e.g. shape analysis and recognition. In 2005, Chazal and Lieutier introduced the @l-medial axis as a new concept for computing the medial axis of a shape subject to single parameter filtering. The @l-medial axis is stable under small shape perturbations, as proved by these authors. In this article, a discrete @l-medial axis (DLMA) is introduced and compared with the recently introduced integer medial axis (GIMA). We show that DLMA provides measurably better results than GIMA, with regard to stability and sensibility to rotations. We give efficient algorithms to compute the DLMA, and we also introduce a variant of the DLMA which may be computed in linear-time.

Surface Thinning in 3D Cubical Complexes

We introduce a parallel thinning algorithm with directional substeps based on the collapse operation, which is guaranteed to preserve topology and to provide a thin result. Then, we propose two variants of a surface-preserving thinning scheme, based on this parallel directional thinning algorithm. Finally, we propose a methodology to produce filtered surface skeletons, based on the above thinning methods and the recently introduced discrete *** -medial axis.

A discrete λ-medial axis

A process and system (60) for controlling the concentration of dust levels in a room (20) within which a paper-making, or finishing, machine (24) is housed involves a ventilation scheme which withdraws air from the room by way of ceiling vents (52) disposed generally above the tissue-making machine and directs fresh air into the room by way of inlet displacement modules (64) located adjacent the walls of the room which creates a moving wall of fresh air through the room. The flow of air being withdrawn from the room is coordinated with the flow of fresh air directed into the room so that a controlled air migration pattern is established and so that the fresh air displaces, rather than is diluted by, the room air. Along with this flow of room air, heat and humidity-generating vapors which are released by the tissue-making machine during operation are also pushed out of the room through the ceiling vents ahead of the fresh air. Consequently, areas surrounding the tissue-making machine at which machine operators are expected to work are appreciably free of dust, heat and vapors released by the tissue-making machine.

Characterizing and detecting toric loops in n-dimensional discrete toric spaces

Toric spaces being non-simply connected, it is possible to find in such spaces some loops which are not homotopic to a point: we call them toric loops. Some applications, such as the study of the relationship between the geometrical characteristics of a material and its physical properties, rely on three-dimensional discrete toric spaces and require detecting objects having a toric loop. In this work, we study objects embedded in discrete toric spaces, and propose a new definition of loops and equivalence of loops. Moreover, we introduce a characteristic of loops that we call wrapping vector: relying on this notion, we propose a linear time algorithm which detects whether an object has a toric loop or not.

Skeleton Based Importance Sampling for Path Tracing

When working with large and complex scenes, situations arise where light flux takes complex paths to reach the observer. In such cases, traditional stochastic algorithms, like ray tracing algorithms, will have difficulties to compute noise-free images. Our present research aims to solve this problem using the 3d scene skeleton as a coarse representation. Indeed, curvilinear skeletons can be used to find light paths with higher energy. This article presents our research to use these skeletons for any ray tracing algorithm, allowing a knowledge-based choice when choosing light paths. Our method adds little computation time while producing a more accurate image.

A 3d curvilinear skeletonization algorithm with application to path tracing

We present a novel 3D curvilinear skeletonization algorithm which produces filtered skeletons without needing any user input, thanks to a new parallel algorithm based on the cubical complex framework. These skeletons are used in a modified path tracing algorithm in order to produce less noisy images in less time than the classical approach.

Coarse irradiance estimation using curvilinear skeleton

Light flux can take complex paths to reach the observer, especially in large and sophisticated scenes. In such situations, global illumination algorithms are used: irradiance caching, path tracing and radiosity allow to precisely compute the irradiance at any point of the scene, but remain quite slow. Our present work aims to evaluate, very coarsely, the irradiance of any point of a scene, allowing to give global illumination algorithms some information about the main direction and intensity of the light flux. We use a coarse representation of the scene using a skeleton of its voids (where the light propagates). We present two heuristics to compute a coarse radiance estimation and the main light stream orientation. Our work gives the possibility to define many other heuristics.

Characterization and Detection of Toric Loops in n-Dimensional Discrete Toric Spaces

Since a toric space is not simply connected, it is possible to find in such spaces some loops which are not homotopic to a point: we call them toric loops. Some applications, such as the study of the relationship between the geometrical characteristics of a material and its physical properties, rely on three-dimensional discrete toric spaces and require detecting objects having a toric loop.In this work, we study objects embedded in discrete toric spaces, and propose a new definition of loops and equivalence of loops. Moreover, we introduce a characteristic of loops that we call wrapping vector: relying on this notion, we propose a linear time algorithm which detects whether an object has a toric loop or not.