# Multigrid Convergence and Surface Area Estimation

@inproceedings{Coeurjolly2002MultigridCA, title={Multigrid Convergence and Surface Area Estimation}, author={David Coeurjolly and Fr{\'e}d{\'e}ric Flin and Olivier Teytaud and Laure Tougne}, booktitle={Theoretical Foundations of Computer Vision}, year={2002} }

Surface area of discrete objects is an important feature for model-based image analysis. In this article, we present a theoretical framework in order to prove multigrid convergence of surface area estimators based on discrete normal vector field integration. The paper details an algorithm which is optimal in time and multigrid convergent to estimate the surface area and a very efficient algorithm based on a local but adaptive computation.

## 32 Citations

### On Multigrid Convergence of Local Algorithms for Intrinsic Volumes

- Computer ScienceJournal of Mathematical Imaging and Vision
- 2013

It is shown that local algorithms for intrinsic volumes other than volume are not multigrid convergent on the class of convex polytopes, and for convex particles in 2D with a lower bound on the interior angles, a multigride convergent local algorithm for the Euler characteristic is constructed.

### 3 D Object Digitization : Volume and Surface Area Estimation

- Computer Science
- 2005

Good estimators should be multigrid convergent, i.e. the error goes to zero with increasing sampling density, and such estimators both for volume and for surface area estimation based on simple counting of voxels are given.

### Multigrid Convergence of Discrete Geometric Estimators

- Mathematics, Computer Science
- 2012

Global geometric estimators of area, length, moments, as well as local geometric estimator of tangent and curvature are presented, and their multigrid convergence is studied, a fundamental property which guarantees that the estimation tends toward the exact one as the sampling resolution gets finer and finer.

### Segmentation of Noisy Discrete Surfaces

- Computer ScienceIWCIA
- 2008

A flexible approach considering arithmetic discrete planes with a variable width is used to avoid the oversegmentation that might happen when classical segmentation algorithms based on regular discrete planes are used to decompose the surface of the object.

### Surface area estimation of digitized 3D objects using quasi-Monte Carlo methods

- MathematicsPattern Recognit.
- 2010

### Geometric Feature Estimators for Noisy Discrete Surfaces

- Mathematics, Computer ScienceDGCI
- 2008

We present in this paper robust geometric feature estimators on the border of a possibly noisy discrete object. We introduce the notion of patch centered at a point of this border. Thanks to a width…

### Surface area estimation of digitized 3D objects using weighted local configurations

- MathematicsImage Vis. Comput.
- 2005

### On the Computations of Specific Surface Area and Specific Grain Contact Area from Snow 3 D Images

- Environmental Science
- 2011

Estimating the Specific Surface Area (SSA) of snow and firn using three-dimensional (3D) images is now widely used in the snow and ice community. However, little information is available about…

### 3D noisy discrete objects: Segmentation and application to smoothing

- Computer SciencePattern Recognit.
- 2009

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