title: Adaptive estimation of normals and surface area for discrete 3-D objects: application to snow binary data from X-ray tomography.
abstract: Estimating the normal vector field on the boundary of discrete three-dimensional objects is essential for rendering and image measurement problems. Most of the existing algorithms do not provide an accurate determination of the normal vector field for shapes that present edges. Here, we propose a new and simple computational method in order to obtain accurate results on all types of shapes, whatever their local convexity degree. The presented method is based on the gradient vector field analysis of the object distance map. This vector field is adaptively filtered around each surface voxel using angle and symmetry criteria so that as many relevant contributions as possible are accounted for. This optimizes the smoothing of digitization effects while preserving relevant details of the processed numerical object. Thanks to the precise normal field obtained, a projection method can be proposed to immediately derive the surface area from a raw discrete object. An empirical justification of the validity of such an algorithm in the continuous limit is also provided. Some results on simulated data and snow images from X-ray tomography are presented, compared to the Marching Cubes and Convex Hull results, and discussed.
authors.affiliation: Laboratory of Phase Transition Dynamics, Institute of Low Temperature Science, Hokkaido University, Hokkaido 060-0819, Japan. flin@lowtem.hokudai.ac.jp
authors.forename: Frédéric
authors.initials: F
authors.lastname: Flin
authors.forename: Jean-Bruno
authors.initials: JB
authors.lastname: Brzoska
authors.forename: David
authors.initials: D
authors.lastname: Coeurjolly
authors.forename: Romeu André
authors.initials: RA
authors.lastname: Pieritz
authors.forename: Bernard
authors.initials: B
authors.lastname: Lesaffre
authors.forename: Cécile
authors.initials: C
authors.lastname: Coléou
authors.forename: Pascal
authors.initials: P
authors.lastname: Lamboley
authors.forename: Olivier
authors.initials: O
authors.lastname: Teytaud
authors.forename: Gérard L
authors.initials: GL
authors.lastname: Vignoles
authors.forename: Jean-François
authors.initials: JF
authors.lastname: Delesse
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D016000:Cluster Analysis; D005246:Feedback; D021621:Imaging, Three-Dimensional / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods; D010363:Pattern Recognition, Automated / Q000379:methods*; D011856:Radiographic Image Enhancement / Q000379:methods; D011857:Radiographic Image Interpretation, Computer-Assisted / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted; D014056:Tomography, X-Ray / Q000379:methods*