title: On curvature estimation of ISO surfaces in 3D gray-value images and the computation of shape descriptors.
abstract: In this paper, we present a novel method to estimate curvature of iso gray-level surfaces in gray-value images. Our method succeeds where standard isophote curvature estimation methods fail. There is neither a segmentation of the surface needed nor a parametric model assumed. Our estimator works on the orientation field of the surface. This orientation field and a description of local structure is obtained by the Gradient Structure Tensor. The estimated orientation field has discontinuities mod pi. It is mapped via the Knutsson mapping to a continuous representation. The principal curvatures of the surface, a coordinate invariant property, are computed in this mapped representation. From these curvatures, locally the bending energy is computed to describe the surface shape. An extensive evaluation shows that our curvature estimation is robust even in the presence of noise, independent of the scale of the object and furthermore the relative error stays small.
authors.affiliation: Pattern Recognition Group, Department of Applied Physics, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands. bernd@ph.tn.tudelft.nl
authors.forename: Bernd
authors.initials: B
authors.lastname: Rieger
authors.forename: Frederik J
authors.initials: FJ
authors.lastname: Timmermans
authors.forename: Lucas J
authors.initials: LJ
authors.lastname: van Vliet
authors.forename: Piet W
authors.initials: PW
authors.lastname: Verbeek
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D016000:Cluster Analysis; D003116:Color; D003124:Colorimetry / Q000379:methods; D003196:Computer Graphics; D007089:Image Enhancement / Q000379:methods; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods*; D009716:Numerical Analysis, Computer-Assisted; D010363:Pattern Recognition, Automated / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted; D014584:User-Computer Interface