Smoothing and Matching of 3-D Space Curves

International audienceWe present a new approach to the problem of matching 3-D curves. The approach has a low algorithmic complexity in the number of models, and can operate in the presence of noise and partial occlusions. Our method builds upon the seminal work of Kishon et al. (1990), where curves are first smoothed using B-splines, with matching based on hashing using curvature and torsion measures. However, we introduce two enhancements: -- We make use of nonuniform B-spline approximations, which permits us to better retain information at highcurvature locations. The spline approximations are controlled (i.e., regularized) by making use of normal vectors to the surface in 3-D on which the curves lie, and by an explicit minimization of a bending energy. These measures allow a more accurate estimation of position, curvature, torsion, and Frtnet frames along the curve. -- The computational complexity of the recognition process is relatively independent of the number of models and is considerably decreased with explicit use of the Frtnet frame for hypotheses generation. As opposed to previous approaches, the method better copes with partial occlusion. Moreover, following a statistical study of the curvature and torsion covariances, we optimize the hash table discretization and discover improved invariants for recognition, different than the torsion measure. Finally, knowledge of invariant uncertainties is used to compute an optimal global transformation using an extended Kalman filter. We present experimental results using synthetic data and also using characteristic curves extracted from 3-D medical images. An earlier version of this article was presented at the 2nd European Conference on Computer Vision in Italy

Autonomous and non-autonomous regulation of mammalian neurite development by Notch1 and Delta1

AbstractBackground: On the basis of experiments suggesting that Notch and Delta have a role in axonal development in Drosophila neurons, we studied the ability of components of the Notch signaling pathway to modulate neurite formation in mammalian neuroblastoma cells in vitro.Results: We observed that N2a neuroblastoma cells expressing an activated form of Notch, Notch1IC, produced shorter neurites compared with controls, whereas N2a cell lines expressing a dominant-negative Notch1 or a dominant-negative Delta1 construct extended longer neurites with a greater number of primary neurites. We then compared the effects on neurites of contacting Delta1 on another cell and of overexpression of Delta1 in the neurite-extending cell itself. We found that N2a cells co-cultured with Delta1-expressing quail cells produced fewer and shorter neuritic processes. On the other hand, high levels of Delta1 expressed in the N2a cells themselves stimulated neurite extension, increased numbers of primary neurites and induced expression of Jagged1 and Notch1.Conclusions:These studies show that Notch signals can antagonize neurite outgrowth and that repressing endogenous Notch signals enhances neurite outgrowth in neuroblastoma cells. Notch signals therefore act as regulators of neuritic extension in neuroblastoma cells. The response of neuritic processes to Delta1 expressed in the neurite was opposite to that to Delta1 contacted on another cell, however. These results suggest a model in which developing neurons determine their extent of process outgrowth on the basis of the opposing influences on Notch signals of ligands contacted on another cell and ligands expressed in the same cell