Geometrical Significance of Isothermal Conjugacy of a Net of Curves

1920 ◽  
Vol 42 (4) ◽  
pp. 211 ◽  
Author(s):  
E. J. Wilczynski
Keyword(s):  
Geometrical Significance

scholarly journals Geometrical significance of the Löwner-Heinz inequality

1999 ◽  
Vol 128 (4) ◽  
pp. 1031-1037 ◽  
Author(s):  
E. Andruchow ◽  
G. Corach ◽  
D. Stojanoff
Keyword(s):  
Heinz Inequality ◽  
Geometrical Significance

scholarly journals Tracking of Multiple Maneuvering Random Hypersurface Extended Objects Using High Resolution Sensors

2021 ◽  
Vol 13 (15) ◽  
pp. 2963
Author(s):  
Lifan Sun ◽  
Haofang Yu ◽  
Jian Lan ◽  
Zhumu Fu ◽  
Zishu He ◽  
...  
Keyword(s):  
High Resolution ◽  
Object Tracking ◽  
Gaussian Mixture ◽  
Joint Estimation ◽  
Accurate Estimation ◽  
Interacting Multiple Model ◽  
Multiple Model ◽  
Probability Hypothesis Density ◽  
Extended Object ◽  
Geometrical Significance

With the increased resolution capability of modern sensors, an object should be considered as extended if the target extent is larger than the sensor resolution. Multiple maneuvering extended object tracking (MMEOT) uses not only measurements of the target centroid but also high-resolution sensor measurements which may resolve individual features or measurement sources. MMEOT aims to jointly estimate object number, centroid states, and extension states. However, unknown and time-varying maneuvers of multiple objects produce difficulties in terms of accurate estimation. For multiple maneuvering star-convex extended objects using random hypersurface models (RHMs) in particular, their complex maneuvering behaviors are difficult to be described accurately and handled effectively. To deal with these problems, this paper proposes an interacting multiple model Gaussian mixture probability hypothesis density (IMM-GMPHD) filter for multiple maneuvering extended object tracking. In this filter, linear maneuver models derived from RHMs are utilized to describe different turn maneuvers of star-convex extended objects accurately. Based on these, an IMM-GMPHD filtering recursive form is given by deriving new update and merging formulas of model probabilities for extended objects. Gaussian mixture components of different posterior intensities are also pruned and merged accurately. More importantly, the geometrical significance of object extension states is fully considered and exploited in this filter. This contributes to the accurate estimation of object extensions. Simulation results demonstrate the effectiveness of the proposed tracking approach—it can obtain the joint estimation of object number, kinematic states, and object extensions in complex maneuvering scenarios.

The geometrical significance of the Laplacian

2015 ◽  
Vol 83 (12) ◽  
pp. 992-997 ◽  
Author(s):  
Daniel F. Styer
Keyword(s):  
Geometrical Significance
Sign in / Sign up

Export Citation Format

Share Document