scholarly journals Real-Time Camera Tracking and 3D Reconstruction Using Signed Distance Functions

2013 ◽  
Author(s):  
Erik Bylow ◽  
Jürgen Sturm ◽  
Christian Kerl ◽  
Fredrik Kahl ◽  
Daniel Cremers
Keyword(s):  
3D Reconstruction ◽  
Real Time ◽  
Distance Functions ◽  
Camera Tracking ◽  
Signed Distance ◽  
Signed Distance Functions

scholarly journals Operations on Signed Distance Functions

2019 ◽  
Vol 24 (1) ◽  
pp. 17-28
Author(s):  
Csaba Bálint ◽  
Gábor Valasek ◽  
Lajos Gergó
Keyword(s):  
Banach Spaces ◽  
Distance Functions ◽  
Signed Distance ◽  
Set Of Points ◽  
Theoretical Overview ◽  
Signed Distance Functions

We present a theoretical overview of signed distance functions and analyze how this representation changes when applying an offset transformation. First, we analyze the properties of signed distance and the sets they describe. Second, we introduce our main theorem regarding the distance to an offset set in (X,||.||) strictly normed Banach spaces. An offset set of D in X is the set of points equidistant to D. We show when such a set can be represented by f(x)-c=0, where c denotes the radius of the offset. Finally, we explain these results for applications that offset signed distance functions.

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