Paper Info
Title
Cramér-Rao Bounds for Estimating the Position and Width of 3D Tubular Structures and Analysis of Thin Structures with Application to Vascular Images
Abstract
In this work we derive analytic lower bounds for estimating the position and width of 3D tubular structures. Based on a continuous image model comprising blur and noise introduced by an imaging system we analyze three different intensity models of 3D tubular structures with increasing complexity. The derived formulas indicate that quantification of 3D tubular structures can be performed with very high precision under certain assumptions. We also determine conditions under which the model parameters are coupled or uncoupled. For uncoupled parameters the lower bounds are independent of prior knowledge about other parameters, and the derivation of the bounds is simplified. The theoretical results are substantiated by experimental investigations based on discretized and quantized 3D image data. Moreover, we study limits on estimating the width of thin tubular structures in 3D images. We use the derived lower bound of the width estimate as a benchmark and compare it with three previously proposed accuracy limits for vessel width estimation.
Year
DOI
Venue
2008
https://doi.org/10.1007/s10851-007-0041-6
Journal of Mathematical Imaging and Vision
Keywords
Field
DocType
Cramér-Rao Bound (CRB),3D tubular structures,3D position and widt estimate,Performance characterization,Thin structures,Vessel segmentation
Cramér–Rao bound,Vessel segmentation,Discretization,Mathematical optimization,Upper and lower bounds,Quantization (physics),Mathematics,3d image
Journal
Volume
Issue
ISSN
30
2
0924-9907
Citations 
PageRank 
References 
3
0.43
17
Authors
2
Name
Order
Citations
PageRank
Stefan Wörz125632.58
Karl Rohr234048.69