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Cramér-Rao Bounds for Estimating the Position and Width of 3D Tubular Structures and Analysis of Thin Structures with Application to Vascular Images

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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.

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Authors and Affiliations

  1. Department Bioinformatics and Functional Genomics, Biomedical Computer Vision Group, University of Heidelberg, BIOQUANT, IPMB, and DKFZ Heidelberg, Im Neuenheimer Feld 267, 69120, Heidelberg, Germany

    Stefan Wörz & Karl Rohr

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  1. Stefan Wörz
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  2. Karl Rohr
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Correspondence to Stefan Wörz.

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Wörz, S., Rohr, K. Cramér-Rao Bounds for Estimating the Position and Width of 3D Tubular Structures and Analysis of Thin Structures with Application to Vascular Images. J Math Imaging Vis 30, 167–180 (2008). https://doi.org/10.1007/s10851-007-0041-6

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  • DOI: https://doi.org/10.1007/s10851-007-0041-6

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