March 2012
Volume 53, Issue 14
ARVO Annual Meeting Abstract  |   March 2012
A Study of the Retinal Vascular Parent Branch-Daughter Branch Relationship Based on an Automatic Vessel Width Measurement Method
Author Affiliations & Notes
  • Xiayu Xu
    Biomedical Engineering,
    University of Iowa, Iowa City, Iowa
  • Joseph Reinhardt
    Biomedical Engineering,
    University of Iowa, Iowa City, Iowa
  • John Goree
    Physics and Astronomy,
    University of Iowa, Iowa City, Iowa
  • Michael D. Abramoff
    Ophthalmology & Visual Sciences, Univ of Iowa Hospitals & Clinics, Iowa City, Iowa
  • Footnotes
    Commercial Relationships  Xiayu Xu, None; Joseph Reinhardt, None; John Goree, None; Michael D. Abramoff, None
  • Footnotes
    Support  VA Merit grant, NIH EY018853, Research to Prevent Blindness
Investigative Ophthalmology & Visual Science March 2012, Vol.53, 2180. doi:
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      Xiayu Xu, Joseph Reinhardt, John Goree, Michael D. Abramoff; A Study of the Retinal Vascular Parent Branch-Daughter Branch Relationship Based on an Automatic Vessel Width Measurement Method. Invest. Ophthalmol. Vis. Sci. 2012;53(14):2180.

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      © ARVO (1962-2015); The Authors (2016-present)

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To study the retinal vascular parent branch-daughter branch relationship on fundus images using an automatic retinal vascular branching vessel width measurement method.


The automatic method designed for vessel width measurement at branching points is a graph-based method. An electric field theory based graph construction method is introduced. This method is motivated by the non-intersection property of the electric lines of force. After the vessel boundaries are determined, the vessel width is determined as the Euclidean distance between the two nodes on the vessel boundary that are extended from the same vessel centerline pixel. The parent branch-daughter branch relationship was studied on a set of 150 fundus images from a population study. A set of 331 arteriolar branchings and 573 venular branchings were measured.


Typical result images are given in Figure 1 (b). Our result showed that the parent branch-daughter branch relationship in retinal arterial branchings fitted the Murray’s proposal very well. The parentbranch-daughter branch relationship followed closely to a third power relationship, as shown in Figure 2(a). However, the relationship in venular branchings was different. The best fitting was found with a power of 2.4 as shown in Figure 2(b).


We propose a fully automatic method designed for retinal vascular branching width measurement. This method was used to study the parent branch-daughter branchrelationship. Our result showed that the retinal arteriolar branchings follow the Murray’s Law very well, while the venular branchings deviated from the Murray’s Law.  


Keywords: image processing • imaging/image analysis: non-clinical 

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