Page 115 - Computational Retinal Image Analysis

108 CHAPTER 6 Retinal vascular analysis: Segmentation, tracing, and beyond

Variational approaches have also been considered in this context. Inspired
biologically by the cortical orientation columns in primary visual cortex, Bekkers
et al. [121] advocate a special Euclidean group, SE(2), on which to base their
retinal vessel tracking system. Bekkers and co-workers subsequently introduce an
interesting differential geometry approach [122], where vessel tracing is formulated
as sub- Riemannian geodesics on a projective line bundle. This is further investigated
in Ref. [123] as a nilpotent approximations of sub-Riemannian distances for fast
perceptual grouping of blood vessels in 2D and 3D. Abbasi-Sureshjani et al. [124]
consider a 5D kernel approach obtained as the fundamental solution of the Fokker-
Planck equation to deal with the presence of interrupted lines or highly curved blood
vessels in retinal images. A mathematical contour completion scheme is proposed
by Zhang et al. [125] based on the rotational-translational group SE(2). The original
2D disconnected vessel segments are lifted to a 3D space of 2D location and an
orientation, where crossing and bifurcations can be separated by their distinct
orientations. The contour completion problem can then be characterized by left-
invariant PDE solutions of the convection-diffusion process on SE(2).
The tracing problem has indeed attracted research attentions from diverse
perspectives that go beyond the paradigms mentioned so far. In terms of deep
learning, the work of Ventura et al. [126] extracts the retinal artery and vein vessel
networks by iteratively predicting the local connectivity from image patches using
deep CNN. Uslu and Bharath [127] consider a multitask neural network approach
to detect junctions in retinal vasculature, which is empirically examined in DRIVE
and IOSTAR benchmarks with satisfactory results. A fluid dynamic approach is
introduced in Ref. [128] to determine the connectivity of overlapping venous and
arterial vessels in fundus images. Moreover, aiming to balance the trade-off between
performance and real-time computation budget, Shen et al. design and analyze
in Ref. [129] the optimal scheduling principle in achieving early yield of tracing
the vasculature and extracting crossing and branching junctions. It is also worth
mentioning that similar problem has also been encountered by the neuronal image
analysis community with numerous studies of datasets and methods [130–132].
There are also efforts in addressing the more general problem of tracing tubular
structured objects that include retinal vessel tracing as a special case [117,118,126].

4.3 Arterial/venous vessel classification
The classification of blood vessels into arterioles and venules is a fundamental step in
retinal vasculature analysis, and is a basis of clinical measurement calculation, such
as AVR. This requires not only identifying individual vessel trees, but also assigning
each vessel tree as being formed by either arteries or veins. Interested readers may
consult Miri et al. [17] for a detailed review of this subject.
As an early research effort, Akita and Kuga [11] consider the propagation of
artery/vein labeling by a structure-based relaxation scheme on the underlying
vascular graph. A vessel tracking method is presented in Ref. [111] to resolve
the connectivity issues of bifurcations and crossings. A semiautomatic system