Page 114 - Computational Retinal Image Analysis

4 Vessel tracing 107

and k-means, then utilizes a combined cross-point number method for thinning, and
pattern-matching classification of the junction points as either branching or crossover.
Calvo et al. [106] consider the detection and classification of key points pertaining to
bifurcations and crossovers in the retinal vessel trees. A two-step method is proposed,
which uses filters and morphologic operations for detection, and the extracted key
point-based features for classification into either bifurcations or crossovers. Started
with a segmented retinal image, Azzopardi and Petkov [28] deploy a set of blurred and
shifted Gabor filters that are trained from a set of predefined bifurcation prototypes,
and demonstrate satisfactory detection performance on DRIVE and STARE datasets.
In addition to their initial work [107] where self-organizing feature maps are used
to perceptually group the retinal segments around the junction points, Qureshi et al.
[108] develop a probabilistic model of various junction points such as terminals,
bridges, and bifurcations, and their configurations.

4.2 Vascular tree separation

The work of Tamura et al. [109] is among the early efforts, where the blood vessels
are traced by a second-order derivative Gaussian filter from an initial point, while the
width of the blood vessel is obtained as the zero-crossing interval of the filter output.
Similarly, starting from a set of initial points, the work of Can et al. [110] tracks
vessels by recursively applying a set of directional low-pass filters to the proper
directions along the vessel centerlines detected so far from the input retinal angiogram
images. It also extracts the branching and crossover points as a by-product. A three-
step approach is proposed in Ref. [111] to reliably detect vascular bifurcations and
crossovers, which involves initialization of junction locations, iterative estimation,
and backtrace-based refinement.
Kalman filter-based tracking method could be a natural choice, which has been
considered by, for example, Yedidya and Hartley [112]. To reconstruct individual
retinal vascular trees, Lin et al. [113] start by spreading initial seeds along the vessels.
The vessel segments are then extracted via a likelihood ratio test. At a junction point,
the vessel tree assignment is then resolved by applying a locally minimum-cost
matching as well as extended Kalman filtering.
One important observation is that both local and global contexts are helpful in
resolving the bifurcation and crossover issue. For example, at a junction, it is valuable
to examine the angular, morphological, and textural properties of all segments at
the junction. In fact, the inclusion of information from nearby junctions could also
facilitate a better local decision at current junction. This line of thoughts inspires the
graph-based formulation where each vessel segment becomes a node, and a contact
between two adjacent segments is represented by an edge between the two nodes.
This naturally leads to an undirected graph representation. The tracing problem has
been thus formulated as an inference problem in a Markov random field [114], a
label propagation problem on undirected graphs [115], or directed graphs [116–118].
Similar graph-based methods are also adopted in Refs. [119, 120].