Segmentation of vessel-like patterns using mathematical morphology and curvature evaluation

TLDR

Vessel‑like patterns are ubiquitous in medical images, and detecting them aids in estimating blood‑flow parameters and aligning multimodal images due to their tree‑like geometry; they are defined as bright, piecewise‑connected, locally linear structures that fit a morphological description. The study proposes an algorithm that employs mathematical morphology and curvature evaluation to detect vessel‑like patterns in noisy environments. The algorithm segments images using a precise morphological model, applies noise reduction, enhances Gaussian‑like linear patterns, evaluates cross‑curvature to distinguish vessels from background, and then performs linear filtering to isolate vessel structures. When tested on real images of diverse modalities, the method proved robust and accurate even in the presence of noise.

Abstract

This paper presents an algorithm based on mathematical morphology and curvature evaluation for the detection of vessel-like patterns in a noisy environment. Such patterns are very common in medical images. Vessel detection is interesting for the computation of parameters related to blood flow. Its tree-like geometry makes it a usable feature for registration between images that can be of a different nature. In order to define vessel-like patterns, segmentation is performed with respect to a precise model. We define a vessel as a bright pattern, piece-wise connected, and locally linear, mathematical morphology is very well adapted to this description, however other patterns fit such a morphological description. In order to differentiate vessels from analogous background patterns, a cross-curvature evaluation is performed. They are separated out as they have a specific Gaussian-like profile whose curvature varies smoothly along the vessel. The detection algorithm that derives directly from this modeling is based on four steps: (1) noise reduction; (2) linear pattern with Gaussian-like profile improvement; (3) cross-curvature evaluation; (4) linear filtering. We present its theoretical background and illustrate it on real images of various natures, then evaluate its robustness and its accuracy with respect to noise.