Multi-Scale Anisotropic Fourth-Order Diffusion Improves Ridge and Valley Localization

TL;DR

This paper introduces a multi-scale anisotropic fourth-order diffusion filter that enhances vessel centerlines in images by smoothing along vessels and sharpening orthogonal features, outperforming previous filters.

Contribution

It presents a novel multi-scale anisotropic fourth-order diffusion method that adapts locally for improved vessel and ridge localization in noisy and multi-scale images.

Findings

Better restoration of vessel centerlines compared to previous filters.

Effective in noisy and multi-scale vessel images.

Demonstrated on synthetic and real fundus images.

Abstract

Ridge and valley enhancing filters are widely used in applications such as vessel detection in medical image computing. When images are degraded by noise or include vessels at different scales, such filters are an essential step for meaningful and stable vessel localization. In this work, we propose a novel multi-scale anisotropic fourth-order diffusion equation that allows us to smooth along vessels, while sharpening them in the orthogonal direction. The proposed filter uses a fourth order diffusion tensor whose eigentensors and eigenvalues are determined from the local Hessian matrix, at a scale that is automatically selected for each pixel. We discuss efficient implementation using a Fast Explicit Diffusion scheme and demonstrate results on synthetic images and vessels in fundus images. Compared to previous isotropic and anisotropic fourth-order filters, as well as established second-order vessel enhancing filters, our newly proposed one better restores the centerlines in all cases.