R-PLUS: a Riemannian anisotropic edge detection scheme for vascular segmentation

Area of Science:

• Medical image analysis
• Computer vision
• Differential geometry

Background:

• Edge detection is crucial for image segmentation, particularly in applications like vessel segmentation where structures have intrinsic orientation.
• Standard edge detection methods can fail in oriented fields, leading to contour leakage or inaccurate delineation.
• Anisotropic edge detection is beneficial for segmenting structures with preferred orientations.

Purpose of the Study:

• To develop and generalize an anisotropic edge detection scheme on a Riemannian manifold for oriented fields.
• To improve the accuracy of edge detection in vessel segmentation by minimizing contour leakage.
• To provide a more robust method for curved edge detection compared to existing techniques.

Main Methods:

• Generalization of the PLUS operator for anisotropic edge detection.
• Utilizing the local structure tensor on a Riemannian manifold.
• Comparison with the state-of-the-art flux maximizing flow method.

Main Results:

• The proposed anisotropic edge detection method demonstrates significant improvements in leakage minimization.
• The methodology achieves thinner vessel delineation compared to flux maximizing flow.
• The generalized PLUS operator effectively handles edge detection in oriented fields.

Conclusions:

• The developed anisotropic edge detection scheme offers superior performance for oriented field segmentation.
• This method enhances accuracy and reduces artifacts in vessel segmentation.
• The approach provides a valuable tool for medical image analysis and related fields.