Fully Isotropic Fast Marching Methods on Cartesian Grids.

Area of Science:

• Computational Mathematics
• Numerical Analysis
• Image Processing

Background:

• Existing Fast Marching Methods (FMM) solve the Eikonal equation using discontinuous models for traveling cost, leading to directional biases.
• This anisotropy in cost estimation affects the accuracy of accumulated cost calculations.
• Directional dependency in FMM can limit its effectiveness in certain applications.

Purpose of the Study:

• To develop a truly isotropic Fast Marching Method (FMM) for solving the Eikonal equation.
• To eliminate directional biases in the estimation of traveling costs within the FMM framework.
• To demonstrate the improved accuracy and computational efficiency of the proposed isotropic method.

Main Methods:

• Proposed an FMM that estimates traveling cost using a locally continuous model via interpolation.
• Employed an interpolation scheme specifically designed to be directionally unbiased.
• Validated the method's performance against existing state-of-the-art FMM techniques.

Main Results:

• The proposed method achieves true isotropy by interpolating traveling costs along the propagation direction.
• Demonstrated the significance of removing directional bias in specific applications of the Fast Marching Method.
• Achieved superior accuracy and comparable or improved computation times compared to existing FMM techniques.

Conclusions:

• The proposed locally continuous, directionally unbiased interpolation scheme significantly enhances FMM performance.
• The isotropic FMM offers a more accurate and robust solution for problems involving the Eikonal equation.
• This advancement holds promise for various applications requiring precise wave propagation modeling.