Interpolation

The simplest zero-order method that assigns the value of the closest original voxel to the target grid point. It is computationally trivial but introduces significant aliasing artifacts and blocky discontinuities.

• Mechanism: No weighted averaging; pure sample-and-hold.
• Use Case: Strictly reserved for segmentation masks where preserving discrete integer labels is mandatory.
• Trade-off: Maximum speed, zero blurring, but unacceptable geometric distortion for anatomical imagery.

A first-order extension of bilinear logic into 3D space, computing the weighted average of the 8 nearest voxels based on their Euclidean distance to the target point. It is the standard baseline for real-time volume rendering.

• Mechanism: Linear weighting along the X, Y, and Z axes sequentially.
• Artifact: Introduces low-pass filtering that smooths sharp edges and reduces texture contrast.
• Application: Suitable for rapid MPR navigation where speed is prioritized over ultimate fidelity.

A high-quality polynomial kernel that fits a smooth curve through a 4x4x4 neighborhood of control points. It produces visually pleasing results with continuous first derivatives, minimizing Mach banding artifacts.

• Kernel Width: 4 voxels in each dimension.
• Characteristic: Provides excellent isotropic resolution but inherently smooths the data slightly more than a Catmull-Rom spline.
• Efficiency: Computationally heavier than linear methods but widely hardware-accelerated on modern GPUs.

The theoretical gold standard for resampling, approximating the ideal sinc function truncated by a Lanczos window. It preserves the maximum amount of high-frequency detail without introducing ringing artifacts beyond the window boundary.

• Kernel Support: Typically 2 or 3 lobes (Lanczos-2/Lanczos-3).
• Advantage: Superior modulation transfer function (MTF) preservation compared to linear or cubic methods.
• Cost: High computational overhead due to the large support region; used primarily for offline high-fidelity reconstruction.

A radially symmetric kernel based on the Gaussian distribution, often used as a pre-filtering step to suppress Nyquist aliasing before resampling. It acts as a strict low-pass filter with no negative lobes.

• Parameter: Controlled by sigma (σ), defining the smoothing radius.
• Property: Guarantees no overshoot or negative values, making it ideal for Hounsfield Unit (HU) preservation in CT.
• Limitation: Introduces significant blurring; rarely used alone for final reconstruction without a sharpening deconvolution step.

A practical approximation of the ideal brick-wall filter where the infinite sinc function is multiplied by a Hamming or Hann window to force finite support. This balances sharpness and ringing.

• Ringing Control: The window function tapers the kernel edges to suppress Gibbs phenomenon artifacts.
• Comparison: Offers slightly sharper output than Lanczos but with potentially more visible halos at high-contrast edges.
• Usage: Common in k-space regridding for non-Cartesian MRI reconstruction.