.. _api-differentiate:

Differentiate
=============

The :class:`splineops.differentiate.differentials` class implements a suite of functions to compute image differentials using cubic B‑spline interpolation, including:

- **Gradient Magnitude** – the rate of intensity change.
- **Gradient Direction** – the orientation of maximum change.
- **Laplacian** – the sum of second-order derivatives.
- **Largest Hessian Eigenvalue** – the maximal curvature.
- **Smallest Hessian Eigenvalue** – the minimal curvature.
- **Hessian Orientation** – the principal direction of curvature.

.. automodule:: splineops.differentiate.differentials
   :members:
   :show-inheritance:
   :special-members: __init__, run, get_cross_hessian, get_horizontal_gradient, get_horizontal_hessian, get_vertical_gradient, get_vertical_hessian, anti_symmetric_fir_mirror_on_bounds, symmetric_fir_mirror_on_bounds, get_gradient, get_hessian, get_spline_interpolation_coefficients, get_initial_causal_coefficient_mirror_on_bounds, get_initial_anti_causal_coefficient_mirror_on_bounds, gradient_magnitude, gradient_direction, laplacian, largest_hessian, smallest_hessian, hessian_orientation
   :member-order: bysource