The Laplace operator, denoted as ∆ or ∇², is defined as the divergence of the gradient of a function. In Cartesian coordinates for a function f(x, y, z), it is expressed as: \[ \Delta f = \frac{\partial^2 f}{\partial x^2} + \frac{\partial^2 f}{\partial y^2} + \frac{\partial^2 f}{\partial z^2} \] In the context of 2D images, often used in histological studies, the operator simplifies to: \[ \Delta f = \frac{\partial^2 f}{\partial x^2} + \frac{\partial^2 f}{\partial y^2} \]
