Laplacian operator is the rate at which the average value of f over spheres centered at p, deviates from f(p) as the radius of the sphere grows

http://docs.opencv.org/doc/tutorials/imgproc/imgtrans/laplace_operator/laplace_operator.html

 is the rate at which the average value of f over spheres centered at p, deviates from f(p) as the radius of the sphere grows

http://en.wikipedia.org/wiki/Laplace_operator

In mathematics the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a function on Euclidean space. It is usually denoted by the symbols ∇·∇, ∇² or ∆. The Laplacian ∆f(p) of a function f at a point p, up to a constant depending on the dimension, is the rate at which the average value of f over spheres centered at p, deviates from f(p) as the radius of the sphere grows. In a Cartesian coordinate system, the Laplacian is given by sum of second partial derivatives of the function with respect to each independent variable. In other coordinate systems such as cylindrical and spherical coordinates, the Laplacian also has a useful form.