## Rotation-invariant Laplacian for 2D grids

14 min.

The Laplacian operator $\Delta u$ is the divergence of the gradient, that is the sum of the second-order partial derivatives $\nabla^2 u$ of a multivariate function, which represents the local curvature of this function. This operator is widely used for edge-detection1, as well as in partial-differential equations (Poisson, etc.), and other problems of machine-learning minimisation. For numerical applications in orthogonal graphs, sampled only at integer coordinates (like pixels in an image), a discrete Laplacian has to be used, and several approaches are available, that will be detailed hereafter.

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