Image analysis


Examples include:

  • Random fields [1,2]
  • Classical Image analysis

The Minkowski functionals and tensors can robustly quantify the shape of noisy, pixelated images. Due to their additivity, they can be calculated by an efficient linear-time algorithm using a look-up table that includes the contributions of each 2\times2 neighborhood. For the Minkowski tensors, a marching-square algorithm is applied []. Caveat: any such local algorithm will not in general converge to the Minkowski tensors of the unpixelated domain [].

Examples are presented in the 2D online tool, see “Grayscale Image”. The four samples included there are explained in the following.

Gaussian random field


… [1-3]


Shot-noise field








[1] Adler R J 1981 The Geometry of Random Fields Classics in Applied Mathematics (SIAM, Philadelphia)
[2] Vanmarcke E 2010 Random Fields: Analysis and Synthesis (World Scientific, Singapore)
[3] Berry M V 1977 J. Phys. A: Math. Gen. 10 2083