Algorithmic Curvature Theories in Image Processing


In differential geometry, there exists different quantities of discrete 3D surfaces, like e.g. Gaussian curvature, which can be directly or indirectly extracted from the so called fundamental forms.

The aims of this dissertation are:

  • Efficient numerical methods for the determination of differential quantities on volume images and surface lattices
  • Differential characteristics as features of 3D structures (e.g. fiber endpoints, fiber-fiber contacts, sinter necks, intussusceptive pillars and sprouting approaches in lung growth)
  • Classification of 3D structures using the aforementioned characteristics
  • Applications in medicine and material science