A 2-D/3-D model-based method to quantify the complexity of microvasculature imaged by in vivo multiphoton microscopy

Vessels are modeled using a family of super-Gaussian functions that are based on the superquadric modeling primitive common in computer vision. The superquadric generalizes a simple ellipsoid by including shape parameters that allow it to approximate a cylinder with elliptical cross-sections (generalized cylinder). The super-Gaussian is obtained by composing a superquadric with an exponential function giving a form that is similar to a standard Gaussian function but with the ability to produce level sets that approximate generalized cylinders. Importantly, the super-Gaussian is continuous and differentiable so it can be fit to image data using robust non-linear regression. This fitting enables quantification of the intrinsic complexity of vessel data vis-a-vis the super-Gaussian model within a minimum message length (MML) framework. The resulting measures are expressed in units of information (bits). Synthetic and real-data examples are provided to illustrate the proposed measures.