• Processing : a program with some input/output images.
    • Filtering: remove the noise in preserving the geometrical features
      Erosion an iterative point process

      time evolution with Non-linear anisotropic diffusion

    • Segmentation: convert the grey(color)-level image to a labelled image


      Watershed segmentation

  • Analysis: a program with an input image and an output metric.
    • Metric: 2-point correlation, VER porosity, fractal box, curvature,…


    • Topology: Euler-Poincare number, percolation-opening,…

      Topological graph

    • Physics: coefficient of self-diffusion, permeability

      Velocity field relaxation

      Pressure field relaxation

  • Visualization: a program with a visualization output
    • Label image: representation of the labelled image

      Euclidean distance

    • OpenGL: 3d visualization

      Grain decompisition

  • PDE: partial difference equation solved by a finite difference scheme

    Grain decomposition

    Allen-Cahn regularization

  • Statistics: Mathematical analysis of function oriented statistics

    Sampling random variables from multi-variate normal distribution using the Cholesky decomposition

  • Linear Algebra: Matrix transformation

    Image rotation

  • Representation: time-space domain


    FFT representation