In this project we develop new mathematical methods for computer-aided classification of grayscale images. To accomplish this the grayscale images are split into several binary images that allow the computing of what we refer to as intrinsic volumes. The intrinsic volumes are morphological parameters that describe the structure of binary images. In the 2D case they correspond to the area, the boundary length and the porosity of the black phase. Two grayscale images are members of the same morphological class if the intrinsic volumes of their associated binary images are similar in a certain sense.

Within the scope of this project we develop new techniques for the computation of the intrinsic volumes that are well-founded in a mathematical sense and can be implemented efficiently using Java. This includes an analysis of the error resulting from the discretization of the continuous data to pixel-based images.

The computing methods are tested using synthetic (i.e. simulated) data first, before they are applied to real data. Data can be collected from different fields of research e.g. cancer research (see figure 1), traffic research, actuarial mathematics (see figure 2), etc.

Contact persons: Prof. Spodarev and Daniel Meschenmoser

Figure 1: Grayscale image of mammary gland tissue: white: glands, gray: holes in the glands, black: surrounding tissue
Figure 2: Amount of policy cancellations at an automobile insurance in Bavaria; dark gray indicates a high cancellation rate

Classification of grayscale images