Image Analysis

Gray-scale images are analyzed by constructing insocontours with the (interpolated) marching squares algorithm and analyzing the shapes with Minkowski Tensors.

Isocontours of a gray-scale image

Gray-scale images are analyzed with the interpolated marching squares algorithm, an enhancement of the regular marching squares algorithm. The difference between the regular and the interpolated marching squares algorithm is illustrated in the following images.

regular marching squares,
details see e.g. Wikipedia
Interpolated marching squares,
details see e.g. Ref. [1]

The isocontours can be analyzed with the morphometer or papaya. By changing the threshold parameter, different isocontour shapes can be generated and analyzed with the Minkowski structure metrics.

[1] [doi] H. Mantz, K. Jacobs, and K. Mecke, “Utilizing Minkowski functionals for image analysis: a marching square algorithm,” Journal of statistical mechanics: theory and experiment, vol. 2008, iss. 12, p. P12015, 2008.