Reeb graph based image representation for phenotyping of plants

While genotypes are defined as the set of genes an organism holds, its phenotype is defined as the set of its observable characteristics. To determine the correlation of genotype and phenotype or how a phenotype is affected by environmental conditions, an evaluation on large datasets is needed. An automatic analysis of image data and extraction of characteristics allows for large scale evaluations. This thesis presents a comparison of two types of graph-based image representations: medial axis transformation and Reeb graphs and evaluates the feasibility of using this representations in image based plant phenotyping. A presegmented binary image of roots (of the plant Arabidopsis thaliana) is the basis for generating the well-known medial axis and the Reeb graphs. For phenotyping of plants their root structure is analyzed. The main characteristics used here are branching points, branch endings as well as the length and width of individual branches. These characteristics are captured by the presented graph representations. For the computation of the Reeb graphs two different Morse functions are used: height function and geodesic distance. As the roots are pictured as 2D image data, the projection of a 3D structure to a 2D space might result in an overlap of branches in the image. One major advantage, when analyzing roots based on Reeb graphs, is posed by the ability to immediately distinguish between branching points and overlaps in the root structure as the overlap introduces a cycle and thereby a certain type of node (saddle - merge) in the Reeb graph. This differentiation is not as easily possible by a medial axis representation or by an analysis solely based on contours. In order to use the advantages of different representations and the characteristics provided by them, a possibility to combine different graph representations of one root image is needed. Therefore the equality of graphs is evaluated. This thesis shows that all three representations of a root are either isomorphic graphs or isomorphic subgraphs. For isomorphic graphs the characteristics, the nodes are attributed with, such as length or width, can be directly combined for matching nodes. For isomorphic subgraphs only the attributes of the matching subgraphs can be combined.