Using topological entities like neighborhood, path, connected path and monotonicity, concepts are outlined for a structural description of image content without a-priori.
Image objects are defined as path connected sets of pixels, one group by increasing paths and the other by decreasing paths. Both groups build a partition of the image up to 4-connected thin deviding lines. A local neighborhood of the objects of each group can be defined by common deviding lines. The unique local extremum of each object can be considered as support of the image object supplied with the appropriate neighborhood and quantitative features (of the image object).
The algorithms are presented for digital images above square grids and illustrated for the densitometrical image of a cell nucleus. There is no restriction applying the methods to any other image or transformation of an image.
The resulting image description consisting of the objects, their neighborhoods and features can be considered as a weighted or marked graph accessible for further steps of analysis. In the laboratory of the author these graphs are extensively used for the quantitative description of local interdependencies in tissue architecture and chromatin expression.