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An effort has been made to show mathematicians some new ideas applied toimage analysis. Gray images are presented as tilings. Based on topologicalproperties of the tiling, a number of gray convex hulls: maximal, minimal, andoriented ones are constructed and some are proved. They are constructed withonly one operation. Two tilings are used in the Constraint and Allowance typesof operations. New type of concavity described: a dale. All operations areparallel, possible to realize clock-less. Convexities define what is thebackground. They are treated as separate gray objects. There are multiplerelations among them and their descendants. Via that, topological size ofconcavities is proposed. Constructed with the same type of operations, Rays andAngles in a tiling define possible spatial relations. Notions like "strokes"are defined through concavities. Unusual effects on levelized gray objects areshown. It is illustrated how alphabet and complex hieroglyphs can be describedthrough concavities and their relations. A hypothesis of living organisms imageanalysis is proposed. A number of examples with symbols and a human face arecalculated with new Asynchwave C++ software library.

Construction of Convex Sets on Quadrilateral Ordered Tiles or Graphs  with Propagation Neighborhood Operations. Dales, Concavity Structures.  Application to Gray Image Analysis of Human-Readable Shapes