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
This work proposes a novel mathematical framework for image analysis, potentially benefiting researchers in computer vision and pattern recognition, though it appears incremental in applying existing topological concepts to gray images.
The paper tackles the problem of analyzing gray images by representing them as tilings and constructing various gray convex hulls (maximal, minimal, oriented) using a single parallel operation, with applications to describing shapes like alphabet characters and hieroglyphs through concavities and their relations. It demonstrates examples with symbols and a human face using a new Asynchwave C++ library.
An effort has been made to show mathematicians some new ideas applied to image analysis. Gray images are presented as tilings. Based on topological properties of the tiling, a number of gray convex hulls: maximal, minimal, and oriented ones are constructed and some are proved. They are constructed with only one operation. Two tilings are used in the Constraint and Allowance types of operations. New type of concavity described: a dale. All operations are parallel, possible to realize clock-less. Convexities define what is the background. They are treated as separate gray objects. There are multiple relations among them and their descendants. Via that, topological size of concavities is proposed. Constructed with the same type of operations, Rays and Angles in a tiling define possible spatial relations. Notions like "strokes" are defined through concavities. Unusual effects on levelized gray objects are shown. It is illustrated how alphabet and complex hieroglyphs can be described through concavities and their relations. A hypothesis of living organisms image analysis is proposed. A number of examples with symbols and a human face are calculated with new Asynchwave C++ software library.