Igor Polkovnikov

Igor Polkovnikov

More often than not, there is a need to understand the structure of complex computer code: what functions and in what order they are called, how information travels around static, input, and output variables, what depends on what. As a rule, executable code and data are scattered among multiple files and even multiple modules. Information is transmitted among variables which often change names. These tangled relations greatly complicate the development, maintenance, and redevelopment of code, its analysis for complexity and its robustness. As of now, there is no tool which is capable of presenting the real-life, useful diagram of actual code. Conventional flowcharts fail. Proposed is the method which overcomes these difficulties. The main idea is that functionality of software can be described through flows of control, which is essentially flows of time, and flows of data. These are inseparable. The second idea is to follow very strict system boundaries and distinctions with respect to modules, functions, blocks, and operators, as well as data holders, showing them all as subsystems, in other words, by clearly expressing the system structure when every piece of executable code and every variable may have its own graphical representation. The third is defining timelines as the entities clearly separated from the connected blocks of code. Timelines allow presentation of nesting of the control flow as deep as necessary. As a proof of concept, the same methods successfully describe production systems. Keywords: flowchart, UML, software diagram, visual programming, extreme programming, extreme modeling, control flow, data flow.

Igor Polkovnikov

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.

Igor Polkovnikov

A variety of operations of cellular automata on gray images is presented. All operations are of a wave-front nature finishing in a stable state. They are used to extract shape descripting gray objects robust to a variety of pattern distortions. Topographic terms are used: "lakes", "dales", "dales of dales". It is shown how mutual object relations like "above" can be presented in terms of gray image analysis and how it can be used for character classification and for gray pattern decomposition. Algorithms can be realized with a parallel asynchronous architecture. Keywords: Pattern Recognition, Mathematical Morphology, Cellular Automata, Wave-front Algorithms, Gray Image Analysis, Topographical Shape Descriptors, Asynchronous Parallel Processors, Holes, Cavities, Concavities, Graphs.