Systems and methods for identifying printers using Voronoi diagrams

1. A method for identifying a printer that generated a printed document, comprising:

generating an electronic image of the printed document;

obtaining, by the computing device, a dot pattern contained on the printed document via an analysis of the electronic image;

overlaying, by the computing device, the dot pattern on Voronoi diagrams;

selecting, by the computing device, a first Voronoi diagram from the Voronoi diagrams that has a single dot of the dot pattern in each of at least some cells thereof; and

identifying, by the computing device, a printer associated with the first Voronoi diagram that was selected from the Voronoi diagrams;

wherein the printer associated with the first Voronoi diagram comprises the printer that generated a printed document.

2. The method according to claim 1 , further comprising autonomously or automatedly controlling operations of an electronic device based on the identifying.

3. The method according to claim 1 , wherein none of the cells of the first Voronoi diagram has two or more dots of the dot pattern contained therein.

4. The method according to claim 1 , wherein the selecting the first Voronoi diagram from the Voronoi diagrams comprises eliminating a second Voronoi diagram from further consideration for selection when the second Voronoi diagram has at least one cell with two or more dots of the dot pattern contained therein.

5. The method according to claim 1 , wherein the selecting the first Voronoi diagram from the Voronoi diagrams comprises eliminating a second Voronoi diagram from further consideration for selection when the second Voronoi diagram has less than a threshold number of cells with dots of the dot pattern contained therein.

6. The method according to claim 1 , wherein the selecting the first Voronoi diagram from the Voronoi diagrams comprises eliminating a second Voronoi diagram from further consideration for selection when the second Voronoi diagram has at least one cell without any dot of the dot pattern contained therein or located within a distance from a cell boundary thereof.

7. The method according to claim 1 , further comprising assigning a different dot pattern to each printer of a plurality of printers.

8. The method according to claim 7 , further comprising generating the Voronoi diagrams from the different dot patterns.

9. The method according to claim 8 , further comprising:

obtaining, by the computing device, another dot pattern contained on another printed document;

overlaying, by the computing device, the another dot pattern on the Voronoi diagrams;

selecting, by the computing device, a second Voronoi diagram from the Voronoi diagrams based on the another dot pattern; and

identifying, by the computing device, another printer which is associated with the second Voronoi diagram that was selected from the Voronoi diagrams;

wherein the another printer generated the another printed document.

10. The method according to claim 1 , wherein the dot pattern was printed on first documents by the printer during a first period of time and another different dot pattern was printed on second documents by the printer during a second period of time.

11. The method according to claim 10 , further comprising identifying, by the computing device, when the printer printed one of the second documents based on results from analyzing the Voronoi diagram with the another different dot pattern overlaid thereon.

12. A system, comprising:

a processor; and

a non-transitory computer-readable storage medium comprising programming instructions that are configured to cause the processor to implement a method for identifying a printer that generated a printed document, wherein the programming instructions comprise instructions to:

generate an electronic image of the printed document;

obtain a dot pattern contained on the printed document via an analysis of the electronic image;

overlay the dot pattern on Voronoi diagrams;

select a first Voronoi diagram from the Voronoi diagrams that has a single dot of the dot pattern in each of at least some cells thereof; and

identify a printer associated with the first Voronoi diagram that was selected from the Voronoi diagrams;

wherein the printer associated with the first Voronoi diagram comprises the printer that generated a printed document.

13. The system according to claim 12 , wherein none of the cells of the first Voronoi diagram has two or more dots of the dot pattern contained therein.

14. The system according to claim 12 , wherein the programming instructions comprise instructions to eliminate a second Voronoi diagram from further consideration for selection when the second Voronoi diagram has at least one cell with two or more dots of the dot pattern contained therein.

15. The system according to claim 12 , wherein the programming instructions comprise instructions to eliminate a second Voronoi diagram from further consideration for selection when the second Voronoi diagram has less than a threshold number of cells with dots of the dot pattern contained therein.

16. The system according to claim 12 , wherein the programming instructions comprise instructions to eliminate a second Voronoi diagram from further consideration for selection when the second Voronoi diagram has at least one cell without any dot of the dot pattern contained therein or located within a distance from a cell boundary thereof.

17. The system according to claim 12 , the programming instructions comprise instructions to assign a different dot pattern to each printer of a plurality of printers.

18. The system according to claim 17 , the programming instructions comprise instructions to generate the Voronoi diagrams from the different dot patterns.

19. The system according to claim 18 , the programming instructions comprise instructions to:

obtain another dot pattern contained on another printed document;

overlay the another dot pattern on the Voronoi diagrams;

select a second Voronoi diagram from the Voronoi diagrams based on the another dot pattern; and

identify another printer which is associated with the second Voronoi diagram that was selected from the Voronoi diagrams;

wherein the another printer generated the another printed document.

20. The system according to claim 12 , wherein

the dot pattern was printed on first documents by the printer during a first period of time and another different dot pattern was printed on second documents by the printer during a second period of time; and

the programming instructions comprise instructions to identify when the printer printed one of the second documents based on results from analyzing the Voronoi diagram with the another different dot pattern overlaid thereon.