WO2022140708A1

WO2022140708A1 - A new decimal numeral symbolic

Info

Publication number: WO2022140708A1
Application number: PCT/US2021/065198
Authority: WO
Inventors: Khodja SALAH; Mostefai MESSAOUD
Original assignee: Salah Khodja
Priority date: 2020-12-26
Filing date: 2021-12-27
Publication date: 2022-06-30

Abstract

The invention consists on a new decimal numeral system inspired from the human body anatomy. Proposed symbolic allows a best concordance with decimal digits values and open up new opportunities, which are not possible with existing numeration systems. Both humans and machines are able to read the same codes without requiring sophisticated systems and software to perform the recognition task. Proposed OILU symbolic allows generating a new type of number series based on multi facets numbers splitting process. On the other hand, this new symbolic has been used in the development of new efficient visual markers, highly required for augmented reality and UAV's navigation applications.

Description

OILU Symbolic: A New Decimal Numeral Symbolic

Inventors: Messaoud MOSTEFAI & Salah KHODJA

Priority Claim

This application claims the benefit of priority of US provisional application No. 63/199,424 filed on Dec. 26, 2020.

Field of the Invention

The present disclosure relates to data representation and codification using a new numeral symbolic, which is composed of a set of basic rotating symbols. The Main application fields covered by this invention are numbering systems, Number Series Generators, Visual Tags and Markers.

Background of the Invention

Numbers are by far the most important thing human beings have ever invented to manage their daily lives, starting from basic counting to the resolution of complex problems [G. Ifrah 1985] [K.Meninger 2011 ] [ Encyclopedia Britannica 2019], Despite the fact that they have been able, to computerize their ability to compute and code, humans continue to use a symbol-based numbering system that is not well suited to their machines.

The US patent [5651075A to James F. Frazier et al.] describes for example an automatic number plates recognition scheme, which requires dedicated system and software to perform successful recognition within varying conditions, taking in account the perspective distortion

Moreover, the humans are unable to visually decipher produced machine’s Markers. Indeed, beginning with the US patent ID Barcode [2612994A to N. J. WOODLAND et al.] and ending with the latest 2D visual markers such as those presented in US Patent [2017/0061186A1 to A. LAURENT et al] [ US 7.231,063B2 to Naimark et al] [ US 2003/0076980 Al to Xiang Zhang et al], humans need machines to translate Marker’s embedded information into the well-known decimal numbering system.

The disclosed OILU numeration system has the main faculty to be easily readable by both humans and machines. The disclosed OILU numeration system allows viewing and manipulating numbers as real multifacets objects.

The disclosed OILU numeration system allows generating new number series based on an efficient digit splitting process.

The disclosed OILU numeration system allows generating new robust 2D markers, easily recognizable by both humans and machines, and less sensitive to damages and perspective distortions,

References Cited

Books and Articles

Karl Menninger, Number Words and Number Symbols: A Cultural History of Numbers, Dover Publications, Reprint Edition, 2011.

Georges Ifirah, “From One to Zero: A Universal History of Numbers”, Viking 1985 [G.Ifrah 1985] [K.Meninger 2011],

Encyclopedia Britannica, Numerals and numeral systems, britannica.com/science/numeral, 2019.

Y. Chahir, M. Mostefai, S. Khodja, OILU Tag: A Projective Invariant Fiducial System, World Academy of Science, Engineering and Technology, International Journal of Computer and Information Engineering Vol 15, N° 9, 520-524, 2021.

Y. Chahir, M. Mostefai, S. Hamza, New Efficient Visual OILU Marker, the 25^th International Conference on Image Processing, Computer Vision & Pattern Recognition, IPCV’21 : July 26-29, 2021, USA. Will appear in SPRINGER Nature Research Book Series on 15-17 December 2021.

Patents

US 2612994, Classifying apparatus and methods. . ., N. J. WOODLAND ET AL.

US 2017/0061186A1, Methods and systems for embedding and retrieving information through marker transformation, LAURENT et al.

US 7.231,063 B2, Fiducial Detection System, Leonid Naimark et al.

US 2003/0076980 Al, Coded visual Makers for tracking and camera calibration in mobile computing systems, Xiang Zhang et al.58Al.

BRIEF DESCRIPTION OF THE DRAWINGS FIG.1 shows the process of generating lacking symbols form the basic symbols FIG.2 shows the process of symbols affectation according to their orientation FIG.3 shows the pyramidal disposition of classical and OILU digits FIG.4 shows two examples of OILU Numbers FIG.5 shows the OILU symbols codification table FIG.6 shows the seven-segment digits splitting results FIG.7 shows examples of digits and numbers splitting process FIG.8 shows a multi facets splitting process of a number

FIG.9 shows the different types of square OILU Tags and markers with possible damages and possible embedding modes

FIG.10 shows circular OILU Symbols and examples of circular OILU Markers.

Detailed Description of the Invention

Referring to FIG.l, the OILU Symbolic is directly inspired from the human body anatomy (100) composed principally of a head, a spinal column and both upper and lower limbs. The main forms that emerge from these dynamic parts are: ‘O’ for the head ‘I’ for the spinal column ‘L’ and ‘U’ for both upper and lower limbs. Thus, developed decimal numeral symbolic consists of the following four basic symbols: {O, I, L, U}.

O: Correspond to the value zero (110) I: Correspond to the value one (120)

L: Correspond to the value two (130) U: Correspond to the value three (140)

As we all know, the decimal numeral system requires ten distinct symbols to represent the whole digits. In order to allow the OILU symbolic such representation, we will doubt it, as it is the case for a human, with the rotation faculty. Indeed, the last is able to reproduce these four basic forms in different spatial orientations. In our case, only some orientations of “L” and “U” symbols are necessary to complete the OILU symbolic list. Thus, by applying three successive counterclockwise rotations (of quarter turn: Qt) to these two symbols, we will obtain the six lacking symbols (150). The complete OILU symbolic list (160) is now ready to be affected to the decimal numeral digits. Referring to FIG.2, and if we exclude the «O» and «I» symbols which are not concerned by the rotation and are automatically affected to digits «0» and «1», the rest of symbols are affected (according to their orientations) to the corresponding 8 directions (200). Thus, each OILU symbol has a unique decimal value (210). Moreover, OILU symbolic allows symbols to be superimposed without losing the number’s value (220). This feature makes OILU numbers more compact for industrial marking.

Key strengths of the OILU Symbolic

The OILU symbolic open up new opportunities, which are not possible with the classical numeration. Amongst these, we have:

Pyramidal Superimposition of Symbols

Referring to FIG.3, we present examples of classical and OILU symbols superimposition. If we try to superimpose (or stack) a classical number (for example 1976) digits one on top of the other (300), we will certainly obtain a work of art, but the number value will be lost. This is not the case with the OILU Symbolic, which allows a large symbols superimposition with an easy and direct readability. This can be done by placing the following OILU symbols on a virtual pyramid (310). The lecture sense will be from the outside to the inside.

A Multi facets Numbers View

Unlike the classical numeral symbolic, the OILU symbolic allows to view a number as an object with its four facets. An example of two numbers 4670 and 3172 top view representation is shown in FIG.4. We can extract from each point of view a different number value. Thus, Groups of related numbers are formed:

The first group of numbers is: 4670 - 2450 - 8230 - 6890 (400)

The second group of numbers is: 3172 - 9158 - 7136 - 5194 (410)

OILU Symbols Codification Referring to FIG.5, the OILU symbols are composed of the following connected (500) or disconnected (510) segments: Seg A, Seg B, Seg C and Seg D. Symbols codification (520) is based on the state of the composing segments (‘0’= OFF, ‘ l’=ON). Generated codes allow unambiguous OILU symbols implementation within any software or hardware application.

This leads us to the main developed applications in mathematical and engineering fields.

First Application: Number Series Generator

Referring to FIG.6, OILU Symbolic allows generating a new type of numbers series based on an alternative transition between Decimal/Hexadecimal (Dec/Hex) and OILU symbols. This feature enables generating infinite sequence of growing numbers. The transition from Dec/Hex representation to OILU representation is done by splitting the seven-segment used to represent Dec/hex digits (600) into two distinct parts (610). This operation can be performed in three different strategies: the first strategy (a) considers the central horizontal segment as a shareable segment between the two parts. The second strategy (b) consider the central horizontal segment as belonging to the upper part, and finally the last strategy (c) considers the central segment as belonging to the lower part. In (620), we present the Dec/Hex digits splitting into OILU symbols, starting from the digit “0” to digit “F”.

To ensure a total reversibility, and in order to avoid any confusion, produced extra symbols (not OILU symbols) are replaced with symbols produced by the splitting strategy (a). This is the case of:

• The digit “4” with the splitting strategy “c” (622)

• The digit “A” with the splitting strategy “b” (624)

• The digit “B” with the splitting strategy “c” (626)

• The digit “F” with the splitting strategy “b” (628)

Hierarchical Splitting Process

The Iterative splitting process (starting from a DEC/Hex digit or number), allows generating a series of related numbers. The following examples presented in FIG.7, shows a three-level splitting of digit zero using the three splitting strategies (a) (700), (b) (710), (c) (720), and a two- level splitting of a hexadecimal number using the splitting strategy (a) (730). Splitting digit “0” using strategy (a): 0 — 73 90 11 95 95 (700)

Splitting the digit “0” using strategy (b): 0 —

93 11 94 31 (710)

Splitting the digit “0” using strategy (c): 0 —

80 11 94 85 (720)

Splitting the number “A9” using strategy (a): A9 — 82

00 59 73 95 (730)

Depending on the starting point and the adopted splitting strategy, a list of linked numbers is produced. Note that a combination of different splitting strategies is also possible within the same process.

Multi facets Numbers Splitting Process

As noted, before, OILU numbers are multi facets numbers. To enlarge the amount of produced numbers series, we can apply successive splitting operations to the different facets. The example presented in FIG.8, shows a hierarchical multi facets splitting process of the number seven three [73] (800). As seen from this example, various numbers series can be produced, according to pre- established navigation rules (chosen facet and splitting strategy). Such produced numbers and rules can be the basis for the construction of efficient and secure encryption and rekeying schemes.

Second Application: A New Product Labeling Tag

Product labeling is the most important operation required for product identification. Several labeling Tags have been developed to perform such operation. The most well-known are ID and 2D Barcodes. Although in general use, these two technologies are very susceptible to environmental damages (dirt, corner blocks erasing etc...).

Referring to FIG.9, proposed 2D labeling Tag (900) combines the two technologies to gain in simplicity and robustness. The simplicity of the symbol’s patterns as well as the regularity of the lines hardly simplify the automatic lecture task. A supplementary digit (fixed to one) is added to indicate the reading direction (910). Produced Tags are easily printed using a standard black and white printer. Depending on the print out size, OILU Tag is able of encoding the same amount of data in lowest space of a traditional bar code Tag. OILU symbolic allows (in case of dirt or damage) a high percentage of codewords reconstruction. Indeed, the pyramidal disposition of symbols makes the code visible even if several parts of the code are scratched (920) or removed (930).

OILU code can easily embed alphabetic symbols. For this, each bar is divided into small bars. The number/position of discontinuities is used to code the whole alphabetic symbols (940). Thus, OILU code zone can have one of the following three configurations:

• Only numeral symbols using continuous bars (950)

• Both numeral and alphanumeric characters using dotted bars (960)

• Only alphanumeric characters using dotted zero symbols (970)

Third Application: Fiducial Visual Marker

OILU symbolic is well suited for the development of real time visual markers, required for Augmented Reality and indoor/outdoor UAV’s applications. Indeed, the simplicity of the code (composed of horizontal and vertical segments) allows producing efficient visual markers, less computational and robust to the most known distortions. There are many conceptions of visual markers in the literature. In our case, two types of visual OILU markers will be presented.

Square OILU Markers

Square Markers are widely used in AR and UAV’s navigation applications. Referring to FIG.10, the square OILU marker characteristics (embedded OILU number, size and symbols lines thickness) are chosen according to the environment requirements. For a better visibility and real time performances, symbols lines are colored according to the space surrounding the mark. For clear spaces (Blank wall for example), OILU symbols are drawn in black on white background and delimited by a black frame to ease localization (980). For dark spaces, OILU symbols are drawn in white on black background, and are delimited by a blank frame (990). Thus, produced images are easily processed with basic image processing algorithms for the localization of the marker and the extraction of the corresponding embedded code. Circular OILU Markers

OILU Symbolic is easily adaptable to circular patterns. Indeed, instead of working with squared symbols, we can affect to each OILU Symbol a circular pattern. FIG.ll presents the basic forms used to represent the four OILU symbols (1000). The ‘O’ Symbol corresponds to a complete circle (1002), the ‘L symbol corresponds to an arc or a quarter circle (1004), the (L) symbol corresponds to a half circle (1006) and the (U) symbol corresponds to a ³/4 of a circle (1008). The Remaining digits are obtained by performing successive Quarter turns (Qt) on symbols (L) and (U) (1010).

The use of circular OILU symbolic allows developing a new type of circular Markers which (referring to the state of art), are more precise and robust to distortions than square Markers. But, unlike classical circular Markers, circular OILU Markers are asymmetrical and provide a larger information-coding capacity. As it is the case with squared OILU markers, a supplementary on top digit (fixed to one) is added to indicate the reading direction of circular OILU Markers (1020).

Claims

APPENDED CLAIMS. In summary, what has been disclosed is a method for generating a decimal numeration system from a set of four basic symbols and actions. Such method has been used to generate growing serial numbers and to develop specific square and circular visual tags and markers. Three important novelties are to be protected: • A new decimal numbering system called OILU Numeral system. • A New Number Series Generator based on OILU Splitting process. • New Visual Tags and Markers based on a pyramidal OILU symbols superimposition.Accordingly, other embodiments are within the scope of the following claims. What is claimed is:

1. A method for generating a decimal numeration system from a set of basic symbols and a set of actions.

2. The method as in claim 1, wherein the set of basic symbols comprises the following four basic symbols: O, I, L and LJ.

3. The method as in claim 2, wherein the basic symbols are represented with segments or circular arcs.

4. The method as in claim 3, wherein the basic symbols are represented with connected or disconnected segments.

5. The method as in claim 4, wherein the basic symbol (O) corresponds to the value 0 and is represented with four identical segments.

6. The method as in claim 4, wherein the basic symbol (I) corresponds to the value 1 and is represented with one segment.

7. The method as in claim 4, wherein the basic symbol (L) corresponds to the value 2 and is represented with two identical segments.

8. The method as in claim 4, wherein the basic symbol (LJ) corresponds to the value 3 and is represented with three identical segments.

9. The method as in claim 3, wherein the basic symbols are represented with arcs.

10. The method as in claim 9, wherein the basic symbol (O) corresponds to the value 0 and is represented with a circle.

9 The method as in claim 9, wherein the basic symbol (I) corresponds to the value 1 and is represented with a quarter circle. The method as in claim 9, wherein the symbol (L) corresponds to the value 2 and is represented with a half circle. The method as in claim 9, wherein the symbol (LJ) corresponds to the value 3 and is represented with a 3/4 circle. The method as in claim 1, wherein the said actions are counterclockwise quarter-turns. The method as in claim 1, wherein the said actions concern only the two symbols L and LJ. The method as in claim 15, wherein the application of successive three quarter-turns of the basic symbol L generate successively three symbols corresponding successively to the three even digits: 4, 6 and 8. The method as in claim 9, wherein the application of successive three quarter-turns of the basic symbol LJ generate successively three symbols corresponding successively to the three odd digits: 5, 7 and 9. The method as in claiml, wherein the generated decimal numeration system is composed of four basic symbols and six generated symbols. The ten symbols are called OILU symbolic. The method as in claim 18, wherein the number composing symbols are written with the same size and read from left to right. The method as in claim 18, wherein the number composing symbols are superimposed regularly one on top of the other and from the smallest to the largest. The method as in claim 20, wherein the lecture sense is from outside to inside. A method of generating a sequence of growing numbers by splitting the seven segments used to represent decimal or hexadecimal digits into two OILU symbols. Obtained OILU symbols are then replaced by their equivalent value in decimal. The method as in claim 22, wherein splitting process is performed according to the following three different strategies: The first strategy (a), consider the central horizontal segment as a shareable segment between the two parts. The second strategy (b), consider the central horizontal segment as belonging to the upper part, and finally the last strategy (c), consider the central segment as belonging to the lower part. The method as in claim 22, wherein a hierarchical and repetitive splitting process of decimal or hexadecimal numbers allows generating a series of related numbers. A method for generating 2D product labeling tags and 2D visual markers, based on the called OILU symbolic. The method as in claim 25, wherein the used OILU symbols are superimposed. The method as in claim 25, wherein the lecture sense is indicated by the position of additional external I symbol. The method as in claim 25, wherein labeling tag’s or marker’s symbols could be numerical only, alphanumerical or alphabetical. The method as in claim 25, wherein labeling tag’s or marker’s symbols could be printed in black and white or in color, and could be easily mounted on walls, ceiling, objects, landing platforms, drones, and on top vehicles. A method for generating 3D product labeling tags and 3D visual markers, based on the called OILU symbolic. The method as in claim 30 wherein the number composing symbols are displayed on one or more facet of a 3D cube, each facet symbols superimposed regularly one on top of the other and from the smallest to the largest. The method as in claim 31, wherein the lecture sense of facet is on any sequence. A method for generating a decimal numeration system from a set of basic symbols, wherein the number composing symbols are placed on a predetermined concentric array of squares, and read from any predetermined direction. The method as in claim 33, wherein the numbers composing symbols are read with one scan of horizontal axis and one scan of vertical axis. The method as in claim 33, wherein the number composing symbols are placed on a predetermined concentric array of squares, and read from outside-to-inside, inside-to- outside, left-to-right, right-to-left, top-to-down or down-to-top.

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