Methodology for data structure characterization, indexing, storage and retrieval

A method of providing an identifying data image index (I) for a two dimensional data image consisting of a multiplicity of pixels, said method comprising the steps of:

• a. determining Eigenvalues for essentially the entire data image, said Eigenvalues being a major axis and a minor axis of a characteristic virtual ellipse, then calculating a first (I1) non-degenerate data image index element using a formula which operates on said major and minor axes Eigenvalues;
• b. dividing said essentially entire two dimensional data image into at least first and second data image parts about an axis selected from the group consisting of:
• said minor axis;
• said major axis;
• and
• an axis intermediate thereto;
• and for each of said at least first and second data image parts independently determining Eigenvalues therefore, said Eigenvalues being a major axis and a minor axis for a first of said separate characteristic virtual ellipses, and major axis and a minor axis for a second of said separate characteristic virtual ellipses, and optionally independently determining a major axis and a minor axis for at least some of any additional data image parts, and then calculating at least second (I2) and/or third (I3) non-degenerate data image index elements determined from two of said at least two data image parts, using formulas which return a non-degenerate result;
• c. concatenating at least two of said first (I1), second (I2) and/or third (3) non-degenerate data image index elements in any functional permuted order to provide said identifying data image index (I).

A method of providing an identifying data image index (I) for a two dimensional data image consisting of a multiplicity of pixels, comprising the steps of:

• a. determining Eigenvalues for essentially the entire data image, said Eigenvalues being a major axis (λ11) and a minor axis (λ21) of a characteristic virtual ellipse, then calculating a first (I1) non-degenerate data image index element using the formula:
• I 1 = ( λ 11 - λ 21 ) 2 λ 11 + λ 21
• b. dividing said essentially entire two dimensional data image into first and second data image parts about an axis selected from the group consisting of:
• said minor axis;
• said major axis;
• and
• an axis intermediate thereto;
• and for each of said first and second data image parts independently determining Eigenvalues therefore, said Eigenvalues being a major axis (λ12) and a minor axis (λ22) for the first of said separate characteristic virtual ellipses, and major axis (λ13) and a minor axis (λ23) for the second of said separate characteristic virtual ellipses, and then calculating second (I2) and third (I3) non-degenerate data image index elements using the formulas:
• I 2 = ( λ 12 - λ 22 ) 2 λ 12 + λ 22 ⁢ ⁢ I 3 = ( λ 13 - λ 23 ) 2 λ 13 + λ 23
• c. dividing said each of said first and second image parts from step b., each about an axis selected from the group consisting of:
• said minor axis;
• said major axis;
• and
• an axis intermediate thereto;
• to produce third, forth, fifth and sixth image parts and for at least one of said third, forth, fifth and sixth image parts independently determining Eigenvalues thereof, said determined Eigenvalues being selected from the group consisting of:
• a major axis (λ14) and a minor axis (λ24) for the third of said separate characteristic virtual ellipses, and major axis (λ15) and a minor axis (λ25) for the forth of said separate characteristic virtual ellipses, a major axis (λ16) and a minor axis (λ26) for the fifth of said separate characteristic virtual ellipses, and major axis (λ17) and a minor axis (λ27) for the sixth of said separate characteristic virtual ellipses, and then calculating forth (I4), fifth (I5), sixth (I6) and seventh (I7) non-degenerate data image index elements using as appropriate the formulas:
• I 4 = ( λ 14 - λ 24 ) 2 λ 14 + λ 24 ⁢ I 5 = ( λ 15 - λ 25 ) 2 λ 15 + λ 25 I 6 = ( λ 16 - λ 26 ) 2 λ 16 + λ 26 ⁢ I 7 = ( λ 17 - λ 27 ) 2 λ 17 + λ 27
• d. concatenating said first (I1), and at least one produced non-degenerate data index element(s) selected from the group consisting of said:
• second (I2), third (I3), forth (I4), fifth, (I5), sixth (I6) and seventh (I7) non-degenerate data index elements;
• in any functional permuted order, to provide said identifying data image index (I).

A method of providing an identifying data image index (I) for a two dimensional data image consisting of a multiplicity of pixels, said method comprising the defining of a gradient range selection criteria based on a selection from the group consisting of:

• an intensity gradiant;
• a color gradient;
• and
• a gradiant based on intensity and color;
• and pre-selecting pixels within a selected range of gradients in said two dimensional data set based upon the meeting of said intensity and/or color gradient determining pre-selection criteria;
• said method further comprising the steps of:
• a. determining Eigenvalues for pre-selected pixels in essentially the entire data image, said Eigenvalues being a major axis (λ11) and a minor axis (λ21) of a characteristic virtual ellipse, then calculating a first (I1) non-degenerate data image index element using the formula:
• I 1 = ( λ 11 - λ 21 ) 2 λ 11 + λ 21
• b. dividing said essentially entire two dimensional data image into first and second data image parts about an axis selected from the group consisting of:
• said minor axis;
• said major axis;
• and
• an axis intermediate thereto;
• and for pre-selected pixels in each of said first and second data image parts independently determining Eigenvalues therefore, said Eigenvalues being a major axis (λ12) and a minor axis (λ22) for the first of said separate characteristic virtual ellipses, and major axis (λ13) and a minor axis (λ23) for the second of said separate characteristic virtual ellipses, and then calculating second (I2) and third (I3) non-degenerate data image index elements using the formulas:
• I 2 = ( λ 12 - λ 22 ) 2 λ 12 + λ 22 ⁢ ⁢ I 3 = ( λ 13 - λ 23 ) 2 λ 13 + λ 23
• c. concatenating said first, second and third non-degenerate data image index elements to provide said identifying data image index (I) by a selection from the group consisting of:
• I=I1 I2 I3;
• I=I1 I3 I2;
• I=I2 I1 I3;
• I=I2 I3 I1;
• I=I3 I1 I2;
• and
• I=I3 I2 I1.

A method of providing an identifying data image index (I) for a two dimensional data image consisting of a multiplicity of pixels, said method comprising the defining of a gradient range selection criteria based on a selection from the group consisting of:

• an intensity gradiant;
• a color gradient;
• and
• a gradiant based on intensity and color;
• and pre-selecting pixels within a selected range of gradients in said two dimensional data set based upon the meeting of said intensity and/or color gradient determining pre-selection criteria;
• said method comprising the steps of:
• a. determining Eigenvalues for pre-selected pixels in essentially the entire data image, said Eigenvalues being a major axis and:a minor axis of a characteristic virtual ellipse, then calculating a first (I1) non-degenerate data image index element using a formula which operates on said major and minor axes Eigenvalues.

A method of providing an identifying data structure index (I) for an “N” dimensional data structure consisting of a multiplicity of pixels, said method comprising the defining of a gradient range selection criteria based on a selection from the group consisting of:

• an intensity gradiant;
• a color gradient;
• and
• a gradiant based on intensity and color;
• and pre-selecting pixels within a selected range of gradients in said “N” dimensional data set based upon the meeting of said intensity and/or color gradient determining pre-selection criteria;
• said method comprising the step of:
• a. determining Eigenvalues for pre-selected pixels in essentially the entire data structure, said Eigenvalues being a major axis and (N−1) minor axes of a characteristic virtual data structure mathematical object, then calculating a first non-degenerate data structure index element using a formula which operates on said major axis and at least one of said (N−1) minor axes.

A method of providing an identifying data image, index (I) for a two dimensional data image consisting of a multiplicity of pixels, said method comprising the defining of a gradient range selection criteria based on a selection from the group consisting of:

• an intensity gradiant;
• a color gradient;
• and
• a gradiant based on intensity and color;
• and pre-selecting pixels within a selected range of gradients in said two dimensional data set based upon the meeting of said intensity and/or color gradient determining pre-selection criteria;
• said method further comprising the steps of:
• a. determining Eigenvalues for pre-selected pixels in essentially the entire data image, said Eigenvalues being a major axis (λ11) and a minor axis (λ21) of a characteristic virtual ellipse, then calculating a first (I1) non-degenerate data image index element using the formula:
• I 1 = ( λ 11 - λ 21 ) 2 λ 11 + λ 21
• b. dividing said essentially entire two dimensional data image into first and second data image parts about an axis selected from the group consisting of:
• said minor axis;
• said major axis;
• and
• an axis intermediate thereto;
• and for pre-selected pixels in each of said first and second data image parts independently determining Eigenvalues therefore, said Eigenvalues being a major axis (λ12) and a minor axis (λ22) for the first of said separate characteristic virtual ellipses, and major axis (λ13) and a minor axis (λ23) for the second of said separate characteristic virtual ellipses, and then calculating second (I2) and third (I3) non-degenerate data image index elements using the formulas:
• I 2 = ( λ 12 - λ 22 ) 2 λ 12 + λ 22 ⁢ ⁢ I 3 = ( λ 13 - λ 23 ) 2 λ 13 + λ 23
• c. dividing said each of said first and second image parts from step b., each about an axis selected from the group consisting of:
• said minor axis;
• said major axis thereof;
• and
• an axis intermeidate thereto;
• to produce third, forth, fifth and sixth image parts and for at least one of said third, forth, fifth and sixth image parts, based upon pre-selected pixels therein, independently determining Eigenvalues thereof, said determined Eigenvalues being selected from the group consisting of:
• a major axis (λ14) and a minor axis (λ24) for the third of said separate characteristic virtual ellipses, and major axis (λ15) and a minor axis (λ25) for the forth of said separate characteristic virtual ellipses, a major axis (λ16) and a minor axis (λ26) for the fifth of said separate characteristic virtual ellipses, and major axis (λ17) and a minor axis (λ27) for the sixth of said separate characteristic virtual ellipses, and then calculating forth (I4), fifth (I5), sixth (I6) and seventh (I7) non-degenerate data image index elements using as appropriate the formulas:
• I 4 = ( λ 14 - λ 24 ) 2 λ 14 + λ 24 ⁢ I 5 = ( λ 15 - λ 25 ) 2 λ 15 + λ 25 I 6 = ( λ 16 - λ 26 ) 2 λ 16 + λ 26 ⁢ I 7 = ( λ 17 - λ 27 ) 2 λ 17 + λ 27
• d. concatenating said first (I1), and at least one produced non-degenerate data index element(s) selected from the group consisting of said:
• second (I2);
• third (I3);
• forth (I4);
• fifth (I5);
• sixth (I6);
• and seventh (I7);
• non-degenerate data index elements), in any functional permuted order, to provide said identifying data image index (I).

A method of providing an identifying data image index (I) for a two dimensional data image consisting of a multicity of pixels, said method comprising the defining of a gradient range selection criteria based on a selection from the group consisting of:

• an intensity gradiant;
• a color gradiant;
• and
• a gradiant based on intensity and color;
• and pre-selecting pixels within a selected range of gradients in said two dimensional data set based upon the meeting of said intensity and/or color gradient determining pre-selection criteria;
• said method further comprising the steps of:
• a. determining Eigenvalues for pre-selected pixels in essentially the entire data image, said Eigenvalues being a major axis (λ11) and a minor axis (λ21) of a characteristic virtual ellipse, then calculating a first (I1) non-degenerate data image index element using a formula which operates on said Eigenvalues:
• b. dividing said essentially entire two dimensional data image into first, second, third and forth data image parts using said minor axis and said major axis as dividing means, said first, second, third and forth data image parts being oriented in a first, second, third and forth gradiant pattern defined by said major and minor axes, in said two dimensional data image;
• c. for at least one of said first, second, third and forth data image parts, based upon pre-selected pixels therein, independently determining Eigenvalues of a characteristic virtual ellipse therefore, said Eigenvalues being selected from the group consisting of:
• a major axis (λ12) and a minor axis (λ22) for the first of said separate characteristic virtual ellipses;
• and a major axis (λ13) and a minor axis (λ23) for the second of said separate characteristic virtual ellipses;
• a major axis (λ14) and a minor axis (λ24) for the third of said separate characteristic virtual ellipses and a major axis (λ15) and a minor axis (λ25) for the forth of said separate characteristic virtual ellipses;
• d. calculating at least one additional non-degenerate data image image index element using formula(s) which operates on Eigenvalues corresponding to said at least one of said first, second, third and forth data image parts determined in step. c;
• and
• e. concatenating at least two resulting non-degenerate data index elements, in any functional permuted order, to provide said identifying data image index (I).