Handwritten word recognition based on geometric decomposition

• US 20060193518A1
• Filed: 01/30/2006
• Published: 08/31/2006
• Est. Priority Date: 01/28/2005
• Status: Active Grant

• Current Assignee: IMDS Software, Inc.
• Original Assignee: IMDS Software, Inc.
• Inventors: Dong, Jianxiong
• Granted Patent: US 8,077,973 B2
• Time in Patent Office: Days
• US Class Current: 382/186
• CPC Class Codes: G06V 2201/133 Survey article
• CPC Class Codes: G06V 30/10 Character recognition
• CPC Class Codes: G06V 30/1478 of characters or characters lines
• CPC Class Codes: G06V 30/182 by coding the contour of the pattern
• CPC Class Codes: G06V 30/2264 using word shape

Abstract

A method of recognizing a handwritten word of cursive script comprising providing a template of previously classified words, and optically reading a handwritten word so as to form an image representation thereof comprising a bit map of pixels. The external pixel contour of the bit map is extracted and the vertical peak and minima pixel extrema on upper and lower zones respectively of this external contour are detected. Feature vectors of the vertical peak and minima pixel extrema are determined and compared to the template so as to generate a match between the handwritten word and a previously classified word. A method for classifying an image representation of a handwritten word of cursive script is also provided. Also provided is an apparatus for recognizing a handwritten word of cursive script. This apparatus comprises a template of previously classified words, a reader for optically reading a handwritten word, and a controller being linked thereto for generating a match between the handwritten word and the previously classified words. Two algorithms are provided for respectively correcting the skew and slant of a word image.

Claims

1. A method of recognizing a handwritten word of cursive script, said method comprising:

providing a template of previously classified words;

optically reading a handwritten word so as to form an image representation thereof comprising a bit map of pixels;

extracting an external pixel contour of said bit map;

detecting vertical peak and minima pixel extrema on upper and lower zones of said external contour respectively;

determining respective feature vectors of said vertical peak and minima pixel extrema and

comparing said feature vectors with said template so as to generate a match between said handwritten word and a said previously classified word.

2. A method according to claim 1 further comprising organizing said peak and minima pixel extrema into respective independent peak and minima sequences before said determining respective feature vectors of said vertical peak and minima pixel extrema.

3. A method according to claim 2, wherein said determining comprises determining feature vectors of said vertical peak and minima sequences.

4. A method according to claim 1, wherein said providing a template of words having been previously classified according to feature vectors comprises:

optically reading a handwritten word so as to form an image representation thereof comprising a bit map of pixels;

extracting a pixel contour of said bit map;

detecting vertical peak and minima pixel extrema on upper and lower zones of said contour respectively;

determining the respective feature vectors of said vertical peak and minima pixel extrema; and

classifying said word image according to said peak and minima feature vectors within a template.

5. A method according to claim 1 further comprising organizing said peak and minima pixel extrema into respective independent peak and minima sequences before said determining respective feature vectors of said vertical peak and minima pixel extrema.

6. A method according to claim 5, wherein said determining comprises determining feature vectors of said vertical peak and minima sequences.

7. A method according to claim 1, wherein said optically reading comprises scanning.

8. A method according to claim 1, wherein a said vertical peak pixel extrema comprises a pixel point on said upper zone of said pixel contour wherein neighbouring pixel segments are convex relative thereto,

9. A method according to claim 1, wherein a said vertical minima pixel extrema comprises a pixel point on said lower zone of said pixel contour wherein neighbouring pixel segments are concave relative thereto.

10. A method according to claim 2 , wherein said organizing said peak and minima pixel extrema into said respective independent peak and minima sequences comprises extracting features at each said extrema selected from the group consisting of:

the number of local extrema neighbouring a given said extrema on a same closed curve of said word image contour, said local extrema having a convex attribute corresponding to that of said given extrema;

the number of local extrema neighbouring a given said extrema on a same closed curve of said word image contour, said local extrema having a different convex attribute from said given extrema;

the lesser of the height difference between a given said extrema and a left neighbouring extrema and of the heignt difference between said given extrema and a right neighbouring extrema, wherein said left and right neighbouring extrema have convex attribute corresponding to that of said given extrema;

the lesser of the height difference between a given said extrema and a left neighbouring extrema and of the height difference between said given extrema and a right neighbouring extrema, wherein said left and right neighbouring extrema have a different convex attribute than that of said given extrema;

the number of peaks above a said given extrema divided by the total number of peaks on said pixel contour;

the number of peaks below a said given extrema divided by the total number of peaks on said pixel contour;

the y/h position of said given extrema, wherein y represents the y-axis coordinate of said given extrema and h represents the height of said word image;

the lesser of a contour portion length between a given said extrema and a left neighbouring peak and of a contour portion length between a given said extrema and a right neighbouring peak, wherein said neighbouring peaks and said given extrema are on a same closed curve;

the lesser of a contour portion length between a given said extrema and a left neighbouring minima and of a contour portion length between a given said extrema and a right neighbouring minima, wherein said neighbouring minima and said given extrema are on a same closed curve;

the lesser of a height difference between a given said extrema and a left neighbouring peak and of a given said extrema and a and right neighbouring peak, wherein said neighbouring peaks and said given extrema are on a same closed curve;

the lesser of a height difference between a given said extrema and a left neighbouring minima and of a given said extrema and a and right neighbouring minima, wherein said neighbouring minima and said given extrema are on a same closed curve;

the height ratio of a given said extrema and neighbouring left and right extrema as defined by

(y_A−

y_tl)/(y_n−

y_tln)

wherein a given said extrema is represented by A, a lowest extrema of said left or right neighbouring extrema is represented by n, y_tl represents the y-coordinate of the top-left corner of a said contour or a said closed curve, y_tln represents the top-left corner of a said contour or a said closed curve where point n is located y_A and y_n represent the y-coordinate of A and n resepecfully;

the distance between a given said extrema and a vertical intersection point; and

any combination thereof.

11. A method according to claim 10, wherein said organizing further comprises classifying extrema into two sequences of extrema on respective said upper and lower zones of said word image pixel contour.

12. A method according to claim 1, wherein said determining said respective feature vectors comprises extracting features at each said extrema selected from the group consisting of:

height difference between a given said extrema and a left neighbouring extrema having a convex attribute corresponding to the that of said given extrema;

height difference between a given said extrema and a right neighbouring extrema having a convex attribute corresponding to the that of said given extrema;

relative horizontal position of given said extrema defined by;

$f_3^c=\frac{x-x_{\mathrm{lt}}}{w}$

wherein said word image pixel contour is enclosed in a rectangle, the width and height of said rectangle being w and h the coordinates of a given said extrema being (x, y) and the coordinate of the top-left corner of said rectangle being (x_lt,y_lt)

relative vertical position of a given said extrema defined by;

$\left(f_4^c=\frac{y-y_{\mathrm{lt}}}{h}\right)$

wherein said word image pixel contour is enclosed in a rectangle, the width and height of said rectangle being w and h the coordinates of a given said extrema being (x, y) and the coordinate of the top-left corner of said rectangle being (x_lt, y_lt)

projection ratio in the horizontal direction of a given said extrema defined by;

$f_5^c=\frac{{\int <br><br>}_a^c<br><br>p<br><br>\left(x\right)<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>x}{{\int <br><br>}_a^b<br><br>p<br><br>\left(x\right)<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>x}$

wherein said given extrema is represented by c and having the coordinates (x, y), and p(x) represents the projection function bounded by the x-axis interval [a, b],

projection ratio in the vertical direction (f₆^c) of a given said extrema defined by

$f_6^c=\frac{{\int <br><br>}_a^c<br><br>p<br><br>\left(y\right)<br><br>d<br><br>y}{{\int <br><br>}_a^b<br><br>p<br><br>\left(y\right)<br><br>d<br><br>y}$

wherein said given extrema is represented by c and having the coordinates (x, y), and p(y) represents the projection function bounded by the y-axis interval [a, b];

the greater of a height difference between a given said extrema and a left neighbouring extrema and of a given said extrema and a right neighbouring extrema, wherein said left and right neighbouring extrema comprise convex attributes corresponding to that of said given extrema

if there is an inner loop below a said given extrema this feature is set to 1, if there is no inner loop below a said given extrema this feature is set to 0;

total number of said peaks of said pixel contour on which said given extrema is located said

total number of said minima of said pixel contour on which said given extrema is located

a height ratio of a given said extrema and neighbouring left and right extrema as defined by

(y_A−

y_tl)/(y_n−

y_tln)

wherein a given said extrema is represented by A, a lowest extrema of said left or right neighbouring extrema is represented by n, y_tl represents the y-coordinate of the top-left corner of a said contour or a said closed curve, y_tln represents the top-left corner of a said contour or a said closed curve where point n is located y_A and y_n represent the y-coordinate of A and n resepecffully;

contour portion length between a given said extrema and a left neighbouring extrema comprising a convex attribute that is different than that of said given extrema;

contour portion length a given said extrema and a right neighbouring extrema comprising a convex attribute that is different than that of said given extrema;

height difference between a given said extrema and a left neighbouring extrema comprising a convex attribute that is different than that of said given extrema;

height difference between a given said extrema and a right neighbouring extrema comprising a convex attribute that is different than that of said given extrema;

number of pixels with a horizontal orientation on a contour portion between a given said pixel and left neighbouring extrema comprising a convex attribute that is different than that of said given extrema;

number of pixels with a vertical orientation on a contour portion between a given said pixel and left neighbouring extrema comprising a convex attribute that is different than that of said given extrema;

number of pixels with a horizontal orientation on a contour portion between a given said pixel and right neighbouring extrema comprising a convex attribute that is different than that of said given extrema;

number of pixels with a vertical orientation on a contour portion between a given said pixel and right neighbouring extrema comprising a convex attribute that is different than that of said given extrema;

projection ratio of local extrema neighbouring a given said extrema, said local extrema being on the left of said given extrema given in a horizontal direction, said projection ration being defined by;

$f_{20}^c-\frac{{\int <br><br>}_a^c<br><br>p<br><br>\left(x\right)<br><br>d<br><br>x}{{\int <br><br>}_a^b<br><br>p<br><br>\left(x\right)<br><br>d<br><br>x}$

wherein said given extrema is represented by c and having the coordinates (x, y), and p(x) represents the projection function bounded by the x-axis interval [a, b];

projection ratio of local extrema neighbouring a given said extrema, said local extrema being on the right of said given extrema given in a horizontal direction, said projection ration being defined by

$f_{21}^c=\frac{{\int <br><br>}_a^c<br><br>p<br><br>\left(x\right)<br><br>d<br><br>x}{{\int <br><br>}_a^b<br><br>p<br><br>\left(x\right)<br><br>d<br><br>x}$

wherein said given extrema is represented by c and having the coordinates (x, y), and p(x) represents the projection function bounded by the x-axis interval [a, b];

projection of vertical crossing number of a given said extrema on the x-axis of said word image and quantification of said projection function to vertical crossing number intervals [0,3], [3,5], and [5,+∞

];

crossing ratio in the horizontal direction defined by;

$f_{25}^c=\frac{{\int <br><br>}_a^c<br><br>p<br><br>\left(x\right)<br><br>d<br><br>x}{{\int <br><br>}_a^b<br><br>p<br><br>\left(x\right)<br><br>d<br><br>x}$

wherein said given extrema is represented by c and having the coordinates (x, y), and p(x) represents the projection function bounded by the x-axis interval [a, b];

projection ratio of local extrema neighbouring a said given extreme on the left thereof in a horizontal and having a convex attribute that is different than said given extrema, said projection ration defined by

$f_{25}^c=\frac{{\int <br><br>}_a^c<br><br>p<br><br>\left(x\right)<br><br>d<br><br>x}{{\int <br><br>}_a^b<br><br>p<br><br>\left(x\right)<br><br>d<br><br>x}$

wherein said given extrema is represented by c and having the coordinates (x, y), and p(x) represents the projection function bounded by the x-axis interval [a, b];

projection ratio of local extrema neighbouring a said given extreme on the left thereof in a horizontal and having a convex attribute that is different than said given extrema, said projection ration defined by

$f_{25}^c=\frac{{\int <br><br>}_a^c<br><br>p<br><br>\left(x\right)<br><br>d<br><br>x}{{\int <br><br>}_a^b<br><br>p<br><br>\left(x\right)<br><br>d<br><br>x}$

wherein said given extrema is represented by c and having the coordinates (x, y), and p(x) represents the projection function bounded by the x-axis interval [a, b];

and any combination thereof.

13. A method according to claim 12, wherein said determining said respective feature vectors further comprises normalization, said normalization comprises extracting features at each said extrema selected from the group consisting of:

the number of local extrema neighbouring a given said extrema on a same closed curve of said word image contour, said local extrema having a convex attribute corresponding to that of said given extrema;

the number of local extrema neighbouring a given said extrema on a same closed curve of said word image contour, said local extrema having a different convex attribute from said given extrema;

the lesser of the height difference between a given said extrema and a left neighbouring extrema and of the heignt difference between said given extrema and a right neighbouring extrema, wherein said left and right neighbouring extrema have convex attribute corresponding to that of said given extrema;

the lesser of the height difference between a given said extrema and a left neighbouring extrema and of the heignt difference between said given extrema and a right neighbouring extrema, wherein said left and right neighbouring extrema have a different convex attribute than that of said given extrema;

the number of peaks above a said given extrema divided by the total number of peaks on said pixel contour;

the number of peaks below a said given extrema divided by the total number of peaks on said pixel contour;

the y/h position of said given extrema, wherein y represents the y-axis coordinate of said given extrema and h represents the height of said word image;

the lesser of a contour portion length between a given said extrema and a left neighbouring peak and of a contour portion length between a given said extrema and a right neighbouring peak, wherein said neighbouring peaks and said given extrema are on a same closed curve;

the lesser of a contour portion length between a given said extrema and a left neighbouring minima and of a contour portion length between a given said extrema and a right neighbouring minima, wherein said neighbouring minima and said given extrema are on a same closed curve;

the lesser of a height difference between a given said extrema and a left neighbouring peak and of a given said extrema and a and right neighbouring peak, wherein said neighbouring peaks and said given extrema are on a same closed curve;

the lesser of a height difference between a given said extrema and a left neighbouring minima and of a given said extrema and a and right neighbouring minima, wherein said neighbouring minima and said given extrema are on a same closed curve;

the height ratio of a given said extrema and neighbouring left and right extrema as defined by

(y_A−

y_tl)/(y_n−

y_tln)

wherein a given said extrema is represented by A, a lowest extrema of said left or right neighbouring extrema is represented by n, y_tl represents the y-coordinate of the top-left corner of a said contour or a said closed curve, y_tln represents the top-left corner of a said contour or a said closed curve where point n is located y_A and y_n represent the y-coordinate of A and n resepectfully;

the distance between a given said extrema and a vertical intersection point; and

any combination thereof.

14. A method according to claim 1 further comprising correcting a skew of said bit map before said extracting of said pixel contour.

15. A method according to claim 14, further comprising correcting a slant of said bit map when correcting said skew.

16. A method according to claim 1 further comprising correcting a slant of said bit map before said extracting of said pixel contour.

17. A method according to claim 16, further comprising correcting a skew of said bit map when correcting said slant.

18. A method according to claim 14, wherein said skew correction comprises:

pre-computing a look-up table of the image representation that maps Cartesian coordinates to polar coordinates;

performing a Radon transform in the polar domain of the image representation; and

calculating a slant angle from the Radon transform in the polar domain.

19. A method according to claim 18, wherein said calculating comprises calculating the angle φ

by means of the following equation;

${\mathrm{\varphi <br><br>}}^{*}=\frac{{\int <br><br>}_0^{\mathrm{\pi <br><br>}}<br><br>{\int <br><br>}_{-\mathrm{\infty <br><br>}}^{\mathrm{\infty <br><br>}}<br><br>I<br><br>\left(\mathrm{\varphi <br><br>},s\right)<br><br>g<br><br>\left(\mathrm{\varphi <br><br>},s\right)<br><br>\mathrm{\varphi <br><br>}<br><br>d<br><br>\mathrm{\varphi <br><br>}<br><br>d<br><br>s}{{\int <br><br>}_0^{\mathrm{\pi <br><br>}}<br><br>{\int <br><br>}_{-\mathrm{\infty <br><br>}}^{\mathrm{\infty <br><br>}}<br><br>I<br><br>\left(\mathrm{\varphi <br><br>},s\right)<br><br>g<br><br>\left(\mathrm{\varphi <br><br>},s\right)<br><br>d<br><br>\mathrm{\varphi <br><br>}<br><br>d<br><br>s},$

wherein g(φ

,s) g(phi, s) is the radon transorm and I(φ

,s) is an indicator function.

20. A method according to claim 16, wherein said slant correction comprises

pre-computing a look-up table of the image representation that maps Cartesian coordinates to polar coordinates;

prerforming a Radon transform in the polar domain of the image representation

calculating a skew angle from the Radon transform.

21. A method according to claim 20, wherein said calculating comprises calculating the skew angle φ

by means of the following equation

${\mathrm{\varphi <br><br>}}^{*}=\arg <br><br>\text{\hspace{1em}<br><br>}<br><br>\underset{\mathrm{\varphi <br><br>}}{\max }<br><br>{\int <br><br>}_{-\mathrm{\infty <br><br>}}^{\mathrm{\infty <br><br>}}<br><br>g<br><br>\left(\mathrm{\varphi <br><br>},s\right)<br><br>g^{\mathrm{\prime <br><br>}}<br><br>\left(\mathrm{\varphi <br><br>},s\right)<br><br>d<br><br>s$

wherein g(φ

,s) g (phi, s) is the radon transform and g′

(φ

,s) is the radon transform of flow gradient

22. A method according to claim 1 further comprising pruning invalid peak and minima extrema before said determining of said respective feature vectors.

23. A method according to claim 1, wherein said comparing is performed by dynamic time wrapping.

24. A method for classifying an image representation of a handwritten word of cursive script, said method comprising:

optically reading a handwritten word so as to form an image representation thereof comprising a bit map of pixels;

extracting a pixel contour of said bit map;

detecting vertical peak and minima pixel extrema on upper and lower zones of said contour respectively;

organizing said peak and minima pixel extrema into respective independent peak and minima sequences,

determining the respective feature vectors of said peak and minima sequences; and

classifying said word image according to said peak and minima feature vectors.

25. A method according to claim 24 further comprising organizing said peak and minima pixel extrema into respective independent peak and minima sequences before said determining respective feature vectors of said vertical peak and minima pixel extrema.

26. A method according to claim 25, wherein said determining comprises determining feature vectors of said vertical peak and minima sequences.

27. A method according to claim 24, wherein said optically reading comprises scanning.

28. A method according to claim 24, wherein a said vertical peak pixel extrema comprises a pixel point on said upper zone of said pixel contour wherein neighbouring pixel segments are convex relative thereto,

29. A method according to claim 24, wherein a said vertical minima pixel extrema comprises a pixel point on said lower zone of said pixel contour wherein neighbouring pixel segments are concave relative thereto.

30. A method according to claim 25, wherein said organizing said peak and minima pixel extrema into said respective independent peak and minima sequences comprises extracting features at each said extrema selected from the group consisting of:

the number of local extrema neighbouring a given said extrema on a same closed curve of said word image contour, said local extrema having a convex attribute corresponding to that of said given extrema;

the number of local extrema neighbouring a given said extrema on a same closed curve of said word image contour, said local extrema having a different convex attribute from said given extrema;

the lesser of the height difference between a given said extrema and a left neighbouring extrema and of the heignt difference between said given extrema and a right neighbouring extrema, wherein said left and right neighbouring extrema have convex attribute corresponding to that of said given extrema;

the lesser of the height difference between a given said extrema and a left neighbouring extrema and of the heignt difference between said given extrema and a right neighbouring extrema, wherein said left and right neighbouring extrema have a different convex attribute than that of said given extrema;

the number of peaks above a said given extrema divided by the total number of peaks on said pixel contour;

the number of peaks below a said given extrema divided by the total number of peaks on said pixel contour;

the y/h position of said given extrema, wherein y represents the y-axis coordinate of said given extrema and h represents the height of said word image;

the lesser of a contour portion length between a given said extrema and a left neighbouring peak and of a contour portion length between a given said extrema and a right neighbouring peak, wherein said neighbouring peaks and said given extrema are on a same closed curve;

the lesser of a contour portion length between a given said extrema and a left neighbouring minima and of a contour portion length between a given said extrema and a right neighbouring minima, wherein said neighbouring minima and said given extrema are on a same closed curve;

the lesser of a height difference between a given said extrema and a left neighbouring peak and of a given said extrema and a and right neighbouring peak, wherein said neighbouring peaks and said given extrema are on a same closed curve;

the lesser of a height difference between a given said extrema and a left neighbouring minima and of a given said extrema and a and right neighbouring minima, wherein said neighbouring minima and said given extrema are on a same closed curve;

the height ratio of a given said extrema and neighbouring left and right extrema as defined by

(y_A−

y_tl)/(y_n−

y_tln)

wherein a given said extrema is represented by A, a lowest extrema of said left or right neighbouring extrema is represented by n, y_tl represents the y-coordinate of the top-left corner of a said contour or a said closed curve, y_tln represents the top-left corner of a said contour or a said closed curve where point n is located y_A and y_n represent the y-coordinate of A and n resepecffully;

the distance between a given said extrema and a vertical intersection point; and

any combination thereof.

31. A method according to claim 30, wherein said organizing further comprises classifying extrema into two sequences of extrema on respective said upper and lower zones of said word image pixel contour.

32. A method according to claim 24, wherein said determining said respective feature vectors comprises extracting features at each said extrema selected from the group consisting of:

height difference between a given said extrema and a left neighbouring extrema having a convex attribute corresponding to the that of said given extrema;

height difference between a given said extrema and a right neighbouring extrema having a convex attribute corresponding to the that of said given extrema;

relative horizontal position of given said extrema defined by;

$f_3^c=\frac{x-x_{\mathrm{lt}}}{w}$

wherein said word image pixel contour is enclosed in a rectangle, the width and height of said rectangle being w and h the coordinates of a given said extrema being (x, y) and the coordinate of the top-left corner of said rectangle being (x_lt, y_lt)

relative vertical position of a given said extrema defined by;

$\left(f_4^c=\frac{y-y_{\mathrm{lt}}}{h}\right)$

wherein said word image pixel contour is enclosed in a rectangle, the width and height of said rectangle being w and h the coordinates of a given said extrema being (x, y) and the coordinate of the top-left corner of said rectangle being (x_lt, y_lt)

projection ratio in the horizontal direction of a given said extrema defined by;

$f_5^c=\frac{{\int <br><br>}_a^c<br><br>p<br><br>\left(x\right)<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>x}{{\int <br><br>}_a^b<br><br>p<br><br>\left(x\right)<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>x}$

wherein said given extrema is represented by c and having the coordinates (x, y), and p(x) represents the projection function bounded by the x-axis interval [a, b],

projection ratio in the vertical direction (f₆^c) of a given said extrema defined by

$f_6^c=\frac{{\int <br><br>}_a^c<br><br>p<br><br>\left(y\right)<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>y}{{\int <br><br>}_a^b<br><br>p<br><br>\left(y\right)<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>y}$

wherein said given extrema is represented by c and having the coordinates (x, y), and p(y) represents the projection function bounded by the y-axis interval [a, b];

the greater of a height difference between a given said extrema and a left neighbouring extrema and of a given said extrema and a right neighbouring extrema, wherein said left and right neighbouring extrema comprise convex attributes corresponding to that of said given extrema

if there is an inner loop below a said given extrema this feature is set to 1, if there is no inner loop below a said given extrema this feature is set to 0;

total number of said peaks of said pixel contour on which said given extrema is located said;

total number of said minima of said pixel contour on which said given extrema is located;

a height ratio of a given said extrema and neighbouring left and right extrema as defined by

(y_A−

t_tl)/(y_n−

y_tln)

wherein a given said extrema is represented by A, a lowest extrema of said left or right neighbouring extrema is represented by n, y_tl represents the y-coordinate of the top-left corner of a said contour or a said closed curve, y_tln represents the top-left corner of a said contour or a said closed curve where point n is located y_A and y_n represent the y-coordinate of A and n resepectfully;

contour portion length between a given said extrema and a left neighbouring extrema comprising a convex attribute that is different than that of said given extrema;

contour portion length a given said extrema and a right neighbouring extrema comprising a convex attribute that is different than that of said given extrema;

height difference between a given said extrema and a left neighbouring extrema comprising a convex attribute that is different than that of said given extrema;

height difference between a given said extrema and a right neighbouring extrema comprising a convex attribute that is different than that of said given extrema;

number of pixels with a horizontal orientation on a contour portion between the a given said pixel and left neighbouring extrema comprising a convex attribute that is different than that of said given extrema;

number of pixels with a vertical orientation on a contour portion between the a given said pixel and left neighbouring extrema comprising a convex attribute that is different than that of said given extrema;

number of pixels with a horizontal orientation on a contour portion between the a given said pixel and right neighbouring extrema comprising a convex attribute that is different than that of said given extrema;

number of pixels with a vertical orientation on a contour portion between the a given said pixel and right neighbouring extrema comprising a convex attribute that is different than that of said given extrema;

projection ratio of local extrema neighbouring a given said extrema, said local extrema being on the left of said given extrema given in a horizontal direction, said projection ration being defined by;

$f_{20}^c=\frac{{\int <br><br>}_a^c<br><br>p<br><br>\left(x\right)<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>x}{{\int <br><br>}_a^b<br><br>p<br><br>\left(x\right)<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>x}$

wherein said given extrema is represented by c and having the coordinates (x, y), and p(x) represents the projection function bounded by the x-axis interval [a, b];

projection ratio of local extrema neighbouring a given said extrema, said local extrema being on the right of said given extrema given in a horizontal direction, said projection ration being defined by

$f_{21}^c=\frac{{\int <br><br>}_a^c<br><br>p<br><br>\left(x\right)<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>x}{{\int <br><br>}_a^b<br><br>p<br><br>\left(x\right)<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>x}$

wherein said given extrema is represented by c and having the coordinates (x, y), and p(x) represents the projection function bounded by the x-axis interval [a, b];

projection of vertical crossing number of a given said extrema on the x-axis of said word image and quantification of said projection function to vertical crossing number intervals [0,3], [3,5], and [5,+∞

];

crossing ratio in the horizontal direction defined by;

$f_{25}^c=\frac{{\int <br><br>}_a^c<br><br>p<br><br>\left(x\right)<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>x}{{\int <br><br>}_a^b<br><br>p<br><br>\left(x\right)<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>x}$

wherein said given extrema is represented by c and having the coordinates (x, y), and p(x) represents the projection function bounded by the x-axis interval [a, b];

projection ratio of local extrema neighbouring a said given extreme on the left thereof in a horizontal and having a convex attribute that is different than said given extrema, said projection ration defined by

$f_{25}^c=\frac{{\int <br><br>}_a^c<br><br>p<br><br>\left(x\right)<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>x}{{\int <br><br>}_a^b<br><br>p<br><br>\left(x\right)<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>x}$

wherein said given extrema is represented by c and having the coordinates (x, y), and p(x) represents the projection function bounded by the x-axis interval [a, b];

projection ratio of local extrema neighbouring a said given extreme on the left thereof in a horizontal and having a convex attribute that is different than said given extrema, said projection ration defined by

$f_{25}^c=\frac{{\int <br><br>}_a^c<br><br>p<br><br>\left(x\right)<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>x}{{\int <br><br>}_a^b<br><br>p<br><br>\left(x\right)<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>x}$

wherein said given extrema is represented by c and having the coordinates (x, y), and p(x) represents the projection function bounded by the x-axis interval [a, b];

and any combination thereof.

33. A method according to claim 32, wherein said determining said respective feature vectors further comprises normalization, said normalization comprises extracting features at each said extrema selected from the group consisting of:

the number of local extrema neighbouring a given said extrema on a same closed curve of said word image contour, said local extrema having a convex attribute corresponding to that of said given extrema;

the number of local extrema neighbouring a given said extrema on a same closed curve of said word image contour, said local extrema having a different convex attribute from said given extrema;

the lesser of the height difference between a given said extrema and a left neighbouring extrema and of the heignt difference between said given extrema and a right neighbouring extrema, wherein said left and right neighbouring extrema have convex attribute corresponding to that of said given extrema;

the lesser of the height difference between a given said extrema and a left neighbouring extrema and of the heignt difference between said given extrema and a right neighbouring extrema, wherein said left and right neighbouring extrema have a different convex attribute than that of said given extrema;

the number of peaks above a said given extrema divided by the total number of peaks on said pixel contour;

number of peaks below a said given extrema divided by the total number of peaks on said pixel contour;

the y/h position of said given extrema, wherein y represents the y-axis coordinate of said given extrema and h represents the height of said word image;

the lesser of a contour portion length between a given said extrema and a left neighbouring peak and of a contour portion length between a given said extrema and a right neighbouring peak, wherein said neighbouring peaks and said given extrema are on a same closed curve;

the lesser of a contour portion length between a given said extrema and a left neighbouring minima and of a contour portion length between a given said extrema and a right neighbouring minima, wherein said neighbouring minima and said given extrema are on a same closed curve;

the lesser of a height difference between a given said extrema and a left neighbouring peak and of a given said extrema and a and right neighbouring peak, wherein said neighbouring peaks and said given extrema are on a same closed curve;

the lesser of a height difference between a given said extrema and a left neighbouring minima and of a given said extrema and a and right neighbouring minima, wherein said neighbouring minima and said given extrema are on a same closed curve;

the height ratio of a given said extrema and neighbouring left and right extrema as defined by

(y_A−

y_tl)/(y_n−

y_tln)

wherein a given said extrema is represented by A, a lowest extrema of said left or right neighbouring extrema is represented by n, y_tl represents the y-coordinate of the top-left corner of a said contour or a said closed curve, y_tln represents the top-left corner of a said contour or a said closed curve where point n is located y_A and y_n represent the y-coordinate of A and n resepectfully;

the distance between a given said extrema and a vertical intersection point; and

any combination thereof.

34. A method according to claim 32 further comprising correcting a skew of said bit map before said extracting of said pixel contour.

35. A method according to claim 34, further comprising correcting a slant of said bit map when correcting said skew.

36. A method according to claim 24 further comprising correcting a slant of said bit map before said extracting of said pixel contour.

37. A method according to claim 36, further comprising correcting a skew of said bit map when correcting said slant.

38. A method according to claim 34, wherein said skew correction comprises:

pre-computing a look-up table of the image representation that maps Cartesian coordinates to polar coordinates;

performing a Radon transform in the polar domain of the image representation; and

calculating a slant angle from the Radon transform in the polar domain.

39. A method according to claim 38, wherein said calculating comprises calculating the angle φ

by means of the following equation;

${\mathrm{\varphi <br><br>}}^{*}=\frac{{\int <br><br>}_0^{\mathrm{\pi <br><br>}}<br><br>{\int <br><br>}_{-\mathrm{\infty <br><br>}}^{\mathrm{\infty <br><br>}}<br><br>I<br><br>\left(\mathrm{\varphi <br><br>},s\right)<br><br>g<br><br>\left(\mathrm{\varphi <br><br>},s\right)<br><br>\mathrm{\varphi <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>\mathrm{\varphi <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>s}{{\int <br><br>}_0^{\mathrm{\pi <br><br>}}<br><br>{\int <br><br>}_{-\mathrm{\infty <br><br>}}^{\mathrm{\infty <br><br>}}<br><br>I<br><br>\left(\mathrm{\varphi <br><br>},s\right)<br><br>g<br><br>\left(\mathrm{\varphi <br><br>},s\right)<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>\mathrm{\varphi <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>s},$

wherein g(φ

,s) g(phi, s) is the radon transorm and I(φ

,s) is an indicator function.

40. A method according to claim 36, wherein said slant correction comprises

pre-computing a look-up table of the image representation that maps Cartesian coordinates to polar coordinates;

prerforming a Radon transform in the polar domain of the image representation

calculating a skew angle from the Radon transform.

41. A method according to claim 40, wherein said calculating comprises calculating the skew angle φ

by means of the following equation

${\mathrm{\varphi <br><br>}}^{*}=\arg <br><br>\text{\hspace{1em}<br><br>}<br><br>\underset{\mathrm{\varphi <br><br>}}{\max }<br><br>{\int <br><br>}_{-\mathrm{\infty <br><br>}}^{\mathrm{\infty <br><br>}}<br><br>g<br><br>\left(\mathrm{\varphi <br><br>},s\right)<br><br>g^{\mathrm{\prime <br><br>}}<br><br>\left(\mathrm{\varphi <br><br>},s\right)<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>s$

wherein g(φ

,s) g (phi, s) is the radon transform and g′

(φ

,s) is the radon transform of flow gradient

42. A method according to claim 24, further comprising pruning invalid peak and minima extrema before said determining of said respective feature vectors.

43. A method according to claim 24, wherein said comparing is performed by dynamic time wrapping.

44. An apparatus for recognizing a handwritten word of cursive script, said apparatus comprising

a template of words having been previously classified according to feature vectors,

a reader for optically reading a handwritten word, and

a controller being linked to said template and said reader;

wherein said controller;

forms an image representation of said handwritten word comprising a bit map of pixels;

extracts a pixel contour of said bit map;

detects vertical peak and minima pixel extrema on upper and lower zones of said contour respectively;

determines respective feature vectors of said peak and minima sequences; and

compares said feature vectors with said template so as to generate a match between said handwritten word and a said previously classified word.

45. An apparatus according to claim 44, wherein said controller organizes said peak and minima pixel extrema into respective independent peak and minima sequences before said determining respective feature vectors of said vertical peak and minima pixel extrema.

46. An apparatus according to claim 45, wherein said controller determines feature vectors of said vertical peak and minima sequences.

47. An apparatus according to claim 45, wherein said controller classifies extrema into two sequences of extrema on respective said upper and lower zones of said word image pixel contour.

48. An apparatus according to claim 44, wherein said controller corrects a skew of said bit map before said extracting of said pixel contour.

49. An apparatus according to claim 48, wherein said controller corrects a slant of said bit map when correcting said skew.

50. An apparatus according to claim 44, wherein said controller corrects a slant of said bit map before said extracting of said pixel contour.

51. An apparatus according to claim 50, wherein said controller corrects a skew of said bit map when correcting said slant.

52. An apparatus according to claim 44, wherein said controller prunes invalid peak and minima extrema before said determining of said respective feature vectors.

53. An apparatus according to claim 44, wherein said template comprises a database.

54. An apparatus according to claim 44, wherein said reader comprises a scanner.

55. An apparatus according to claim 44, wherein said controller comprises a computer.

56. A method for correcting a slant of an image representation of a handwritten word of cursive script comprising a bit map of pixels, said method comprising:

pre-computing a look-up table of the image representation that maps Cartesian coordinates to polar coordinates;

performing a Radon transform in the polar domain of the image representation; and

calculating a slant angle from the Radon transform in the polar domain.

57. A method according to claim 56, wherein said calculating comprises calculating the slant angle φ

by means of the following equation;

${\mathrm{\varphi <br><br>}}^{*}=\frac{{\int <br><br>}_0^{\mathrm{\pi <br><br>}}<br><br>{\int <br><br>}_{-\mathrm{\infty <br><br>}}^{\mathrm{\infty <br><br>}}<br><br>I<br><br>\left(\mathrm{\varphi <br><br>},s\right)<br><br>g<br><br>\left(\mathrm{\varphi <br><br>},s\right)<br><br>\mathrm{\varphi <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>\mathrm{\varphi <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>s}{{\int <br><br>}_0^{\mathrm{\pi <br><br>}}<br><br>{\int <br><br>}_{-\mathrm{\infty <br><br>}}^{\mathrm{\infty <br><br>}}<br><br>I<br><br>\left(\mathrm{\varphi <br><br>},s\right)<br><br>g<br><br>\left(\mathrm{\varphi <br><br>},s\right)<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>\mathrm{\varphi <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>s},$

wherein g(φ

,s) g(phi, s) is the radon transorm and I(φ

,s) is an indicator function.

58. A method for correcting the skew of an image representation of a handwritten word comprising a bit map of pixels, said method comprising:

pre-computing a look-up table of the image representation that maps Cartesian coordinates to polar coordinates;

prerforming a Radon transform in the polar domain of the image representation

calculating a skew angle from the Radon transform.

59. A method according to claim 58, wherein said calculating comprises calculating the skew angle φ

by means of the following equation

${\mathrm{\varphi <br><br>}}^{*}=\arg <br><br>\text{\hspace{1em}<br><br>}<br><br>\underset{\mathrm{\varphi <br><br>}}{\max }<br><br>{\int <br><br>}_{-\mathrm{\infty <br><br>}}^{\mathrm{\infty <br><br>}}<br><br>g<br><br>\left(\mathrm{\varphi <br><br>},s\right)<br><br>g^{\mathrm{\prime <br><br>}}<br><br>\left(\mathrm{\varphi <br><br>},s\right)<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>s$

wherein g(φ

,s)g (phi, s) is the radon transform and g′

(φ

,s) is the radon transform of flow gradient 3