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Handwritten Fonts Modeling Based on Fat Lines of Variable Width
Stanislav KlimenkoMoscow Physicotechnical Institute
Moscow, [email protected]
Leonid MestetskiyMoscow State University
Moscow, [email protected]
Andrey SemenovTver State University
Tver, [email protected]
Fonts DescribingThe 16-th International Conference in Central Europe on
Computer Graphics, Visualization andComputer Vision'2008
Outline description is union of Bezier curves 2
Fonts DescribingDisadvantages of outline description:1. Implementation of “alive” handwriting is difficulty
2. Doesn’t allow implementing variations of stroke width of pen
3. The problem of preservation of contour smoothness
?
3
Handwritten Fonts
4
1. Representation of a font as a trace of pen «with a variable width»
2. Obtaining of a font in the form of curves with a width on the scanned image
Our approach
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],[
})())(())((:),{( 2222
bat
trtvytuxRyxCt
- Fat curve with axis P(t)=(u(t),v(t)) and thickness r(t)
Fat Curve
tCaC
bC
is family of circles of variable radius with centers on smooth curve
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Elementary Fat B-Spline Curve
33
232
231
30
)(
1333)(
463)(
)1()(
ttB
ttttB
tttB
ttB
3
0
*)(61
)(i
ii HtBtC
},,{ iriyixi HHHH
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Composite Fat B-Spline Curve
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The hand-written alphabet (Russian)
Personal hand-written font
Our task
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Step 1• The person writes separate letters by ink pen on a
paper, for example, the alphabet
The method description
Step 2• The image is digitized by the scanner 10
The method description
Binary image Polygonal figure
Step 3• Construction of piecewise-linear boundary as a
polygon of minimal perimeter
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The method description
Polygonal figure Continuous skeleton
Step 4• Construction of continuous skeleton as a set of
medial axes of polygonal figure
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The method descriptionStep 5• Construction of a base skeleton
Continuous skeleton Base skeleton 13
The method descriptionStep 6• Decomposition branches of base skeleton
Base skeleton Base skeleton with circles 14
The method descriptionStep 7• Approximation of base skeleton by a circular figure
Circular figureBase skeleton with circles 15
Fat Curve Outline Smoothing• Recalculation radius value for each control circle:
riirriir HkHkHkH 13211'
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Fat Curve Axis Smoothing• Recalculation center coordinates for each control circle:
.
,
13211'
13211'
yiiyyiiy
xiixxiix
HkHkHkH
HkHkHkH
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Fat Curve Sewing
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Kerning task
What is better ?
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Alignment of letter spacing • Kerning - is a visual alignment of letter spacing in process
of text on raster devices .
How is near ?
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Method of Automatic Kerning1. Rasterization of kerning pair of characters on a common base line of raster
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Method of Automatic Kerning2. Scanning by a horizontal line "from top to bottom" with step of 1 pixel
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Method of Automatic Kerning3. At each position of a scanning line
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4. Defining position of a scanning line at which distance between the points is minimum
Method of Automatic Kerning
Minimal distance
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5. Defining minimal kerning distance
Method of Automatic Kerning
Minimal kerning distance
Is negative kerning25
5. Defining minimal kerning distance
Method of Automatic Kerning
Minimal kerning distance
Is positive kerning26
Some examples
KERNING[я][б] = 15
KERNING[в][а] = -72
Method of Automatic Kerning
Minimal kerning distance is 20
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Kerning table
а б в г .. .. э ю я
а 19 15 8 12 .. -3 11 19
б -13 -17 -5 -8 .. .. -7 -29 -21
в -72 1 -62 -67 .. .. -66 -88 -80
г 19 15 8 10 .. .. -9 10 19
.. .. .. .. .. .. .. .. .. ..
.. .. .. .. .. .. .. .. .. ..
э 4 0 19 19 .. .. 10 -13 -5
ю 16 12 6 3 .. .. 19 2 12
я 19 15 11 17 .. .. 9 19 19
Method of Automatic Kerning
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Method of Automatic Kerning
KERNING[в][ю] = -88 What does it mean ?
Length of this segment is 88
It means how many pixels to the left it is necessary to move the right character
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Some examples
Method of Automatic Kerning
It’s A.S. Pushkin
No kerning30
Some examples
Method of Automatic Kerning
It’s A.S. Pushkin
Kerning is 20 pixels31
Some examples
Method of Automatic Kerning
It’s A.S. Pushkin
Kerning is 40 pixels32
Thickness Pen Modeling
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3D Modeling
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• Modeling of 3D effect by layer painting
“Alive” Handwriting Modeling
iirir HH i - is noise
• Adding of small noise into values of radiuses
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• Adding of small noise into values of radiuses
“Alive” Handwriting Modeling
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• Converting fat curve representation to outline description
Export to famous description
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Fat curves description PostScript description
Summary
• The method of fat curves is efficient tool for modeling of hand-written characters;
• There is possibility of letterspacings controlling (zoom in/out letterspacing);
• There is easy way to modeling “alive” handwriting;
• Our approach can be used as embedded module (plug-in) in font editors.
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