# NAME

Image::Leptonica::Func::skew

# VERSION

version 0.04

`skew.c`

```
skew.c
Top-level deskew interfaces
PIX *pixDeskew()
PIX *pixFindSkewAndDeskew()
PIX *pixDeskewGeneral()
Top-level angle-finding interface
l_int32 pixFindSkew()
Basic angle-finding functions
l_int32 pixFindSkewSweep()
l_int32 pixFindSkewSweepAndSearch()
l_int32 pixFindSkewSweepAndSearchScore()
l_int32 pixFindSkewSweepAndSearchScorePivot()
Search over arbitrary range of angles in orthogonal directions
l_int32 pixFindSkewOrthogonalRange()
Differential square sum function for scoring
l_int32 pixFindDifferentialSquareSum()
Measures of variance of row sums
l_int32 pixFindNormalizedSquareSum()
==============================================================
Page skew detection
Skew is determined by pixel profiles, which are computed
as pixel sums along the raster line for each line in the
image. By vertically shearing the image by a given angle,
the sums can be computed quickly along the raster lines
rather than along lines at that angle. The score is
computed from these line sums by taking the square of
the DIFFERENCE between adjacent line sums, summed over
all lines. The skew angle is then found as the angle
that maximizes the score. The actual computation for
any sheared image is done in the function
pixFindDifferentialSquareSum().
The search for the angle that maximizes this score is
most efficiently performed by first sweeping coarsely
over angles, using a significantly reduced image (say, 4x
reduction), to find the approximate maximum within a half
degree or so, and then doing an interval-halving binary
search at higher resolution to get the skew angle to
within 1/20 degree or better.
The differential signal is used (rather than just using
that variance of line sums) because it rejects the
background noise due to total number of black pixels,
and has maximum contributions from the baselines and
x-height lines of text when the textlines are aligned
with the raster lines. It also works well in multicolumn
pages where the textlines do not line up across columns.
The method is fast, accurate to within an angle (in radians)
of approximately the inverse width in pixels of the image,
and will work on a surprisingly small amount of text data
(just a couple of text lines). Consequently, it can
also be used to find local skew if the skew were to vary
significantly over the page. Local skew determination
is not very important except for locating lines of
handwritten text that may be mixed with printed text.
```

# FUNCTIONS

## pixDeskew

PIX * pixDeskew ( PIX *pixs, l_int32 redsearch )

```
pixDeskew()
Input: pixs (any depth)
redsearch (for binary search: reduction factor = 1, 2 or 4;
use 0 for default)
Return: pixd (deskewed pix), or null on error
Notes:
(1) This binarizes if necessary and finds the skew angle. If the
angle is large enough and there is sufficient confidence,
it returns a deskewed image; otherwise, it returns a clone.
```

## pixDeskewGeneral

PIX * pixDeskewGeneral ( PIX *pixs, l_int32 redsweep, l_float32 sweeprange, l_float32 sweepdelta, l_int32 redsearch, l_int32 thresh, l_float32 *pangle, l_float32 *pconf )

```
pixDeskewGeneral()
Input: pixs (any depth)
redsweep (for linear search: reduction factor = 1, 2 or 4;
use 0 for default)
sweeprange (in degrees in each direction from 0;
use 0.0 for default)
sweepdelta (in degrees; use 0.0 for default)
redsearch (for binary search: reduction factor = 1, 2 or 4;
use 0 for default;)
thresh (for binarizing the image; use 0 for default)
&angle (<optional return> angle required to deskew,
in degrees; use NULL to skip)
&conf (<optional return> conf value is ratio
of max/min scores; use NULL to skip)
Return: pixd (deskewed pix), or null on error
Notes:
(1) This binarizes if necessary and finds the skew angle. If the
angle is large enough and there is sufficient confidence,
it returns a deskewed image; otherwise, it returns a clone.
```

## pixFindDifferentialSquareSum

l_int32 pixFindDifferentialSquareSum ( PIX *pixs, l_float32 *psum )

```
pixFindDifferentialSquareSum()
Input: pixs
&sum (<return> result)
Return: 0 if OK, 1 on error
Notes:
(1) At the top and bottom, we skip:
- at least one scanline
- not more than 10% of the image height
- not more than 5% of the image width
```

## pixFindNormalizedSquareSum

l_int32 pixFindNormalizedSquareSum ( PIX *pixs, l_float32 *phratio, l_float32 *pvratio, l_float32 *pfract )

```
pixFindNormalizedSquareSum()
Input: pixs
&hratio (<optional return> ratio of normalized horiz square sum
to result if the pixel distribution were uniform)
&vratio (<optional return> ratio of normalized vert square sum
to result if the pixel distribution were uniform)
&fract (<optional return> ratio of fg pixels to total pixels)
Return: 0 if OK, 1 on error or if there are no fg pixels
Notes:
(1) Let the image have h scanlines and N fg pixels.
If the pixels were uniformly distributed on scanlines,
the sum of squares of fg pixels on each scanline would be
h * (N / h)^2. However, if the pixels are not uniformly
distributed (e.g., for text), the sum of squares of fg
pixels will be larger. We return in hratio and vratio the
ratio of these two values.
(2) If there are no fg pixels, hratio and vratio are returned as 0.0.
```

## pixFindSkew

l_int32 pixFindSkew ( PIX *pixs, l_float32 *pangle, l_float32 *pconf )

```
pixFindSkew()
Input: pixs (1 bpp)
&angle (<return> angle required to deskew, in degrees)
&conf (<return> confidence value is ratio max/min scores)
Return: 0 if OK, 1 on error or if angle measurment not valid
Notes:
(1) This is a simple high-level interface, that uses default
values of the parameters for reasonable speed and accuracy.
(2) The angle returned is the negative of the skew angle of
the image. It is the angle required for deskew.
Clockwise rotations are positive angles.
```

## pixFindSkewAndDeskew

PIX * pixFindSkewAndDeskew ( PIX *pixs, l_int32 redsearch, l_float32 *pangle, l_float32 *pconf )

```
pixFindSkewAndDeskew()
Input: pixs (any depth)
redsearch (for binary search: reduction factor = 1, 2 or 4;
use 0 for default)
&angle (<optional return> angle required to deskew,
in degrees; use NULL to skip)
&conf (<optional return> conf value is ratio
of max/min scores; use NULL to skip)
Return: pixd (deskewed pix), or null on error
Notes:
(1) This binarizes if necessary and finds the skew angle. If the
angle is large enough and there is sufficient confidence,
it returns a deskewed image; otherwise, it returns a clone.
```

## pixFindSkewOrthogonalRange

l_int32 pixFindSkewOrthogonalRange ( PIX *pixs, l_float32 *pangle, l_float32 *pconf, l_int32 redsweep, l_int32 redsearch, l_float32 sweeprange, l_float32 sweepdelta, l_float32 minbsdelta, l_float32 confprior )

```
pixFindSkewOrthogonalRange()
Input: pixs (1 bpp)
&angle (<return> angle required to deskew; in degrees cw)
&conf (<return> confidence given by ratio of max/min score)
redsweep (sweep reduction factor = 1, 2, 4 or 8)
redsearch (binary search reduction factor = 1, 2, 4 or 8;
and must not exceed redsweep)
sweeprange (half the full range in each orthogonal
direction, taken about 0, in degrees)
sweepdelta (angle increment of sweep; in degrees)
minbsdelta (min binary search increment angle; in degrees)
confprior (amount by which confidence of 90 degree rotated
result is reduced when comparing with unrotated
confidence value)
Return: 0 if OK, 1 on error or if angle measurment not valid
Notes:
(1) This searches for the skew angle, first in the range
[-sweeprange, sweeprange], and then in
[90 - sweeprange, 90 + sweeprange], with angles measured
clockwise. For exploring the full range of possibilities,
suggest using sweeprange = 47.0 degrees, giving some overlap
at 45 and 135 degrees. From these results, and discounting
the the second confidence by @confprior, it selects the
angle for maximal differential variance. If the angle
is larger than pi/4, the angle found after 90 degree rotation
is selected.
(2) The larger the confidence value, the greater the probability
that the proper alignment is given by the angle that maximizes
variance. It should be compared to a threshold, which depends
on the application. Values between 3.0 and 6.0 are common.
(3) Allowing for both portrait and landscape searches is more
difficult, because if the signal from the text lines is weak,
a signal from vertical rules can be larger!
The most difficult documents to deskew have some or all of:
(a) Multiple columns, not aligned
(b) Black lines along the vertical edges
(c) Text from two pages, and at different angles
Rule of thumb for resolution:
(a) If the margins are clean, you can work at 75 ppi,
although 100 ppi is safer.
(b) If there are vertical lines in the margins, do not
work below 150 ppi. The signal from the text lines must
exceed that from the margin lines.
(4) Choosing the @confprior parameter depends on knowing something
about the source of image. However, we're not using
real probabilities here, so its use is qualitative.
If landscape and portrait are equally likely, use
@confprior = 0.0. If the likelihood of portrait (non-rotated)
is 100 times higher than that of landscape, we want to reduce
the chance that we rotate to landscape in a situation where
the landscape signal is accidentally larger than the
portrait signal. To do this use a positive value of
@confprior; say 1.5.
```

## pixFindSkewSweep

l_int32 pixFindSkewSweep ( PIX *pixs, l_float32 *pangle, l_int32 reduction, l_float32 sweeprange, l_float32 sweepdelta )

```
pixFindSkewSweep()
Input: pixs (1 bpp)
&angle (<return> angle required to deskew, in degrees)
reduction (factor = 1, 2, 4 or 8)
sweeprange (half the full range; assumed about 0; in degrees)
sweepdelta (angle increment of sweep; in degrees)
Return: 0 if OK, 1 on error or if angle measurment not valid
Notes:
(1) This examines the 'score' for skew angles with equal intervals.
(2) Caller must check the return value for validity of the result.
```

## pixFindSkewSweepAndSearch

l_int32 pixFindSkewSweepAndSearch ( PIX *pixs, l_float32 *pangle, l_float32 *pconf, l_int32 redsweep, l_int32 redsearch, l_float32 sweeprange, l_float32 sweepdelta, l_float32 minbsdelta )

```
pixFindSkewSweepAndSearch()
Input: pixs (1 bpp)
&angle (<return> angle required to deskew; in degrees)
&conf (<return> confidence given by ratio of max/min score)
redsweep (sweep reduction factor = 1, 2, 4 or 8)
redsearch (binary search reduction factor = 1, 2, 4 or 8;
and must not exceed redsweep)
sweeprange (half the full range, assumed about 0; in degrees)
sweepdelta (angle increment of sweep; in degrees)
minbsdelta (min binary search increment angle; in degrees)
Return: 0 if OK, 1 on error or if angle measurment not valid
Notes:
(1) This finds the skew angle, doing first a sweep through a set
of equal angles, and then doing a binary search until
convergence.
(2) Caller must check the return value for validity of the result.
(3) In computing the differential line sum variance score, we sum
the result over scanlines, but we always skip:
- at least one scanline
- not more than 10% of the image height
- not more than 5% of the image width
(4) See also notes in pixFindSkewSweepAndSearchScore()
```

## pixFindSkewSweepAndSearchScore

l_int32 pixFindSkewSweepAndSearchScore ( PIX *pixs, l_float32 *pangle, l_float32 *pconf, l_float32 *pendscore, l_int32 redsweep, l_int32 redsearch, l_float32 sweepcenter, l_float32 sweeprange, l_float32 sweepdelta, l_float32 minbsdelta )

```
pixFindSkewSweepAndSearchScore()
Input: pixs (1 bpp)
&angle (<return> angle required to deskew; in degrees)
&conf (<return> confidence given by ratio of max/min score)
&endscore (<optional return> max score; use NULL to ignore)
redsweep (sweep reduction factor = 1, 2, 4 or 8)
redsearch (binary search reduction factor = 1, 2, 4 or 8;
and must not exceed redsweep)
sweepcenter (angle about which sweep is performed; in degrees)
sweeprange (half the full range, taken about sweepcenter;
in degrees)
sweepdelta (angle increment of sweep; in degrees)
minbsdelta (min binary search increment angle; in degrees)
Return: 0 if OK, 1 on error or if angle measurment not valid
Notes:
(1) This finds the skew angle, doing first a sweep through a set
of equal angles, and then doing a binary search until convergence.
(2) There are two built-in constants that determine if the
returned confidence is nonzero:
- MIN_VALID_MAXSCORE (minimum allowed maxscore)
- MINSCORE_THRESHOLD_CONSTANT (determines minimum allowed
minscore, by multiplying by (height * width^2)
If either of these conditions is not satisfied, the returned
confidence value will be zero. The maxscore is optionally
returned in this function to allow evaluation of the
resulting angle by a method that is independent of the
returned confidence value.
(3) The larger the confidence value, the greater the probability
that the proper alignment is given by the angle that maximizes
variance. It should be compared to a threshold, which depends
on the application. Values between 3.0 and 6.0 are common.
(4) By default, the shear is about the UL corner.
```

## pixFindSkewSweepAndSearchScorePivot

l_int32 pixFindSkewSweepAndSearchScorePivot ( PIX *pixs, l_float32 *pangle, l_float32 *pconf, l_float32 *pendscore, l_int32 redsweep, l_int32 redsearch, l_float32 sweepcenter, l_float32 sweeprange, l_float32 sweepdelta, l_float32 minbsdelta, l_int32 pivot )

```
pixFindSkewSweepAndSearchScorePivot()
Input: pixs (1 bpp)
&angle (<return> angle required to deskew; in degrees)
&conf (<return> confidence given by ratio of max/min score)
&endscore (<optional return> max score; use NULL to ignore)
redsweep (sweep reduction factor = 1, 2, 4 or 8)
redsearch (binary search reduction factor = 1, 2, 4 or 8;
and must not exceed redsweep)
sweepcenter (angle about which sweep is performed; in degrees)
sweeprange (half the full range, taken about sweepcenter;
in degrees)
sweepdelta (angle increment of sweep; in degrees)
minbsdelta (min binary search increment angle; in degrees)
pivot (L_SHEAR_ABOUT_CORNER, L_SHEAR_ABOUT_CENTER)
Return: 0 if OK, 1 on error or if angle measurment not valid
Notes:
(1) See notes in pixFindSkewSweepAndSearchScore().
(2) This allows choice of shear pivoting from either the UL corner
or the center. For small angles, the ability to discriminate
angles is better with shearing from the UL corner. However,
for large angles (say, greater than 20 degrees), it is better
to shear about the center because a shear from the UL corner
loses too much of the image.
```

# AUTHOR

Zakariyya Mughal <zmughal@cpan.org>

# COPYRIGHT AND LICENSE

This software is copyright (c) 2014 by Zakariyya Mughal.

This is free software; you can redistribute it and/or modify it under the same terms as the Perl 5 programming language system itself.