Fred's ImageMagick Scripts



    Licensing:

    Copyright © Fred Weinhaus

    My scripts are available free of charge for non-commercial use, ONLY.

    For use of my scripts in commercial (for-profit) environments or non-free applications, please contact me (Fred Weinhaus) for licensing arrangements. My email address is fmw at alink dot net.

    If you: 1) redistribute, 2) incorporate any of these scripts into other free applications or 3) reprogram them in another scripting language, then you must contact me for permission, especially if the result might be used in a commercial or for-profit environment.

    Usage, whether stated or not in the script, is restricted to the above licensing arrangements. It is also subject, in a subordinate manner, to the ImageMagick license, which can be found at: http://www.imagemagick.org/script/license.php

POLAR


Applies either a rectangular (cartesian) to polar transformation or a polar to rectangular (cartesian) transformation on an image.

Download Script

last modified: April 25, 2015



USAGE: polar [-m mode] [-c xc,yc] [-r rmn,rmx] [-a amn,amx] [-v vpmode] [-b bgcolor] infile outfile
USAGE: polar [-h or -help]

-m .... mode ......... rect2polar or polar2rect; default=rect2polar
-c .... xc,yc ........ coordinates of the transformation center;
...................... default is image center
-r .... rmn,rmx ...... min and max radius; default=0,(half image diagonal);
...................... non-negative floats; rmx can be w, h, d or m for
...................... width/2, height/2, diagonal/2 or min(width,height)/2 of image
-a .... amn,amx ...... min and max angle; default=-180,180;
...................... floats between -180 and 180
-v .... vpmode ....... virtual-pixel mode to use to fill area of output image
...................... that are outside the input image; default=edge
-b .... bgcolor ...... background color for virtual-pixel=background
...................... any valid IM color is allowed. The default=black

PURPOSE: To apply either a rectangular (Cartesian) to polar transformation or a polar to rectangular (Cartesian) transformation on an image.

DESCRIPTION: POLAR applies either a rectangular (Cartesian) to polar transformation or a polar to rectangular (Cartesian) transformation on an image. The user has control of the range of radius, angle and center in the transformation.

ARGUMENTS:

-m mode ... MODE is the transformation mode, which can be either rect2polar (rectangular to polar) or polar2rect (polar to rectangular). The former, rect2polar, treats the input as a normal rectangular image with columns representing X and rows representing Y and treats the output as having columns representing angle and rows representing radius. The latter, polar2rect, treats the input as having columns representing angle and rows representing radius and treats the output as having columns representing X and rows representing Y. Note that in a polar image, nominally the left column is angle=amn=-180, the middle column is angle=0 and the right column is angle=amx=180. Similarly, the top row is radius=rmn=0 and the bottom row is radius=rmx=(half image diagonal).

-c xc,yc ... XC,YC are the pixel coordinates for the transformation center. The default is the image center.

-r rmn,rmx ... RMN,RMX are the min and max radii. By default, rmn=0 and rmx=(half image diagonal). This provides a transformation that includes the whole image. However, for the rect2polar mode, this will cause the output image to contain areas that are outside the input image. They will be filled as determined by the virtual pixel setting. Value are non-negative floats. Values are generally non-negative floats, but four other choices are allowed: w, h, d and m, where w=width/2, h=height/2, d=diagonal/2 and m=min(width,height)/2.

-a amn,amx ... AMN,AMX are the min and max angles. By default, amn=-180 and amx=180. Values for amn and amx are floats between -180 and 180.

-v vpmode ... VPMODE is the virtual-pixel mode. Any valid IM virtual-pixel setting is allowed. The default is edge.

-b bgcolor ... BGCOLOR is the background color to use with vpmode=background. Any valid IM color may be used. The default is black.

Note that this script may be slow due to the use of -fx.

CAVEAT: No guarantee that this script will work on all platforms, nor that trapping of inconsistent parameters is complete and foolproof. Use At Your Own Risk.


EXAMPLES


Rectangular To Polar Transformation -- Full 360 Degree Range, Max Radius = Diagonal/2, Vary Y Center Coordinate

Original Image
(red dot inserted at center)

Rect2Polar
Arguments:
-m rect2polar -c 49.5,49.5
-r 0,h -a -180,180 -v black

Rect2Polar
Arguments:
-m rect2polar -c 49.5,30
-r 0,h -a -180,180 -v black

Rect2Polar
Arguments:
-m rect2polar -c 49.5,10
-r 0,h -a -180,180 -v black

Rect2Polar
Arguments:
-m rect2polar -c 49.5,0
-r 0,h -a -180,180 -v black



Rectangular To Polar Transformation -- 180 Degree Range, Max Radius = Diagonal/2, Vary Center Y Coordinate

Original Image
(red dot inserted at center)

Rect2Polar
Arguments:
-m rect2polar -c 49.5,49.5
-r 0,h -a -90,90 -v black

Rect2Polar
Arguments:
-m rect2polar -c 49.5,30
-r 0,h -a -90,90 -v black

Rect2Polar
Arguments:
-m rect2polar -c 49.5,10
-r 0,h -a -90,90 -v black

Rect2Polar
Arguments:
-m rect2polar -c 49.5,0
-r 0,h -a -90,90 -v black



Rectangular To Polar Transformation Followed By Polar To Rectangular

Original Image
(red dot inserted at center)

Rect2Polar
(rmax=diagonal/2)
(-180<=angle<=180)
Arguments:
-m rect2polar -r 0,h -v white

Polar2Rect
On Rect2Polar Image
Arguments:
-m polar2rect -r 0,h -v white

Original Image
(red dot inserted at center)

Rect2Polar
(rmax=min(width,height)/2)
(-180<=angle<=180)
Arguments:
-m rect2polar -r 0,m -v black

Polar2Rect
On Rect2Polar Image
Arguments:
-m polar2rect -r 0,m -v black

Original Image
(red dot inserted at center)

Rect2Polar
(rmax=diagonal/2)
(-90<=angle<=90)
(y center = 0)
Arguments:
-m rect2polar -c 49.5,0
-r 0,m -a -90,90 -v black

Polar2Rect
On Rect2Polar Image
Arguments:
-m polar2rect -c 49.5,0
-r 0,h -a -90,90 -v black



Polar To Rectangular Transformation -- Full 360 Degree Range

Original Image
(red dot inserted at center)

Polar2Rect
(rmax=diagonal/2)
Arguments:
-m polar2rect -r 0,h -v black

Polar2Rect
(rmax=min(width,height)/2)
Arguments:
-m polar2rect -r 0,m -v white

Polar2Rect
(rmax=diagonal/2)
(original image flipped)
Arguments:
convert <input> -flip <output>
-m polar2rect -r 0,h -v black



Polar To Rectangular Transformation -- Vary Angular Range, Max Radius = 100, Center Y = 0

Original Image
(red dot inserted at center)

Polar2Rect
Arguments:
-m polar2rect -c 49.5,0
-r 0,100 -a -90,90 -v black

Polar2Rect
Arguments:
-m polar2rect -c 49.5,0
-r 0,100 -a -60,60 -v black

Polar2Rect
Arguments:
-m rect2polar -c 49.5,0
-r 0,100 -a -30,30 -v black



Polar To Rectangular Transformation -- Full 360 Degree Range, Center Y = 0, Variation In Radii

Original Image
(red dot inserted at center)

Polar2Rect
(rmin=0)
(rmax=diagonal/2)
Arguments:
-m polar2rect -c 49.5,0
-r 0,h -v black

Polar2Rect
(rmin=20)
(rmax=diagonal/2)
Arguments:
-m polar2rect -c 49.5,0
-r 20,h -v black

Polar2Rect
(rmin=20)
(rmax=100)
Arguments:
-m polar2rect -c 49.5,0
-r 20,100-v black



Polar To Rectangular Followed By Rectangular To Polar Transformation

Original Image
(red dot inserted at center)

Polar2Rect
(rmax=max(width,height)/2)
(-180<=angle<=180)
Arguments:
-m rect2polar -r 0,m -v white

Rect2Polar
On Polar2Rect Image
Arguments:
-m polar2rect -r 0,m -v white



Real World Application -- Convert 360 Degree "Fisheye" View To Strip Panorama And Extract Subsection

Example Follows Procedure Outlined At www.0-360.com

Note that this picture is not from a true fisheye lens.
It is from a 360 degree panoramic lens with 115 degree vertical field of view.
But the way the image is recorded makes it look like a fisheye image.

Original Image

 

Trimmed To Size Of Circle

 

Polar Transform
Arguments
-mode rect2polar -r 0,m

 

Flip Image
convert <image> -flip <image_flipped>

 

Resize Image 100% x 39%
convert <image> -resize 100%x39%! <image_resized>

 

Crop Image As Desired
convert <image> -crop ... <image_cropped>

 

Enlarge
convert <image> -resize 400% <image_resized>



Radial Blur

  • specify blur in pixels in radial direction
  • polar -m rect2polar
  • convert blur to percentages to scale down and to resize back up to do the blurring
  • scale down in vertical direction, then resize up vertically to original size
  • polar -m polar2rect

infile="flower.jpg"
blur=20
inname=`convert $infile -format "%t" info:`
polar -m rect2polar $infile ${inname}_rect2polar.jpg
frac=`convert $infile -format "%[fx:1/$blur]" info:`
min=`convert xc: -format "%[fx:100*$frac]" info:`
max=`convert xc: -format "%[fx:100/$frac]" info:`
convert ${inname}_rect2polar.png -scale 100x${min}% -resize 100x${max}% ${inname}_rect2polar_radial${blur}.jpg
polar -m polar2rect ${inname}_rect2polar_radial${blur}.jpg $inname_radial${blur}.jpg

Original Image

Image In Polar Coordinates
Arguments:
-m rect2polar

20 Pixel Vertically Blurred Polar Image

Image Back In Cartesian (Rectangular) Coordinates
Arguments:
-m polar2rect



Angular Blur

  • specify blur in degrees in angular direction
  • polar -m rect2polar
  • convert blur to percentages to scale down and to resize back up to do the blurring
  • scale down in horizontal direction, then resize up horizontally to original size
  • polar -m polar2rect

infile="flower.jpg"
blur=10
inname=`convert $infile -format "%t" info:`
polar -m rect2polar $infile ${inname}_rect2polar.jpg
frac=`convert $infile -format "%[fx:360/($blur*w)]" info:`
min=`convert xc: -format "%[fx:100*$frac]" info:`
max=`convert xc: -format "%[fx:100/$frac]" info:`
convert ${inname}_rect2polar.png -scale ${min}x100% -resize ${max}x100% ${inname}_rect2polar_angular${blur}.jpg
polar -m polar2rect ${inname}_rect2polar_angular${blur}.jpg $inname_angular${blur}.jpg

Original Image

Image In Polar Coordinates
Arguments:
-m rect2polar

10 Pixel Horizontally Blurred Polar Image

Image Back In Cartesian (Rectangular) Coordinates
Arguments:
-m polar2rect



Image Rotation

  • polar -m rect2polar
  • roll the image -- the roll amount as a fraction of width will be the rotation amount
  • polar -m polar2rect

infile="cyclops1.jpg"
rotation=180
inname=`convert $infile -format "%t" info:`
polar -m rect2polar $infile ${inname}_rect2polar.jpg
rollamt=`convert $infile -format "%[fx:w*$rotation/360]" info:`
convert ${inname}_rect2polar.jpg -roll +${rollamt}+0 ${inname}_rect2polar_roll${rollamt}.jpg
polar -m polar2rect ${inname}_rect2polar_roll${rollamt}.jpg ${inname}_rect2polar_roll${rollamt}_polar2rect.jpg

Original Image

Image In Polar Coordinates
Arguments:
-m rect2polar

Roll Image To Rotate 180 deg
-roll +50+0

Image Back In Cartesian (Rectangular) Coordinates
Arguments:
-m polar2rect



What the script does is as follows:

  • Applies an rectangular to polar or polar to rectangular warp to an image
  • Uses -fx; therefore slow

This is equivalent to the following IM commands for the case
of a rectangular to polar warp:

  • compute image dimensions for default center and max radius values
  • convert $infile -virtual-pixel edge -monitor \
    -fx "yy=((j-$rmn)*$rmx/h)*cos((($amx-$amn)*pi/180)*(i/(w-1))+($amn*pi/180))+$yc; \
    xx=((j-$rmn)*$rmx/h)*sin((($amx-$amn)*pi/180)*(i/(w-1))+($amn*pi/180))+$xc; u.p{xx,yy}" \
    $outfile
And this is equivalent to the following IM commands for the case
of a polar to rectangular warp:
  • compute image dimensions for default center and max radius values
  • convert $infile -virtual-pixel edge -monitor \
    -fx "rr=hypot((i-$xc),(j-$yc)); aa=atan2((i-$xc),(j-$yc)); \
    xx=(aa-(pi/180)*$amn)*(w-1)/((pi/180)*($amx-$amn)); \
    yy=(rr-$rmn)*(h-1)/($rmx-$rmn); u.p{xx,yy}" \
    $outfile