Fisheye Projection - Revision history

Erik Krause: clarified panotools fisheye mapping

2013-05-07T19:46:07Z

clarified panotools fisheye mapping

Erik Krause: unified with old version

2013-01-21T23:25:21Z

unified with old version

Thomas at 18:22, 21 January 2013

2013-01-21T18:22:29Z

Jwatters: changed broken external link to one that works

2008-03-16T22:38:05Z

changed broken external link to one that works

Erik Krause: Prepared for new glossary template

2007-11-17T22:34:22Z

Prepared for new glossary template

Bruno: clean up redirecting links

2007-03-15T23:08:25Z

clean up redirecting links

Bruno: linked to stereographic page

2006-09-04T21:11:31Z

linked to stereographic page

Erik Krause: used $for formulas$

2006-07-21T09:23:35Z

used <math> for formulas

WikiSysop: 14 revision(s)

2006-07-13T20:24:36Z

14 revision(s)

WikiSysop: 1 revision(s)

2006-07-13T19:55:18Z

1 revision(s)

@@ Line 19: / Line 19: @@
 | equidistant fisheye
 | <math>R=f\cdot\theta</math>
-| e.g. Peleng 8mm f/3.5 Fisheye
+| e.g. Peleng 8mm f/3.5 Fisheye <br>This is the ideal fisheye projection panotools uses internally
 |-
 | stereographic
@@ Line 32: / Line 32: @@
 (equal-area fisheye)
 | <math> R=2f\cdot \sin\left(\frac{\theta}{2}\right)</math>
 | e. g. Sigma 8mm f/4.0 AF EX, (also convex mirror)
 |-
 | Thoby fisheye
@@ Line 50: / Line 50: @@
 More information on [[fisheyes]] and their distortions from [http://www.bobatkins.com/photography/technical/field_of_view.html Bob Atkins Photography]
-(Content partly based on a mail by Helmut Dersch which can be found at W.J. Markerink's [http://www.a1.nl/phomepag/markerink/fishyfaq.htm page about fisheye analysis])
+Panotools fisheye mapping mentioned by [[Helmut Dersch]] in http://www.panotools.org/mailarchive/msg/6864#msg6864
 [[Category:Glossary]]

@@ Line 9: / Line 9: @@
 There is no single fisheye projection, but instead there are a class of projection transformation all referred to as ''fisheye'' by various lens manufacturers, with names like ''equisolid angle projection'', or ''equidistance fisheye''.  Less common are traditional spherical projections which map to circular images, such as the [http://mathworld.wolfram.com/OrthographicProjection.html orthographic] (lenses commonly designated ''OP'') or [[Stereographic Projection|stereographic]] projections.  Luckily, [[Panorama tools]] and [[Hugin]] can deal with most of these mentioned projections.
-'''<math>\theta\,</math>''' is the angle between a point in the real world and the optical axis, which goes from the center of the image through the center of the lens, <math>f</math> is the focal length of the lens and <math>R</math> is radial position of a point on the image on the film or sensor.
+'''<math>\theta\,</math>''' is the angle in rad between a point in the real world and the optical axis, which goes from the center of the image through the center of the lens, <math>f</math> is the focal length of the lens and <math>R</math> is radial position of a point on the image on the film or sensor.
 {| class="wikitable"
@@ Line 32: / Line 32: @@
 (equal-area fisheye)
 | <math> R=2f\cdot \sin\left(\frac{\theta}{2}\right)</math>
-| e. g. Sigma 8mm f/4.0 AF EX
+| e. g. Sigma 8mm f/4.0 AF EX, (also convex mirror)
 |-
 | Thoby fisheye
@@ Line 41: / Line 41: @@
 |}
+So for example 90 degrees, which would be the maximum
-Old text:
+theta of a lens with 180 degree [[Field of View]], f=8mm, equisolid mapping, you get
-−
-The following explanation is taken from a posting by [[Helmut Dersch]] (link to original see below):
-−
-The focal length f of common fisheye lenses corresponds
-quite simple to <math>\theta</math> and the
-radial position R of a point on the image on the film or sensor:
- <math>R = 2*f*sin\left(\frac{\theta}{2}\right)</math>
-−
 So for 90 degrees, which would be the maximum
 theta of a lens with 180 degree [[Field of View]], f=8mm, you get
 R = 11.3mm, which is the radius of the image circle.
 Btw, a rectilinear lens has a mapping
   <math>R=f*tan(\theta)\,</math>
-We can assume that most newer fisheyes follow the first mapping scheme.
+More information on [[fisheyes]] and their distortions from [http://www.bobatkins.com/photography/technical/field_of_view.html Bob Atkins Photography]
-Complete text of the mail can be found at W.J. Markerink's [http://www.a1.nl/phomepag/markerink/fishyfaq.htm page about fisheye analysis]
+(Content partly based on a mail by Helmut Dersch which can be found at W.J. Markerink's [http://www.a1.nl/phomepag/markerink/fishyfaq.htm page about fisheye analysis])
-−
-More information on [[fisheyes]] and their distortions from [http://www.bobatkins.com/photography/technical/field_of_view.html Bob Atkins Photography]
 [[Category:Glossary]]

@@ Line 7: / Line 7: @@
 Commonly there are two types of fisheye distinguished: circular [[fisheyes]] and fullframe [[fisheyes]]. However, both follow the same projection geometrics. The only difference is one of [[Field of View]]: for a circular fisheye the circular image fits (more or less) completely in the frame, leaving blank areas in the corner. For the full frame variety, the image is over-filled by the circular fisheye image, leaving no blank space on the film or detector.  A circular fisheye can be made full frame if you use it with a smaller sensor/film size (and vice versa), or by zooming a fisheye adaptor on a zoom lens.
-There is no single fisheye projection, but instead there are a class of projection transformation all referred to as ''fisheye'' by various lens manufacturers, with names like ''equisolid angle projection'', or ''equidistance fisheye''.  Less common are traditional spherical projections which map to circular images, such as the [http://mathworld.wolfram.com/OrthographicProjection.html orthographic] (lenses commonly designated ''OP'') or [[Stereographic Projection|stereographic]] projections.  Luckily, most of these related projections can be dealt with in a simple way. The following explanation is taken from a posting by [[Helmut Dersch]] (link to original see below):
+There is no single fisheye projection, but instead there are a class of projection transformation all referred to as ''fisheye'' by various lens manufacturers, with names like ''equisolid angle projection'', or ''equidistance fisheye''.  Less common are traditional spherical projections which map to circular images, such as the [http://mathworld.wolfram.com/OrthographicProjection.html orthographic] (lenses commonly designated ''OP'') or [[Stereographic Projection|stereographic]] projections.  Luckily, [[Panorama tools]] and [[Hugin]] can deal with most of these mentioned projections.
-'''<math>\theta\,</math>''' is the angle between a point in the real world and the optical axis, which goes from the center of the image through the center of the lens.
+'''<math>\theta\,</math>''' is the angle between a point in the real world and the optical axis, which goes from the center of the image through the center of the lens, <math>f</math> is the focal length of the lens and <math>R</math> is radial position of a point on the image on the film or sensor.
 The focal length f of common fisheye lenses corresponds

@@ Line 30: / Line 30: @@
 and succeed more or less.
-For most practical applictions, you won't see a big
+For most practical applications, you won't see a big
 difference between the two.
@@ Line 40: / Line 40: @@
 Complete text of the mail can be found at W.J. Markerink's [http://www.a1.nl/phomepag/markerink/fishyfaq.htm page about fisheye analysis]
-More information on [[fisheyes]] and their distortions in this [http://www.coastalopt.com/pdfs/FisheyeComparison_SPIE.pdf PDF from coastal optics]
+More information on [[fisheyes]] and their distortions from [http://www.bobatkins.com/photography/technical/field_of_view.html Bob Atkins Photography]
 [[Category:Glossary]]

← Older revision		Revision as of 22:34, 17 November 2007
Line 1:		Line 1:
		+	{{Glossary\|A projection where the distance from the centre of the image to a point is proportional to the equivalent spatial angle.}}
	[[Image:big_ben_circ_fisheye.jpg\|frame\|right\|Circular Fisheye projection, with permission from Ben Kreunen]]		[[Image:big_ben_circ_fisheye.jpg\|frame\|right\|Circular Fisheye projection, with permission from Ben Kreunen]]
	[[Image:big_ben_ff_fisheye.jpg\|frame\|right\|Fullframe Fisheye projection, with permission from Ben Kreunen]]		[[Image:big_ben_ff_fisheye.jpg\|frame\|right\|Fullframe Fisheye projection, with permission from Ben Kreunen]]

@@ Line 4: / Line 4: @@
 This is a class of [[Projections|projections]] for mapping a portion of the surface of a sphere to a flat image, typically a camera's film or detector plane.  In a fisheye projection the distance from the centre of the image to a point is close to proportional to the true angle of separation.
-Commonly there are two types of fisheye distinguished: circular [[fisheyes]] and fullframe [[fisheyes]]. However, both follow the same projection geometrics. The only difference is one of [[field of view]]: for a circular fisheye the circular image fits (more or less) completely in the frame, leaving blank areas in the corner. For the full frame variety, the image is over-filled by the circular fisheye image, leaving no blank space on the film or detector.  A circular fisheye can be made full frame if you use it with a smaller sensor/film size (and vice versa), or by zooming a fisheye adaptor on a zoom lens.
+Commonly there are two types of fisheye distinguished: circular [[fisheyes]] and fullframe [[fisheyes]]. However, both follow the same projection geometrics. The only difference is one of [[Field of View]]: for a circular fisheye the circular image fits (more or less) completely in the frame, leaving blank areas in the corner. For the full frame variety, the image is over-filled by the circular fisheye image, leaving no blank space on the film or detector.  A circular fisheye can be made full frame if you use it with a smaller sensor/film size (and vice versa), or by zooming a fisheye adaptor on a zoom lens.
 There is no single fisheye projection, but instead there are a class of projection transformation all referred to as ''fisheye'' by various lens manufacturers, with names like ''equisolid angle projection'', or ''equidistance fisheye''.  Less common are traditional spherical projections which map to circular images, such as the [http://mathworld.wolfram.com/OrthographicProjection.html orthographic] (lenses commonly designated ''OP'') or [[Stereographic Projection|stereographic]] projections.  Luckily, most of these related projections can be dealt with in a simple way. The following explanation is taken from a posting by [[Helmut Dersch]] (link to original see below):

@@ Line 1: / Line 1: @@
 [[Image:big_ben_circ_fisheye.jpg|frame|right|Circular Fisheye projection, with permission from Ben Kreunen]]
 [[Image:big_ben_ff_fisheye.jpg|frame|right|Fullframe Fisheye projection, with permission from Ben Kreunen]]
 This is a class of [[Projections|projections]] for mapping a portion of the surface of a sphere to a flat image, typically a camera's film or detector plane.  In a fisheye projection the distance from the centre of the image to a point is close to proportional to the true angle of separation.
@@ Line 8: / Line 6: @@
 Commonly there are two types of fisheye distinguished: circular [[fisheyes]] and fullframe [[fisheyes]]. However, both follow the same projection geometrics. The only difference is one of [[field of view]]: for a circular fisheye the circular image fits (more or less) completely in the frame, leaving blank areas in the corner. For the full frame variety, the image is over-filled by the circular fisheye image, leaving no blank space on the film or detector.  A circular fisheye can be made full frame if you use it with a smaller sensor/film size (and vice versa), or by zooming a fisheye adaptor on a zoom lens.
-There is no single fisheye projection, but instead there are a class of projection transformation all referred to as ''fisheye'' by various lens manufacturers, with names like ''equisolid angle projection'', or ''equidistance fisheye''.  Less common are traditional spherical projections which map to circular images, such as the [http://mathworld.wolfram.com/OrthographicProjection.html orthographic] (lenses commonly designated ''OP'') or [http://mathworld.wolfram.com/StereographicProjection.html stereographic] projections.  Luckily, most of these related projections can be dealt with in a simple way. The following explanation is taken from a posting by [[Helmut Dersch]] (link to original see below):
+There is no single fisheye projection, but instead there are a class of projection transformation all referred to as ''fisheye'' by various lens manufacturers, with names like ''equisolid angle projection'', or ''equidistance fisheye''.  Less common are traditional spherical projections which map to circular images, such as the [http://mathworld.wolfram.com/OrthographicProjection.html orthographic] (lenses commonly designated ''OP'') or [[Stereographic Projection|stereographic]] projections.  Luckily, most of these related projections can be dealt with in a simple way. The following explanation is taken from a posting by [[Helmut Dersch]] (link to original see below):
 '''<math>\theta\,</math>''' is the angle between a point in the real world and the optical axis, which goes from the center of the image through the center of the lens.

@@ Line 1: / Line 1: @@
-[[Image:big_ben_circ_fisheye.jpg|right|Circular Fisheye projection, with permission from Ben Kreunen]]
+[[Image:big_ben_circ_fisheye.jpg|frame|right|Circular Fisheye projection, with permission from Ben Kreunen]]
-[[Image:big_ben_ff_fisheye.jpg|right|Fullframe Fisheye projection, with permission from Ben Kreunen]]
+[[Image:big_ben_ff_fisheye.jpg|frame|right|Fullframe Fisheye projection, with permission from Ben Kreunen]]
-[[Image:vertical-fisheye.jpg|right|A vertical simple fisheye projection, showing non-conformal distortion around the edges]]
+[[Image:vertical-fisheye.jpg|frame|right|A vertical simple fisheye projection, showing non-conformal distortion around the edges]]
-[[Image:vertical-stereographic.jpg|right|A vertical stereographic fisheye projection, showing conformal mapping]]
+[[Image:vertical-stereographic.jpg|frame|right|A vertical stereographic fisheye projection, showing conformal mapping]]
 This is a class of [[Projections|projections]] for mapping a portion of the surface of a sphere to a flat image, typically a camera's film or detector plane.  In a fisheye projection the distance from the centre of the image to a point is close to proportional to the true angle of separation.
@@ Line 10: / Line 10: @@
 There is no single fisheye projection, but instead there are a class of projection transformation all referred to as ''fisheye'' by various lens manufacturers, with names like ''equisolid angle projection'', or ''equidistance fisheye''.  Less common are traditional spherical projections which map to circular images, such as the [http://mathworld.wolfram.com/OrthographicProjection.html orthographic] (lenses commonly designated ''OP'') or [http://mathworld.wolfram.com/StereographicProjection.html stereographic] projections.  Luckily, most of these related projections can be dealt with in a simple way. The following explanation is taken from a posting by [[Helmut Dersch]] (link to original see below):
-'''theta''' is the angle between a point in the real world and the optical axis, which goes from the center of the image through the center of the lens.
+'''<math>\theta\,</math>''' is the angle between a point in the real world and the optical axis, which goes from the center of the image through the center of the lens.
 The focal length f of common fisheye lenses corresponds
-quite simple to theta and the
+quite simple to <math>\theta</math> and the
 radial position R of a point on the image on the film or sensor:
-<pre> R = 2 * f * sin( theta/2 )</pre>
+ <math>R = 2*f*sin\left(\frac{\theta}{2}\right)</math>
 So for 90 degrees, which would be the maximum
@@ Line 28: / Line 28: @@
 Some older Nikon lenses (e.g. the 7.5mm) try to
 approach a linear mapping (theta in rad)
-<pre>R = f * theta</pre>
+ <math>R = f*\theta\,</math>
 and succeed more or less.
@@ Line 35: / Line 35: @@
 Btw, a rectilinear lens has a mapping
-<pre>R = f * tan( theta )</pre>
+ <math>R=f*tan(\theta)\,</math>
 We can assume that most newer fisheyes follow the first mapping scheme.

← Older revision	Revision as of 20:24, 13 July 2006
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