In photography and cinematography, perspective distortion is a warping or
transformation of an object and its surrounding area that differs
significantly from what the object would look like with a normal focal length,
due to the relative scale of nearby and distant features. Perspective distortion
is determined by the relative distances at which the image is captured and
viewed, and is due to the angle of view of the image being either wider or
narrower than the angle of view at which the image is viewed, hence the apparent
relative distances differing from what is expected. Related to this concept is
axial magnification -- the perceived depth of objects at a given
magnification. Perspective distortion takes two forms:
extension distortion and compression distortion, also called wide-angle
distortion and long-lens or telephoto distortion, when talking about images
with the same field size. Extension or wide-angle distortion can be seen in
images shot from close using a wide-angle lens. Object close to the
lens appears abnormally large relative to more distant objects, and distant
objects appear abnormally small and hence more distant – distances are
extended. Compression, long-lens, or telephoto distortion can be seen in
images shot from a distant using a long focus lens or the more common telephoto
sub-type. Distant objects look approximately the same size – closer
objects are abnormally small, and more distant objects are abnormally large,
and hence the viewer cannot discern relative distances between distant
objects – distances are compressed. Note that linear perspective changes are
caused by distance, not by the lens per se – two shots of the same scene from
the same distance will exhibit identical perspective geometry, regardless of lens
used. However, since wide-angle lenses have a wider field of view, they are
generally used from closer, while telephoto lenses have a narrower field
of view and are generally used from farther away. For example, if standing
at a distance so that a normal lens captures someone's face, a shot with a
wide-angle lens or telephoto lens from the same distance will have exactly the
same linear perspective geometry on the face, though the wide-angle lens may fit
the entire body into the shot, while the telephoto lens captures only the nose.
However, crops of these three images with the same coverage will yield the
same perspective distortion – the nose will look the same in all three.
Conversely, if all three lenses are used from distances such that the face fills
the field, the wide-angle will be used from closer, making the nose larger
compared to the rest of the photo, and the telephoto will be used from farther,
making the nose smaller compared to the rest of the photo.
Outside of photography, extension distortion is familiar to many through
side-view mirrors and peepholes, though these often use a fisheye lens,
exhibiting different distortion. Compression distortion is most familiar
in looking through binoculars or telescopes, as in telescopic sights,
while a similar effect is seen in fixed-slit strip photography, notably a
photo finish, where all capture is parallel to the capture, completely
eliminating perspective. Optics
Consider an idealised Gaussian optical system. For most purposes, we can assume
the image space and the object space are in the same medium. Thus, for an object
in focus, the distance between the lens and image plane , the distance between
lens and the object , and the focal length are related by:
The transverse magnification is related by
The axial magnification of an object at is the rate of change of the lens-image
distance as the lens-object distance changes. For an object of finite depth,
one can conceive of the average axial magnification as the ratio of the depth
of the image and the depth of the object:
One can see that if magnification remains constant, a longer focal length
results in a smaller axial magnification, and a smaller focal
length a larger axial magnification. That is, when using a longer focal
length while moving the camera/lens away from the object to maintain the same
magnification M, objects seem shallower, and the axial distances between objects
seem shorter. The opposite-- increased axial magnification -- happens with
shorter focal lengths while moving the camera/lens towards the object.
Influencing factors Perspective distortion is influenced by
the relationship between two factors: the angle of view at which the image is
captured by the camera and the angle of view at which the photograph of the
subject is presented or viewed. = Angle of view of the capture=
When photographs are viewed at the ordinary viewing distance, the angle of
view at which the image is captured accounts completely for the appearance
of perspective distortion. The general assumption that "undoctored" photos
cannot distort a scene is incorrect. Perspective distortion is particularly
noticeable in portraits taken with wide-angle lenses at short
camera-to-subject distances. They generally give an unpleasant impression,
making the nose appear too large with respect to the rest of the face, and
distorting the facial expression. Framing the same subject identically
while using a moderate telephoto or long focus lens flattens the image to a more
flattering perspective. It is for this reason that, for a 35 mm camera, lenses
with focal lengths from about 85 through 135 mm are generally considered to be
good portrait lenses. It does however make difference, whether the photograph
is taken landscape or portrait. A 50 mm lens is suitable for photographing
people when the orientation is landscape. Conversely, using lenses with
much longer focal lengths for portraits results in more extreme flattening of
facial features, which also may be objectionable to the viewer.
= Photograph viewing distance= Photographs are ordinarily viewed at a
distance approximately equal to their diagonal. When viewed at this distance,
the distortion effects created by the angle of view of the capture are
apparent. However, theoretically, if one views pictures exhibiting extension
distortion at a closer distance, thus widening the angle of view of the
presentation, then the phenomenon abates. Similarly, viewing pictures
exhibiting compression distortion from a greater distance, thus narrowing the
angle of view of the presentation, reduces the effect. In both cases, at
some critical distance, the apparent distortion disappears completely.
= Examples= Below, a series of three photos shows
the same scene shot from the same position with three different lenses: a
normal lens, a wide-angle lens, and a telephoto lens. Notice that because the
proportions in the image do not change with the angle of view, if the photos
made with the wide-angle lens and the normal lens were cropped to contain the
same scene as the photo made with the telephoto lens, then the image content
would be exactly the same. The apparent difference in proportions results solely
from the content added around the edges of the frame in the normal lens photo
and the wide-angle photo. Below, a series of four photos shows an
object framed as nearly the same as possible with four different lenses. As
a result of the different angle of view of each lens, the photographer moved
closer to the object with each photo. Note that the angle of view changes
significantly, and the distance between objects appears greater with each
succeeding image. In the fourth image at the lower right, taken with the widest
lens, the building behind the object appears much further away than in
reality. Photos taken using a 35 mm camera with a
100 mm, a 70 mm, a 50 mm, and a 28 mm lens, at different distances from the
subject. Artistic uses
= Technical background= Although perspective distortion is often
annoying when unintended, it is also intentionally used for artistic
purposes. Extension distortion is often implemented to emphasize some element of
the scene by making it appear larger and spatially removed from the other
elements. Compression distortion is often used to give the appearance of
compressed distance between distant objects, such as buildings or
automobiles in order to convey a feeling of congestion. Longer lenses magnify the
subject more, apparently compressing distance and blurring the background
because of their shallower depth of field. Wider lenses tend to magnify
distance between objects while allowing greater depth of field.
Another result of using a wide-angle lens is a greater apparent perspective
distortion when the camera is not aligned perpendicularly to the subject:
parallel lines converge at the same rate as with a normal lens, but converge more
due to the wider total field. For example, buildings appear to be falling
backwards much more severely when the camera is pointed upward from ground
level than they would if photographed with a normal lens at the same distance
from the subject, because more of the subject building is visible in the
wide-angle shot. Because different lenses generally
require a different camera–subject distance to preserve the size of a
subject, changing the angle of view can indirectly distort perspective, changing
the apparent relative size of the subject and background. If identical
field size is maintained, wide-angle lenses make subjects appear larger by
introducing size differences along with the converging lines mentioned above,
and they make rooms and spaces around the subject appear more vast by
increasing the distance between subject and background.
= Mood effect and famous uses= The mood effect of perspective
distortion achieved by rectilinear extreme wide-angle lenses is that the
resulting image looks grotesque and unsettling, while not looking as
unrealistic as curvilinear fisheye lenses which display barrel distortion.
The effect is especially noticeable the closer the camera is to the subject, as
its amount increases the shorter the focal length is at the same field size.
One notable director that frequently employs rectilinear ultra wide angle
lenses in order to achieve a distinctive signature style defined by extreme
perspective distortion is Terry Gilliam, for instance. Also Stanley Kubrick as
well as Orson Welles, Sam Peckinpah, and Sidney Lumet have occasionally done the
same in the past, though mostly in moderation, for single shots or
sequences only, while Gilliam hardly ever uses any lens longer than 14mm,
which has garnered lenses of that particular focal length the informal
nickname "The Gilliam" among film-makers. Jean-Pierre Jeunet and Marc
Caro, two French filmmakers influenced by Gilliam, adopted his typical
wide-angle photography in their two most "Gilliamesque" features, Delicatessen
and The City of Lost Children. Orson Welles's The Trial is notable for
heavily influencing Gilliam's signature style years before the American
ex-patriate joined the Monty Python comedy troupe while only being a
one-feature style for Welles. Due to the grotesque, unsettling mood
effect peculiar to wide-angle lenses, films making use of such perspective
distortion can often be placed in one of two categories: Grotesque and surreal
satire and fantasy, also to some extent black comedy on the one hand, and
serious, more realistic films with a particular edge for social criticism on
the other, whereas social conventions, collective society, and/or the motives
and acts of leaders are portrayed as grotesque and absurd, and often also
feature tyrannical characters with conformist values who act out in an
extremely hostile and prejudiced way towards individualism and outsiders.
On the other end of the focal length spectre, Leni Riefenstahl used extreme
telephoto lenses to compress large crowds in Triumph of the Will while the
Führer Adolf Hitler is seen through normal lenses and often from a low angle
to appear tall in comparison. In cinematography, perspective
distortion also has bearing on the in-camera special effect known as the
dolly zoom, in which a zoom lens zooms out at the same time as the camera moves
toward the subject, in such a way as to keep the subject the same size in the
frame while the background "changes size" relative to the subject. This
effect was made popular in the films Vertigo and Jaws. Another example of
this can be seen in the first Lord of the Rings film, just before the Black
Rider comes down the road. The dolly zoom is used to create a compression
effect in the road. = Examples=
The photo below of the gondolas is an illustration of the use of extension
distortion, and the photo of the buildings below it is an example of
compression distortion. See also
Foreshortening Perspective Control Lens
Texture gradient Curvilinear perspective
Notes ^ Mark Galer, Photography Foundations
for Art and Design, page 73 ^ A distance approximately equal to the
diagonal of the picture. This appears to produce the perception of normal
perspective when a normal lens was used to take the picture. See, Ira Current,
Best Viewing Distance for Photographers, PSA Journal, Sept., 1990 at
articles.comarticlesis_n9_v56/ai_8851922 Retrieved January 22, 2008. A "normal
lens" is one having a focal length that approximates the diagonal of the image
frame of the camera. ^ Stubbs, Phil: "Terry Gilliam talks
Tideland," Dreams External links
Compressing distance and altering perspective