Image warping is the process of digitally manipulating an image such that any shapes portrayed in the image have been significantly distorted. Warping may be used for correcting image distortion as well as for creative purposes (e.g., morphing

Morphing

Morphing is a special effect in motion pictures and animations that changes one image into another through a seamless transition. Most often it is used to depict one person turning into another through technological means or as part of a fantasy or surreal sequence. Traditionally such a depiction...

). The same techniques are equally applicable to video.

Overview

While an image can be transformed in various ways, pure warping means that points are mapped to points without changing the colors. This can be based mathematically on any function from (part of) the plane to the plane. If the function is injective

Injective function

In mathematics, an injective function is a function that preserves distinctness: it never maps distinct elements of its domain to the same element of its codomain. In other words, every element of the function's codomain is mapped to by at most one element of its domain...

 the original can be reconstructed. If the function is a bijection

Bijection

A bijection is a function giving an exact pairing of the elements of two sets. A bijection from the set X to the set Y has an inverse function from Y to X. If X and Y are finite sets, then the existence of a bijection means they have the same number of elements...

 any image can be inversely transformed.

The following list is not meant to be a partitioning of all available methods into categories.

• Images may be distorted through simulation of optical aberrations.
• Images may be viewed as if they had been projected onto a curved or mirrored surface. (This is often seen in raytraced images.)
• Images can be partitioned into polygons and each polygon distorted.
• Images can be distorted using morphing.

There are at least two ways to generate an image using whatever chosen methods to distort.

• (forward-mapping) a given mapping from sources to images is directly applied
• (reverse-mapping) for a given mapping from sources to images, the source is found from the image

To estimate what kind of warping has taken place between consecutive images, one can use optical flow

Optical flow

Optical flow or optic flow is the pattern of apparent motion of objects, surfaces, and edges in a visual scene caused by the relative motion between an observer and the scene. The concept of optical flow was first studied in the 1940s and ultimately published by American psychologist James J....

 estimation techniques.

In the news

In 2007, a suspected pedophile used the "swirl" effect to hide his face in the pictures he had taken while raping and sexually abusing young children whose "ages appear to range from six to early teens." Interpol

Interpol

Interpol, whose full name is the International Criminal Police Organization – INTERPOL, is an organization facilitating international police cooperation...

 trivially reversed the swirl by swirling in the opposite direction to identify and eventually locate the man in Thailand.

See also

• Anamorphosis
  Anamorphosis
  Anamorphosis or anamorphism may refer to any of the following:*Anamorphosis, in art, the representation of an object as seen, for instance, altered by reflection in a mirror...
  
  
• Softwarp
  Softwarp
  Softwarp is a software technique to warp an image so that it can be projected on a curved screen. This can be done in real time by inserting the softwarp as a last step in the rendering cycle. The problem is to know how the image should be warped to look correct on the curved screen...
  
  , is a software technique to warp an image so that it can be projected on a curved screen.

External links

• McMillan, Leonard “An Image-Based Approach to Three-Dimensional Computer Graphics”, Dissertation, 1997