Unit Square

In a Cartesian coordinate system with coordinates (x , y) is defined as the square consisting of the points where both x and y lie in the unit interval from 0 to 1.

Whether the interval used is open or closed, and at which ends, is at the discretion of the user of the term, who should make it clear which precise definition they are using; however, the term unit interval is most usually used to refer to the closed interval [0,1]

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 the original can be reconstructed. If the function is a bijection 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 can be seen in renderings from the program POV-Ray.)
• 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 estimation techniques.

Scan from a Kodak 400 Color.