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 In geometric optics, distortion is a deviation from rectilinear projection; a projection in which straight lines in a scene remain straight in an image. It is a form of optical aberration. Radial distortion Although distortion can be irreg ...

as well as for creative purposes (e.g.,

morphing Morphing is a special effect in motion pictures and animations that changes (or morphs) one image or shape into another through a seamless transition. Traditionally such a depiction would be achieved through dissolving techniques on film. Sinc ...

Beier, Thaddeus
Feature-Based Image Metamorphosis
Siggraph '92). 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 In mathematics, an injective function (also known as injection, or one-to-one function) is a function that maps distinct elements of its domain to distinct elements; that is, implies . (Equivalently, implies in the equivalent contrapositi ...

the original can be reconstructed. If the function is a

bijection In mathematics, a bijection, also known as a bijective function, one-to-one correspondence, or invertible function, is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other s ...

any image can be inversely transformed. Some methods are: *Images may be distorted through simulation of

optical aberration In optics, aberration is a property of optical systems, such as lenses, that causes light to be spread out over some region of space rather than focused to a point. Aberrations cause the image formed by a lens to be blurred or distorted, with ...

s. *Images may be viewed as if they had been projected onto a curved or mirrored surface. (This is often seen in ray traced images.) *Images can be partitioned into polygons and each polygon distorted. *Images can be distorted using morphing. The most obvious approach to transforming a digital image is the forward mapping. This applies the transform directly to the source image, typically generating unevenly-spaced points that will then be interpolated to generate the required regularly-spaced pixels. However, for injective transforms reverse mapping is also available. This applies the inverse transform to the target pixels to find the unevenly-spaced locations in the source image that contribute to them. Estimating them from source image pixels will require interpolation of the source image. To work out what kind of warping has taken place between consecutive images, one can use

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 a scene. Optical flow can also be defined as the distribution of apparent veloci ...

estimation techniques.

References

* {{citation , author=Wolberg, G., title=Digital Image Warping, publisher=IEEE Computer Society Press , year=1990 , isbn=0-8186-8944-7.

External links

* McMillan, Leonar
“An Image-Based Approach to Three-Dimensional Computer Graphics”
''Dissertation'', 1997 Image processing

Overview

See also

References

External links