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 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. Si ...

). The same techniques are equally applicable to video. 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 of its codomain; that is, implies (equivalently by contraposition, impl ...

the original can be reconstructed. If the function is a

bijection In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between two sets such that each element of the second set (the codomain) is the image of exactly one element of the first set (the domain). Equival ...

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 Lens (optics), lenses and mirrors, that causes the ''image'' created by the optical system to not be a faithful reproduction of the ''object'' being observed. Aberrations cause the i ...

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 image 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 velocit ...

estimation techniques.

Image warping toolbox

ImWIP is an open-source, image warping tool for modeling deformation and motion in digital images, which contains differentiable image warping operators, together with their exact adjoints and derivatives.

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 * Renders, Jen
"ImWIP: Open-source image warping toolbox with adjoints and derivatives"
Image warping toolbox, 2023 Image processing

Image warping toolbox

See also

References

External links