Several photo and video-editing products available today have an Image Warping feature, which allows you to distort the geometry of an image or creating "Morphing" effects on video. These tools are seldom intuitive to use or effective in their results due to a limitation in the underlying process. These processes are described in the books:

• Digital Image Warping by George Wolberg
  IEEE Computer Society Press.
  
• Graphics Gems IV edited by Paul S. Heckbert
  AP Professional.

Serif engineers have devised an entirely new method of implementing image warping which is much more intuitive for the user and produces much better results. The geometry is deformed using an inverse mapping between grids of generalized Coons patches bounded by cubic Beziers. In his Graphics Gems IV paper, Paul S. Heckbert states, "Since the bilinear Coons patch defines a mapping that is very difficult to invert, in general, we will use it directly as the inverse mapping from destination space to source space." It is this approach that makes the tool difficult to use. Ideally the user would like to define an arbitrary grid of Coons patches for both the source and destination bitmaps.

Serifs approach

Serifs engineers have solved the inverse mapping problem for highly generalized grids of Coons patches. The patches are even allowed to "fold over" each other, producing "interesting" results. Resampling can be by nearest pixel, bilinear interpolation or bicubic (convolution) interpolation. The mapping is extremely efficient A 512 x 512 image is warped with bilinear interpolation in less than a second on my Pentium III machine.

The following images illustrate the process from a user perspective:

Initial Image

Defining the source mesh

Defining the destination mesh

End Result

Licensing the Mesh Warping Toolkit

The Serif Mesh Warping Toolkit is not a shrink-wrapped product. It is a core technology of our company's products. It is unlikely to be within the means of the individual or hobbyist programmer. All requests to license the library, in whole or in part will be treated on an individual basis. If you require further information please contact:

Darren Darvill
Head of Development
Serif (Europe) Ltd
Nottingham, UK
Tel +44 (0) 115 9142000