literature on transformation of images

[Paul.Heckbert at HOSTESS.GRAPHICS.CS.CMU.EDU]

 | Date: Wed, 9 Sep 1998 11:48:48 -0400
 | From: yap at jinai.cs.nyu.edu (Chee Yap)
 | To: compgeom-announce at research.bell-labs.com
 | Subject: literature on transformation of images
 | 
 | Is there any open literature about the following
 | basic problem?  Given a raster image I, and a 
 | linear transformation T, to compute the new image T(I).  

The geometric part of this problem has no open problems that I know of,
but there are issues related to top-quality filtering (reconstruction,
sampling, and antialiasing) that raise some open problems in
multidimensional signal processing.

One such question:

    What is the ideal filter to use when resampling a transformed
    raster image while minimizing aliasing?

    I addressed this question in

	Fundamentals of Texture Mapping and Image Warping,
	Paul Heckbert, Master's thesis, UCB/CSD 89/516,
	CS Division, U.C. Berkeley, June 1989.
	http://www.cs.cmu.edu/~ph

    and answered it, I believe, for one definition of "ideal",
    but I have seen surprisingly little discussion of this problem
    elsewhere -- most people have apparently satisfied themselves with
    special case solutions for the cases of downsampling and upsampling
    (scaling a picture down and up, respectively).

There are some other interesting signal processing questions associated with
the multipass algorithms for performing affine transformations on images,
e.g. the 2-pass and 3-pass algorithms, respectively, of:

    Catmull & Smith, 3-D Transformations of Images in Scanline Order,
    Proc. SIGGRAPH '80, 1980

    Alan W. Paeth, A Fast Algorithm for General Raster Rotation,
    Graphics Interface '86, May 1986

i.e. how to do the filtering in these algorithms with highest quality results.

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