Video Orbits of the Projective Group:

A New Perspective on Image Compositing.

Steve Mann


A new technique has been developed for estimating the projective (homographic) coordinate transformation between pairs of images of a static scene, taken with a camera that is free to pan, tilt, rotate about its optical axis, and zoom. The technique solves the problem for two cases: The technique, first published in 1993, has recently been published in more detail in:

  author    = "S. Mann and R. W. Picard",
  title     = "Video orbits of the projective group;
               A simple approach to featureless estimation of parameters",
  institution = "Massachusetts Institute of Technology",
  type      = "TR",
  number    = "338",
  address   = "Cambridge, Ma",
  month     = "See",
  note      = "Also appears {IEEE} Trans. Image Proc., Sept 1997, Vol. 6 No. 9",
  year      = 1995}

(The aspect of the 1993 paper dealing with differently exposed pictures to appear in a later Proc IEEE paper; please contact author of this WWW page if you're interested in knowing more about extending dynamic range by combining differently exposed pictures, or getting a preprint.)

A pdf file of the above publication, as it originally appeared, with the original pagination, etc., is also available.

See also U.S. Pat. 5706416

The new algorithm is applied to the task of constructing high resolution still images from video. This approach generalizes inter-frame camera motion estimation methods which have previously used an affine model and/or which have relied upon finding points of correspondence between the image frames.

The new method, which allows an image to be created by "painting with video" is used in conjunction with a wearable wireless webcam, so that image mosaics can be generated simply by looking around, in a sense, "painting with looks".


Combining multiple pictures of the same static scene allows for a higher "resolution" image to be constructed.: Example of image composite from IS&T 1993 paper (click to see higher resolution version). In the above example, the spatial extent of the image is increased by panning the camera while mosaicing and the spatial resolution is increased by zooming the camera and by combining overlapping frames from different viewpoints.

Note that the author overran the panning to appear twice in the composite picture (this is an old trick dating back to the days of the 1904 Kodak circuit 10 camera which is still used to take the freshman portraits in Killian court, and there are several people who still overrun the camera to get in the picture twice). Note also that the author appears sharper on the right than on the left because of the zooming in ("saliency") at that region of the image.

Note also that, unlike previous methods based on the affine model, the inserts are not parallelogram-shaped (e.g. not affine), because a projective (homographic) coordinate transformation is used here rather than the affine coordinate transformation.

The difference between the affine model and the projective model is evident in the following figure:

For completeness, other coordinate transformations, such as bilinear and pseudo-perspective, are also shown. Note that the models are presented in two categories, models that exhibit the "chirping" effect, and those that do not.


  1. Extreme wide-angle architectural shot. A wide-sweeping panorama is presented in a distortion-free form (e.g. where straight lines map to straight lines).
  2. My point of view at Wal-Mart Click for medium-resolution greyscale image; a much higher resolution version of this same picture, in either 192 bit color (double) or 24 bit color (uchar), is available upon request).
  3. "Claire" image sequence Paul Hubel aims a hand-held video camera at his wife. Although the scene is not completely static and there is no constraint to keep the camera center of projection (COP) fixed, the algorithm produces a reasonable composite image.
  4. An "environment map" of the Media Lab's "computer garden".
  5. Head-mounted camera at a restaurant
  6. Outdoor scene with people, close-up (Alan Alda interviewing me for Sci.Am "FRONTIERS").
  7. National geographic visit

See a gallery of quantigraphic image composites
Obtain latest version of VideoOrbits freewear or if you don't want to obtain the whole tar file, you can take a look at the README.HTML
My original Matlab files upon which the C version of orbits is based (these in-turn were based on my PV-Wave and FORTRAN code)
Version 2.0 will appear on this site in the near future (including a RedHat RPM)