S. Mann, 2022 March 17

Panoramic imaging using algebraic projective geometry (i.e. combining multiple possibly differently exposured images) was first proposed and implemented by Mann, and published in 1993 [1][2].

Broadly there are two kinds of panorams (2 categories under which pictures
can be prefectly combined together):

**Type I panorama:**
the center-of-projection of the camera should remain
at a fixed location, and if there are no moving elements in
the picture, all pictures will be in the same orbit of the projective
group of coordinate transformations.
This type of panorama is often used to capture a full 360 degrees,
as in the selfie below, in which I appear twice (once at the left edge of the
picture at 0 degrees and once at the right edge at 360 degrees):

For this to work perfectly nothing in the image should move.
I didn't do a very good job of staying still while whipping the camera around
in a circle, so I have a different facial expression at 0 degrees than at
360 degrees. But that movement can sometimes be used artistially,
e.g. deliberate
violation of the no-movement rule, as below, where people moved around so they'd
appear in the photo multiple times with different facial expressions and
different poses each time they appear:

.

**Type II panorama:**
the subject matter is planar. An approximate example is shown below:

The (somewhat) flat storefronts are depicted in an approximately true and accurate way. All pictures of static planar subject matter are in the same orbit of the projective group of coordinate transformations. However, objects that violate this assumption, either by moving, or by being away from this planar surface, are not rendered in a true and accurate way. This effect can of course be used creatively, artistically, or the like.

The easiest way to make a Type II panorama is to move the camera parallel to a planar surface, e.g. as a "drive-by shooting" (a photo/video shoot from a moving vehicle, e.g. if you're a passenger in a car or train or bus), or using a wagon or bicycle or track or rail to move the camera in a controlled way.

Alternatively you can capture a planar subject in motion and just hold the camera still, as the object moves.

**Type I versus Type II panoramas:**
The difference between the Type I and Type II panorama is depicted
in the diagram below:

(from Chapter 6 of Intelligent Image Processing, Wiley 2001, author S. Mann)

Here are some examples of Type I panoramas:

In the last example, note the effects of motion.
The camera is panning from right to left (West to East),
from the roof of a building on Dundas
Street West, facing the AGO (Art Gallery of Ontario).
The Eastbound streetcar exhibits prograde ("forward" with respect to the camera)
motion, moving with the camera, and thus appears dilated (stretched).
The Westbound streetcar exhibits retrograde motion, moving against the
direction of the camera, and thus appears contracted (squashed).
While in reality both these streetcars are the same length, Westbound
occupies greater imagespace and Eastbound occupies lesser imagespace then
they are in reality.

Note that the effects of prograde or retrograde motion may still be present.
Here for example (below), we see the effects of retrograde motion on a
passing streetcar:

We might also hold the camera still and let the relative motion arise from
the moving streetcar, or let there be a combination of self motion
(camera motion, i.e. egomotion) and subject-matter motion.
Here's a chance to have some fun:

In the last example, I'm walking along a drugstore shelf, and then I stop and
pan the camera around. The left side of the image is a TypeI and the right side
is a Type II.

Here are some more additional examples (link).

Part A: estimation of image shift (translation). Construct two images that are merely shifted (translated) versions of each other. You can do this by cropping a large image into two smaller overlapping regions. Devise a simple way to estimate the translation (shift). You can use the approach outlined in class, for example. Alternatively, you can consider Fourier cross-correlation, phase-only fitering, or the like, as outlined in the Textbook[4].

Part B: Construct some Type III panorams. Explain your findings, and try to show examples that illustrate your understanding of the differences and similarities between Type I and Type II panoramas.

Post your results on the TypeIII Panorama Instructable.

[2] 1993: Mann was the first to produce an algorithm for automatically combining multiple pictures of the same subject matter, using algebraic projective geometry, to "stitch together" images using automatically estimated perspective correction. This is called the "Video Orbits" algorithm. [32][33][34]

[3] Video orbits

[4] Intelligent Image Processing, Wiley, 2001.

@BOOK{intelligentimageprocessing, author = "Steve Mann", title = "Intelligent Image Processing", publisher = "John Wiley and Sons", pages = "384", month = "November 2", year = "2001", note = "ISBN: 0-471-40637-6", }