Deriving Video Animation from a Single Still Photo (was: physics formulary)

On Feb 15, 10:36 am, "Androcles" <Headmas...@xxxxxxxxxxxxxxxx> wrote:
| >  http://www.androcles01.pwp.blueyonder.co.uk/Smart/LT.gif

This one needs to be fixed: you implemented the Lorentz transform
wrong. It's difficult to see it directly, because the background is
stationary (apart from its motion), so there's no way to see the t and
t' coordinates.

On that account, the Lorentz contraction is also implemented from,
because you have, in effect, t = t'.

The simplest way to implement t is to make the background change color
gradually (e.g., fading from day to night). In the moving frame, it's
darker ahead than it is back of the motion, because of the Lorentz
transform for t'. That means a single frame for the moving system is
derived from MULTIPLE frames of the original system.

The transform should be such that the color of the background as the
train passes by a fixed point is the same in both the stationary and
moving frame.

So, technically, this means that to transform to the fixed frame, you
have to derive the image for snapshot #n in the moving system across
snapshots from the fixed system (all snapshots #1,#2,...). Apart from
the fact that the background is trivial, this would not be an easy
task to implement. In effect, it's a 3-dimensional transform, where
you stack the frames up vertically, then derive the moving system by
slicing across the frame "block" at a slant. The slant for "equal-
time" slices is sloped upward in the direction of motion. So the
"rotation" is described by sinh and cosh, rather than by sin and cos.

Just as a rough idea, I have about 40 hours work in the differential
gif
 http://www.androcles01.pwp.blueyonder.co.uk/Differential.gif
as it was an early attempt in 3D and I was on the learning curve,
I could repeat it today in about 8 hours.

I have over 30 years experience working in animation, but am not quite
familiar with GIF 89, and have never bought video-production equipment
(though I've co-produced short video screenplay segments complete with
scripting, site location, background music, etc.).

I'm going to try something interesting that I don't think has ever
really been done before. Instead of using a cartoon background, I'm
going to use a REAL background -- namely the one in

http://federation.g3z.com/Milwaukee/index.htm

that depicts the ancient railline (now grown over with plants) and the
wooden overhang. I'm going to derive a VIDEO from the still photo.

The first segment will depict a ghost-train running down the tracks
into the horizon (which is 2 miles away) as the scene gradually fades
to back. The second segment starts out the same, but as the ghost
train passes by, the viewer starts to accelerate and move with the
train under and through the overhang into the distance as the scene
fades gradually to black.

This is not a trivial exercise by any stretch of the imagination. It
requires 3 stages, each requiring serious hand-holding for the
computer which would not otherwise easily be able to do this by
itself:

(1) Depth-Tagging.
The picture is, in effect, turned into a contour map with the contour
indicating the lines of equal depth.

The 3-dimensional positions of elements in the picture are determined
by extrapolating off the contour map.

(2) Occlusion Boundaries & Object Presence.
Places where the depth undergoes sharp discontinuity indicate
occlusion boundaries. All the boundaries are either closed curves or
curves that would otherwise be closed but are occluded by other
boundaries. This requires filling in the incomplete boundaries. In
effect, this amounts to inferring hidden objects behind other objects
and is the process known in child development psychology as "object
presence".

The process is the inverse of occlusion.

The picture frame, itself, is treated as an occlusion boundary.

(3) Reverse Projection.
This is decidedly the most non-trivial part of the exercise. For each
frame in the video, a vantage point is selected (if the observer is
moving), and orientation. The individual elements of the frame are
derived by reverse-projecting from the vantage point through the given
orientation.

Projection lines at some point will go from positive depth to negative
depth. If the cross-over occurs away from an occlusion line, this
marks the target of the projection and the element placed in the new
frame is derived from the original frame. Otherwise, the cross-over
occurs on an occlusion line. Certain special cases have to be
correctly handled here (e.g., the projection line re-emerging at
positive depth when coming out from behind the other end of the first
occlusion boundary -- this occurs when the projection line passes
behind an object).
.

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