I have hit the wall of the limit of my math knowledge... limited as it
is

I have been implementing an idea of using least squares to generate an
equation which approximates temporal pixel values. I have a working
version which seems to be working and i would now like to expand the
video codec to use previous frame spatial information.

To allow spatial infromation i will modify the current algorithm to
approximate differences between pixels between frames instead of the
pixel value per frame.

The problem is a sort of "chicken and egg" problem. To give the best
results I need to be able to identify which pixel from a previous
generated frame best matches the current pixel... however the pixels
need to be generated with equation which is needs to know the
differences between pixels between frames!

Probably you'd like to describe your problem in more detail?

Probably you'd like to describe your problem in more detail?

can do.

This currently what happens:

for each pixel
do
do
increment current sequence size
loop (n) from 0 to current sequence size
calculate difference between pixel in frame(n -current
frame) and the pixel in the current frame
end loop
generate equation using least squares to approximate these
differences
loop while PSNR of the approximated differences is above a
threshold.
record the previous equation
loop until no more frames
loop

what i want to do is instead of using the pixel in the same location
in the previous frame to generate the difference, to use the pixel
which most closely matches the current pixel in the current frame from
the previous frame. The problem arises is that i need to be able to
generate the frames in order to know which pixel from a previous frame
best matches the current actual frame so i will need to have an
equation already... however i need to know the differences to make
create the equation in the first place!

moogie schrieb:
Your problem is ill-defined, as it seems. For example, *if* you pick a
pixel from a different frame location, you have to make the decoder
aware of this (namely, correction relative to *which* pixel). Really, I
suggest to have a look into H261 (the first usable video codec, which is
simple, but yet shows many features in modern codes). An alternative
approach, which is closer to your lines, is to estimate motion from a
flow vector field. The first hits in google on "optical flow" can help
you, as well.

The problem with your approach is that you haven't defined the concepts,
which likely causes your confusion.

Just an idea: You shouldn't really try to minimize the prediction error.
I can tell you what the minimal error is, namely *zero*. You most likely
find a pixel of the same luminance somewhere in the previous frame,
which gives you nothing, though, since all the information is then in
the single-pixel motion vector you need to transmit. What you have to do
is not to solve the distortion problem (minimize D), but solve the
rate-distortion problem (minimize D for given R = rate). By that I mean
you need to take the size of the data into account that needs to be
transmitted.