From the videos I have seen that all the systhetic streams are less vivid than the training ones. I guess the smoothing effect of k-average is reason.

I wonder why they used ARMA. Isn't it similar to Markov process. And I think it make more sense to not put equal weights onto the past x(t) but rather a discount factor like, since more recent states should have more impacts on the current state?

Edited by author 05-02-2002 04:13 PM
to answer Dave's quick question: the doted equal sign is \doteq tag in \latex. :Some people use it as "approximately equal". But I think the authors use it whenever they want to define the term at the left hand side or the right hand side of the equation.

Going through section 2.1, I couldn't find "definition" of k. I think it is the parameter for the "moving average".

I have a question about how the experimental methods coincide with the algorithm. They say they use 100 frames, but vary tao, the maximum time used in the algorithm description. Are frames equivalent to timesteps?

Edited by author 05-02-2002 03:28 PM

Dave: Two URLs:

http://documents.wolfram.com/v4/MainBook/DotEqual.html

http://www.wsu.edu/~brians/errors/flesh.html

I  empathize  with  your  mere  mathematical  mortality   (lovely
alliteration!).  The  authors lost me early on, in the definition
of dynamic texture on page 3. Statements of  the  form  ``we  say
that  A  is  a  B  if  there exists a set of C and a D such that,
calling E dotequal F we have E = G with H an I from  D  for  some
choice of J, K and initial condition L'' tend to throw me.

I found equally frustrating their tendency to  introduce  symbols
without  specifying  their  intended  meanings. Perhaps these are
conventional in this  field,  but  I  had  trouble  pinning  down
exactly  what roles were played by w(t), p_w(t), y(t), x(t), A_i,
B, and {Theta}.

Yet another obstacle to my understanding is my unfamiliarity with
the  terminology.  Here's  a  quick  rundown  of things which are
meaningless to  me:  second-order  process,  Lambertian,  albedo,
first-order  ARMA,  spatial filters, auto-regressive, script-L^2,
infinite-dimensional   manifold   of    probability    densities,
Riemannian   metric,  Fisher's  Information  matrix,  first-order
Gauss-Markov models, and the enigmatic phrase ``in the  sense  of
Frobenius''.  (Who  is  this  Frobenius? I didn't find him in the
references.)

I am pleased this is the fourth consecutive  paper  to  reference
Kullback-Leibler divergence. Go KL!

I liked how the authors defined dynamical texture as IID realizations of a sequence of images. I knew that after having stared at the ocean for a long time, there existed some temporal coherence in the pattern of waves but I lacked mathematical rigor and enough motivation to
formulate the problem of reconstructing the observation.

Hopefully today's presentation will clear up some details in section 4.

I really like the problem that this paper presents and the results (particularly the actual videos online). Unfortunately, I had a tough time understanding the algorithm that was used as I am only a mere mathematical mortal. I really wished the paper had given a better introduction and overview of the algorithm presented so that people without the vision background and mathematical adeptness could have gotten an intuitive understanding of how the algorithm worked.

I would have liked to have seen a more complete experimental section. I liked how they showed how their model could "cluster" related image sequences. I think exploring this in more detail over more samples would have been interesting.

To me, the compression information seemed to be a bit out of place. First, I think they either should have addressed that aspect as a single paper, or at least flushed the idea out a bit more. In looking at the results, I don't necessarily know if this type of system would be optimal for compression since the image sequences that are produced are a bit different from those that are trained on.

One last quick question, what does an equal sign with a dot over it stand for?

Edited by author 05-01-2002 06:21 PM
If you guys have a second or two, check out Stefano Stoatto's web page about this stuff. He has a bunch of videos of results. They're pretty cool to take a look at and it helps get a better idea of the actual results:

http://www.cs.ucla.edu/~doretto/projects/dynamic-textures.html