Worth Reading

Ross. Kindermann, Markov Random Fields and Their Applications.
comment: good, yet outdated book for introducing the physical background of Markov Random Fields.

Peter Clifford. Markov Random Fields in Statistics
comment: A readable and principled tutorial for Markov Random Fields. But you need to work through the maths equations carefully (Fortunately I'm good at it). The polygonal coloring measure and the following bla-bla is quite technical (Geometrical Probability, OMG) and I can't afford to dig out and read it.

Hanna M. Wallach, Conditional Random Fields: An Introduction
comment: A readable introduction to Conditional Random Fields, which I think is better to understand than John Lafferty's paper.

John Lafferty, Conditional Random Fields: Probabilistic Models for Segmenting and Labeling Sequence Data.
comment: It's a difficult paper, especially when I lack the background knowledge of NLP.

Worth Reading

Darroch, J.N. & Ratcliff, D. Generalized iterative scaling for log-linear models. 1972
comment: A quite readable paper on a special case (log-linear, kind of exponential distribution) of probability function estimation that can be done in a recursive way like EM (not exactly). It's based on the non-negtive attributes of mutual information between probabilities. So instead of maximized by expectation, it maximizes mutual information. Interesting comparison should be able to be made between this algorithm and EM. But I don't have time to do that and nobody has interest in that specific aspect, maybe.

Andrew McCallum, Maximum Entropy Markov Models for Information Extraction and Segmentation.
comment: A graphical probabilistic model like HMM but it's not generative, rather than descriptive (I name it this way). You construct this model by putting together the transfers you want, not by modeling how the symbols are generated. Yet it's as efficient as HMM.

Worth Reading

T.F Cootes, C.J. Taylor et al. Training Models of Shape from Sets of Examples. 1992

Map Projections-A working Manual, USGS Professional Paper.
comment: maps actually far more complicated than we thought.

P.L. Worthington and E.R. Hancock, "Surface Topography Using Shape-from-Shading," Pattern Recognition. 2001

William A.P. Smith, Edwin R. Hancock, "Recovering Facial Shape Using a Statistical Model of Surface Normal Direction", 2006

Worth Reading

Paul Debevec. Acquiring the Reflectance Field of a Human Face. SIGGRAPH 2000

comment: very interesting.


Polarized Light
http://acept.asu.edu/PiN/rdg/polarize/polarize.shtml

Try this video stuff.

Ray tracing project for the CG class, homework3

Definition

Let X be a topological space. There exists a smallest cosi-algebra beta in X such that every open set in X belongs to beta. The members of beta are called the Borel sets of X.


comment: Borel set is not necessarily defined on R ( as I learned in advanced calculus). It's actually a special algebra defined on arbitrary topological space.

It's a shame

that every classroom has only finite number of markers, but uncountable, and the broken ones constitute a dense set among them......

Worth Reading

Touching Soap Films

http://page.mi.fu-berlin.de/polthier/booklet/intro.html

comment: excellent introduction to minimal surfaces.

Worth Reading

http://www.personal.soton.ac.uk/rchc/Teaching/GTPBootstrap/ExtraDetails/NelderMeadProof.pdf

comment: excellent explanation of Nelder-Mead Method

Ilyan Baran, Automatic Rigging and Animation of 3D Characters.
comment: presentation paper on CG class.

Worth Reading

Frisken, 2000. Adaptively Sampled Distance Fields: A General Representation of Shape for Computer Graphics
comments: An octree representation of volumetric shapes. But unlike octree, the cells split only when the variation of the points in this cell is larger than a bilinear or trilinear interpolation of it's boundary points.

comments: Can we modify this representation for manifold?
Another way to think about it is that whether this representation can be extended beyond scalar field (distance field in the paper) to high dimensional field?

Subtlity of Float Inexactness in Ray Tracing

When a ray R hit a target T at point p, we may create new rays of reflection or refraction R1, R2 starting from point p, and calculate the intersection points for these R1, R2. However, due to the inexactness of floating point, the first intersecting point we obtain will be p itself with tiny perturbations. This point of course should be discarded away, otherwise some rays won't return correct value, the scene would be like this (the blue ball has may inconsistent spots on it)







The right scene should be like this: