Geometry Videos: A New 3D Animation Representation

Hector Briceno (for life)

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This is work done in collaboration of Leonard McMillan, Steven Gortler, Pedro Sander, and Hugues Hoppe.

Abstract

Animations of three-dimensional computer graphics are becoming an increasingly prevalent medium for communication. There are many sources of 3D animations including physical simulations, scientific visualizations, and classic key-frame animations generated by an artist. There are even computer vision systems available today that are capable of capturing 3D time-varying geometric models. In this research, we develop a new representation for an important class of 3D animations, specifically time-varying manifolds. We call this representation a "Geometry Video." At present, a viewer of a 3D animation must either have a similar simulation or animation infrastructure to the animation's producer, or the producer must create a video from a predefined set of viewpoints. Geometry videos provide the ability to encode and transmit a time-varying mesh in a generic, source-independent, and view-independent format.

Geometry videos are created by constructing a global two-dimensional parametrization of a manifold over a rectangular domain. Time sequences of such parametrizations are particularly well-suited to compression using methods akin to video compression.

This system and approach is reported in two publications (the thesis contains the latest developements):

We also recommend further reading on Geometry Images for more understanding of the base process.

For Researchers

For researchers interested in comparing this system, I have made available some of the sequences and numbers found in Symposium of Computer Animation 2003 paper:

Input Sequences as tar files. Vertices are 1-based indexed. Note that not all frames in the sequences were used (starting from 1 ending before the last one). All the meshes have the same connectivity. I thank Matthias Muller for facilitating the Cow and Snake sequences, and MIT CSAIL Graphics Lab for the dance sequence.

Data for figures in the paper is Comma Separated Values (.csv)

Here is the raw data if you need to compare systems. Figures are shown here for illustration purporses, if you need high-resolution versions let me know. Also, please notify me if you use this data and where so that I can keep a bibliography and possible link it from here.

Figure 3



Figure 3.

Models used for comparison in Figure 3, rate distortion curves:

Figure 4

Figure 6

Figure 7

Figure 8

Models in Figure 8:

Some Output Models:

All errors were calculated using the GTS 0.5.1 library using a delta that is 1/200th the diagonal of the bounding box of the first frame. Using a matlab procedure like: l2distance (note that this is just an example and is non functional (without supporting files), I recommend to use many of the mesh comparison tools available on the net). The results of this metric and way of measuring have been validated with those found in other tools like Metro (c).

Other Notes

The underlying Geometry Images coder used for our platform is a reimplementation of that presented in the Geometry Images paper presented in Siggraph 2002. It uses the same underlying parametrization code from Sander. It is also now known that we can improve the parametrizations by using a negative energy factor (see Spherical Wavelets Paper Siggraph 2003).

Geometry Images will achieve better compression ratios with larger meshes. The ones used for comparison in the Geometry Videos paper are not that big (around 10,000 vertices).

The choice of parameters for Geometry Videos are justified in the thesis, nevertheless, it is clear that with more exhaustive methods or better incorporation of video techniques, better parameters can be chosen and higher compression can be achieved.

For the wavelet coder we use an implementation of the Embedded Zero-Tree Wavelets from Ng Mow-Song. http://pesona.mmu.edu.my/~msng/EZW.html