KSU CS Visualization and Graphics Group: Seminar Paper Reviews

Review Period:11/05/2012 - 11/09/2012 Reviewer:_Zhi Yuan____

Paper Title: Discrete Multiscale Vector Field Decomposition

Authors: ___Yiying Tong, Santiago Lombeyda, Anil N. Hirani and Mathieu Desbrun

Publication Venue: ______Siggraph ___ Publication Year:2003______

  1. Summary
  2. What is the research problem the paper attempts to address?

This paper proposed a 2d/3D vector decomposition on arbitrary grid for analysis and visualization. The vector field is decomposed into three components: a divergence - free part, a curl-free part, and a harmonic part similar to Helmotz- Hodge decomposition.

1.2What are the claimed contributions of the paper?

There are two contributions of this paper:

a. a simple and accurate approaching for vector field processing are proposed on arbitrary grids.

b. The global optimization method makes the flow properties accurate, smooth and stable.

1.3Describe the major methodology (math, algorithms, design, etc.) of the paper? Please use concise description.

Following the properties of Hodge decomposition, they converted the traditional vector decomposition method into two global optimization problems on discrete non-uniform grid. Compared with other methods based on local vector properties, their method can

  1. Evaluation
  2. Are the claims and algorithms valid? Why?

Yes,

They have already religiously proved their approach mathematically and methodologically.

2.2Is the research problem significant? Justify your evaluation.

Quite Significant. Flow decomposition can be used to remove the unimportant turbulent part, unveil the important features of the flow.

2.3Are the contributions significant? Justify your evaluation.

Yes, due to their innovation, the decomposition problem can be solved by two linear equations which can be very efficiently solved by traditional methods. This is the first paper who can achieve it.

  1. Synthesis
  2. How the research work can be further improved? Do not repeat the Future Work.

Quite good. I can find nothing for improving.

3.2Does this work related to your or our group’s work? What inspiration can it provides for our own work?

I think so.

Decomposition is quite a good way to locate the features of scalar/vector field. I am thinking that our compression method can be improved under good decomposition algorithm.

  1. Brainstorming: what are the ideas coming up to your mind during your review of this work? Describe anything you can think about here.

variational optimization method is very powerful in analyzing problem, which is worth of further study.