The Volume Graphics Research Group

Torsten Möller

Research Activities:

The focus of my research is to find solutions to problems in computer graphics using principles of applied mathematics and signal processing. I am concentrating my efforts in the following three areas:

Volume Visualization / Signal processing

For my current research I am working together with Prof. Yagel, Raghu Machiraju and Klaus Mueller to improve the calculation of normals of discrete datasets. This is very important since the accuracy of the surface normals determines the quality and appearance of the rendered image. We are trying to combine techniques from the field of Digital Signal Processing with tools known in Numerical Mathematics. All approaches for the rendering pipeline can be classified into 4 categories. Through a Taylor series expansion, we can approximate error bounds for these categories. This enables us to make quantitative and qualitative comparisons of different derivative and interpolation filters. Applying these error bounds to the class of cubic filters, allows us to find an optimal cubic filter for interpolation/derivative estimations. An open problem still is how to apply classical signal processing techniques with irregular sampled data (irregular grids).

Implicit Surfaces

Implicit Surfaces have many advantages over parametric surfaces. Implicitly modeled surfaces have often a more natural, smoother appearance. Their drawbacks include relatively difficult and slow rendering techniques. Together with Prof. Overman of the Department of Mathematics and Prof. Yagel I am working on faster and more accurate methods of rendering implicit surfaces. We are using a modified predictor-corrector method to achieve accuracy and an adaptive step size for speed. We also take into account and correctly render singular points of second degree and some of higher degrees. We have successfully implemented our ideas for 2D curves. These results are summarized in a Technical Report. Currently we are working on an extension in 3D

Virtual reality

This relatively young area faces many challenges, but has great potential for a wide variety of applications. Interactive rendering times of complex scenes are rarely achieved but are essential for immersive systems. Another challenge is the use of virtual technologies to assist and better integrate people with disabilities into our society. At the Advanced Computing Center for the Arts and Design (ACCAD) I am collaborating with researchers from the Ohio Supercomputer Center and from the Department of Civil Engineering to build a Virtual Reality system for Rehabilitation Research purposes. The goal is the examination of the behavior of disabled people under different conditions. The general accessibility of buildings for wheelchair users can be tested as well. With the help of a joystick capable of haptic feedback, we are able to guide a user through a building and minimize the collisions with a wall. Through a network connection we will enable a doctor to examen the behavior of the wheelchair user. The doctor will be able to interactively change the virtual environment to test the users performance and reaction to obstacles etc.

Publications:

• T. Möller, R. Machiraju, K. Mueller, and R. Yagel, "Classification and Local Error Estimation of Interpolation and Derivative Filters for Volume Rendering", accepted to Volume Visualization Workshop, San Francisco, CA, September 1996.

• T. Möller and R. Yagel, "Efficient Rasterization of Implicit Functions", Technical Report, Department of Computer and Information Science, Ohio State University, (OSU-CISRC-11/95-TR50)

Images:

	Derivative Filter alpha = -0.2	Derivative Filter alpha = -0.5	Derivative Filter alpha = -1.0
Interpolation Filter alpha = -0.2
Interpolation Filter alpha = -0.5
Interpolation Filter alpha = -1.0

Address

For more information, please see my personal homepage.

Last modified: October 6, 1996