Clif Kussmaul - Digital Signal Processing & Analysis

Overview

My interests in these areas are somewhere between computer science, engineering, and a number of other areas (mathematics, music, neuroscience, etc). Often, my objective is to identify or develop tools and techniques to help other researchers solve important problems within their disciplines.

For my PhD dissertation, I studied and developed shape analysis methods. The shape of an object is really a description of its surface or surfaces; thus shape analysis can be thought of as a way to reduce a volume of three dimensional data to a two dimensional surface representation. Methods for representing and manipulating three dimensional shape have important applications in fields such as medical imaging, modeling, and computer graphics. The most effective approach will depend on the problem domain, the nature of the 3D dataset, the regularity of the shape, and the types of operations which will need to be performed.

Abstracts, Demos, Papers, etc. (most recent first)

In many applications, the surface of a three dimensional object is modeled by a set of points connected by a mesh of edges and faces. We describe how irregular sampling methods and spatial frequency representations can be used to analyze and manipulate these surface models. Intuitively, these "surface frequency" representations describe how the Cartesian positions of points on a surface vary as a function of intrinsic position along the surface. There are theoretical advantages to representing surfaces with irregular samples; specifically, aliasing is replaced by broadband noise. There are three components to the current approach. First, we optimize the intrinsic (surface-based) coordinates with respect to the extrinsic (Cartesian) coordinates. Second, we weight individual samples based on their proximity to neighboring samples. Third, we use an iterative transform method to correct for the effects of irregular sampling.
We then apply surface frequency methods to deformable models, where an initial surface is progressively deformed until it matches a target object. Since these methods are computationally intensive, it is desirable to use as few samples as possible. Thus, we monitor the surface frequency content of the model as it deforms, and increase the number of samples when there is sufficient evidence that the surface is undersampled. Using this approach, the model uses fewer samples for the early stages of the deformation, and yet achieves comparable fidelity to the target object by the end of the deformation. Furthermore, key parameters in the resampling process can be adjusted to trade computing time for surface fidelity.

Medical imaging, modeling, computer graphics, and computer vision are fields that represent and manipulate three dimensional surfaces. Such surfaces are often represented by irregularly spaced points connected into a mesh of edges and faces. There are many classical signal processing techniques which would also be useful in surface representations. In particular, frequency domain representations of surfaces could be used for filtering, classification, and other tasks. We develop a frequency representation for surfaces using results and methods from nonuniform sampling theory. We then use this representation to adjust the number of samples in a surface as it is deformed to match a target object.

The general organization of this dissertation is as follows. First, we introduce the objective and describe potential applications. Next, we review relevant background material from geometry and signal processing, describe current shape analysis methods, and review useful or related results from the literature. We then present the continuous and discrete versions of our frequency representation for surfaces, including a set of procedures developed in response to specific problems with the surface representation. Next, we use these techniques to adjust the number of samples in a deformable model. Finally, we review the current status of this investigation, and outline the anticipated course of future work.

A number of application domains involve the construction and maintenance of a representation of the shape of an arbitrary object or objects, where the shape of an object is really a description of its surface or surfaces. The most effective shape analysis technique will depend on the problem domain, the nature of the dataset to be modeled, the regularity of the shape, and the types of operations which will need to be performed.

This paper reviews recent research in three-dimensional (3D) shape analysis and proposes a number of important and profitable directions for future work involving the analysis and application of the surface spatial frequency (SSF). Intuitively, the SSF is a description of how the Cartesian positions of surface points vary over the entire surface; its development uses concepts from Fourier analysis and differential geometry.

The relative advantages and disadvantages of existing techniques are described. This leads to an evaluation of areas for further research, and a specific proposal for the design and development of new shape analysis techniques which use SSF. By developing spatial frequency theory and algorithms for arbitrary surfaces, it is possible to apply sampling theorems and other rigorous techniques to shape analysis. This should lead to faster, more accurate, more efficient, and better understood surface representations.

The current progress of this investigation is reviewed, and the anticipated course of future work is outlined. Specifically, this research will involve: 1) further development of a formalism for surface spatial frequency; 2) relationship of SSF to sampling theory; 3) application of SSF in surface analysis to specify spacing between model elements and to capture special surface features; 4) validation of these techniques using real and simulated data.

My electro-acoustic music page describes my efforts to apply wavelet transforms to music, and includes a variety of sounds I've used in compositions.

While I was at Dartmouth, I investigated a variety of approaches to image processing and compression, including Gabor and wavelet transforms, quantization, etc. Unfortunately other projects took priority, and so this stuff is on a back burner somewhere...