CURVATURE-LIMITING MORPHOLOGICAL SIMPLIFICATION

Tightening maps a set to a similar set whose boundary has bounded mean curvature. My work on tightening grew out of a desire to map an input set to an output that is morphologically

*r*-regular, meaning that both its interior and exterior can be expressed as unions of open balls of radius

*r*, while the interior of its boundary is empty. Tightening achieves the same mean curvature bound as morphological regularization, and it behaves symmetrically with respect to set complement.

My initial work computed tightenings using constrained mean curvature flow. As the work developed, it appeared in a workshop, a conference, and a journal:

- J. Williams and J. Rossignac. Tightening: Morphological simplification.
*International Journal of Computational Geometry and Applications*17(5), 2007.

- J. Williams and J. Rossignac. Tightening: Curvature-limiting morphological simplification.
*ACM Symposium on Solid and Physical Modeling*, 2005.

- J. Williams and J. Rossignac. Tightening: Curvature-limiting morphological simplification.
*Fall Workshop on Computational Geometry*, 2004.

I then began work on constructing tightenings with path planning, which is more precise and efficient than curvature flow. To establish a specific tightening topology, I defined the medial cover:

- J. Williams. Relative convexity and the medial cover.
*Fall Workshop on Computational Geometry*, 2008.

PRESSING:

SMOOTH ISOSURFACES WITH FLATS FROM BINARY GRIDS

The goal of the Pressing project was to reconstruct a high-quality isosurface from a binary volume, where each voxel on a regular 3D grid was marked as either inside or outside of a solid. Although prior art provided methods for reconstructing smooth surfaces from binary volumes, we wished to additionally capture flat patches and sharp edges connecting patches. I helped adapt bilaplacian smoothing to the problem's constraints.

- A. Chica, J. Williams, et. al. Pressing: Smooth isosurfaces with flats from binary grids.
*Computer Graphics Forum*27(1), 2007.

MASON:

MORPHOLOGICAL SIMPLIFICATION

The Mason project stemmed from the observation that although compositions of morphological opening and closing with a ball often produce globally blended shapes, opening first and then closing tends to reduce an input set's size, while closing and then opening tends to increase it. Mason performs global blending while treating positive and negative space symmetrically. Notions of symmetry and morphological regularity in Mason shaped my later work on tightening and tight hulls.

- J. Williams and J. Rossignac. Mason: Morphological simplification.
*Graphical Models*67(4), 2005.

SLEEP/PERFORMANCE MODELING

One of the major goals at Walter Reed while I worked there was to develop a model to predict human operational performance as a function of sleep/wake schedule and time of day. I assisted in optimizing model parameters to fit reaction time data, and I recommended methods for handling the data’s unusual statistical properties.

- M. Johnson, G. Belenky, et. al. Modulating the homeostatic process to predict performance during chronic sleep restriction.
*Aviation, Space, and Environmental Medicine*75(3), 2004.