In this paper we study physical knots; that is, knots tied (as closed loops) in real pieces of rope, which have diameter. Intuitively, for a given diameter, one needs a certain minimum length of ropeâ€¦ (More)

Relatively extremal knots are the relative minima of the ropelength functional in the C1 topology. They are the relative maxima of the thickness (normal injectivity radius) functional on the set ofâ€¦ (More)

The properties of normal injectivity radius i(K, M) (thickness), of C 1,1 submanifolds K of complete Riemannian manifolds M are studied. We introduce the notion of geometric focal distance for C 1,1â€¦ (More)

This paper investigates the shape collapse problem in nonrigid image registration. The shape collapse problem is the situation when an appendage of a deforming object does not overlap with the targetâ€¦ (More)

Registering lung CT images is an important problem for many applications including tracking lung motion over the breathing cycle, tracking anatomical and function changes over time, and detectingâ€¦ (More)

The thickness, NIR(K) of a knot or link K is defined to be the radius of the largest open solid tube one can put around the curve without any self intersections of the normal discs, which is alsoâ€¦ (More)

Nonuniform tubular neighborhoods of curves in Rn are studied by using weighted distance functions and generalizing the normal exponential map. Different notions of injectivity radii are introduced toâ€¦ (More)

This paper examines the shape collapse problem that occurs when registering a pair of images or a population of images of the brain to a reference (target) image coordinate system using diffeomorphicâ€¦ (More)