Nuclear magnetic resonance (NMR) residual dipolar couplings (RDCs) provide a unique opportunity for spatially characterizing complex motions in biomolecules with time scale sensitivity extending up to milliseconds. Up to five motionally averaged Wigner rotation elements, (D(0k)2(alphaalpha)), can be determined experimentally using RDCs measured in five linearly independent alignment conditions ...

Many computer vision problems (e.g., camera calibration, image alignment, structure from motion) are solved with nonlinear optimization methods. It is generally accepted that second order descent methods are the most robust, fast, and reliable approaches for nonlinear optimization of a general smooth function. However, in the context of computer vision, second order descent methods have two mai...

Different poses of 3D models are very often given in different positions and orientations in space. Since most of the computer graphics algorithms do not satisfy geometric invariance, it is very important to bring shapes into a canonical coordinate frame before any processing. In this paper we consider the problem of finding the best alignment between two or more different poses of the same obj...

In this paper we describe a method to non-rigidly co-register a 2D slice sequence from real-time 3D echocardiography with a 2D cardiovascular MR image sequence. This is challenging because the imaging modalities have different spatial and temporal resolution. Non-rigid registration is required for accurate alignment due to imprecision of cardiac gating and natural motion variations between card...

This paper gives a method to construct rigid spaces, which is similar to the method used to construct toric schemes.

This paper addresses the problem of estimating postoperative cup alignment from single standard X-ray radiograph with gonadal shielding. The widely used procedure of evaluation of cup orientation following total hip arthroplasty using single standard anteroposterior radiograph is known inaccurate, largely due to the wide variability in individual pelvic position relative to X-ray plate. 2D-3D i...

Different poses of 3D models are very often given in different positions and orientations in space. Since most of the computer graphics algorithms do not satisfy geometric invariance, it is very important to bring shapes into a canonical coordinate frame before any processing. In this paper we consider the problem of finding the best alignment between two or more different poses of the same obj...

Motivation Sequence-order independent structural comparison, also called structural alignment, of small ligand molecules is often needed for computer-aided virtual drug screening. Although many ligand structure alignment programs are proposed, most of them build the alignments based on rigid-body shape comparison which cannot provide atom-specific alignment information nor allow structural vari...

Tensegrity frameworks are defined on a set of points in Rd and consist of bars, cables, and struts, which provide upper and/or lower bounds for the distance between their endpoints. The graph of the framework, in which edges are labeled as bars, cables, and struts, is called a tensegrity graph. It is said to be strongly rigid in Rd if every generic realization in Rd as a tensegrity framework is...

A direction-length framework is a pair (G, p), where G = (V ;D,L) is a ‘mixed’ graph whose edges are labeled as ‘direction’ or ‘length’ edges, and p is a map from V to R for some d. The label of an edge uv represents a direction or length constraint between p(u) and p(v). Let G be obtained from G by adding, for each length edge e of G, a direction edge with the same end vertices as e. We show t...