General trajectory prior for non-rigid reconstruction

Trajectory basis Non-Rigid Structure From Motion (NRSFM) currently faces two problems: the limit of reconstructability and the need to tune the basis size for different sequences. This paper provides a novel theoretical bound on 3D reconstruction error, arguing that the existing definition of reconstructability is fundamentally flawed in that it fails to consider system condition. This insight motivates a novel strategy whereby the trajectory's response to a set of high-pass filters is minimised. The new approach eliminates the need to tune the basis size and is more efficient for long sequences. Additionally, the truncated DCT basis is shown to have a dual interpretation as a high-pass filter. The success of trajectory filter reconstruction is demonstrated quantitatively on synthetic projections of real motion capture sequences and qualitatively on real image sequences.

Locally weighted learning methods for non-rigid robot control

This thesis develops a novel approach to robot control that learns to account for a robot's dynamic complexities while executing various control tasks using inspiration from biological sensorimotor control and machine learning. A robot that can learn its own control system can account for complex situations and adapt to changes in control conditions to maximise its performance and reliability in the real world. This research has developed two novel learning methods, with the aim of solving issues with learning control of non-rigid robots that incorporate additional dynamic complexities. The new learning control system was evaluated on a real three degree-of-freedom elastic joint robot arm with a number of experiments: initially validating the learning method and testing its ability to generalise to new tasks, then evaluating the system during a learning control task requiring continuous online model adaptation.

Closed-form solutions for low-rank non-rigid reconstruction

Recovering the motion of a non-rigid body from a set of monocular images permits the analysis of dynamic scenes in uncontrolled environments. However, the extension of factorisation algorithms for rigid structure from motion to the low-rank non-rigid case has proved challenging. This stems from the comparatively hard problem of finding a linear “corrective transform” which recovers the projection and structure matrices from an ambiguous factorisation. We elucidate that this greater difficulty is due to the need to find multiple solutions to a non-trivial problem, casting a number of previous approaches as alleviating this issue by either a) introducing constraints on the basis, making the problems nonidentical, or b) incorporating heuristics to encourage a diverse set of solutions, making the problems inter-dependent. While it has previously been recognised that finding a single solution to this problem is sufficient to estimate cameras, we show that it is possible to bootstrap this partial solution to find the complete transform in closed-form. However, we acknowledge that our method minimises an algebraic error and is thus inherently sensitive to deviation from the low-rank model. We compare our closed-form solution for non-rigid structure with known cameras to the closed-form solution of Dai et al. [1], which we find to produce only coplanar reconstructions. We therefore make the recommendation that 3D reconstruction error always be measured relative to a trivial reconstruction such as a planar one.

Stationary processes for object detection and non-rigid structure-from-motion

Stationary processes are random variables whose value is a signal and whose distribution is invariant to translation in the domain of the signal. They are intimately connected to convolution, and therefore to the Fourier transform, since the covariance matrix of a stationary process is a Toeplitz matrix, and Toeplitz matrices are the expression of convolution as a linear operator. This thesis utilises this connection in the study of i) efficient training algorithms for object detection and ii) trajectory-based non-rigid structure-from-motion.

Mid-Level Vision and Recognition of Non-Rigid Objects

We address mid-level vision for the recognition of non-rigid objects. We align model and image using frame curves - which are object or "figure/ground" skeletons. Frame curves are computed, without discontinuities, using Curved Inertia Frames, a provably global scheme implemented on the Connection Machine, based on: non-cartisean networks; a definition of curved axis of inertia; and a ridge detector. I present evidence against frame alignment in human perception. This suggests: frame curves have a role in figure/ground segregation and in fuzzy boundaries; their outside/near/top/ incoming regions are more salient; and that perception begins by setting a reference frame (prior to early vision), and proceeds by processing convex structures.

Non-Rigid Shape from Image Streams

We present a framework for estimating 3D relative structure (shape) and motion given objects undergoing nonrigid deformation as observed from a fixed camera, under perspective projection. Deforming surfaces are approximated as piece-wise planar, and piece-wise rigid. Robust registration methods allow tracking of corresponding image patches from view to view and recovery of 3D shape despite occlusions, discontinuities, and varying illumination conditions. Many relatively small planar/rigid image patch trackers are scattered throughout the image; resulting estimates of structure and motion at each patch are combined over local neighborhoods via an oriented particle systems formulation. Preliminary experiments have been conducted on real image sequences of deforming objects and on synthetic sequences where ground truth is known.

The Use of Carboxy Terminated Liquid Natural Rubber (CTNR) as an Adhesive in Bonding Rubber to Rigid and Non-rigid Substrates

Carboxy Terminated Liquid Natural Rubber (CTNR) was prepared by photochemical reaction using maleic anhydride and masticated natural rubber (NR). The use of CTNR as an adhesive in bonding rubber to rubber and rubber to metal was studied. The peel strengths and lap shear strengths of the adherends which were bonded using CTNR were determined. The effect of using a tri isocyanate with CTNR in rubber to metal bonding was also studied. It is found that CTNR can effectively be used in bonding rubber to rubber and rubber to mild steel.

Stereochemically non-rigid helical mercury(II) complexes

Reactions of the 1: 2 condensate (L) of benzil dihydrazone and 2-acetylpyridine with Hg(ClO4)(2) center dot xH(2)O and HgI2 yield yellow [HgL2](ClO4)(2) (1) and HgLI2 (2), respectively. Homoleptic 1 is a 8-coordinate double helical complex with a Hg(II)N-8 core crystallising in the space group Pbca with cell dimensions: a = 16.2250(3), b = 20.9563(7), c = 31.9886(11) angstrom. Complex 2 is a 4-coordinate single helical complex having a Hg(II)N2I2 core crystallising in the space group P2(1)/n with cell dimensions a = 9.8011(3), b = 17.6736(6), c = 16.7123(6) angstrom and b = 95.760(3). In complex 1, the N-donor ligand L uses all of its binding sites to act as tetradentate. On the other hand, it acts as a bidentate N-donor ligand in 2 giving rise to a dangling part. From variable temperature H-1 NMR studies both the complexes are found to be stereochemically non-rigid in solution. In the case of 2, the solution process involves wrapping up of the dangling part of L around the metal. (C) 2008 Elsevier B.V. All rights reserved.