A new distance for scale-invariant 3D shape recognition and registration

This paper presents a method for vote-based 3D shape recognition and registration, in particular using mean shift on 3D pose votes in the space of direct similarity transforms for the first time. We introduce a new distance between poses in this spacethe SRT distance. It is left-invariant, unlike Euclidean distance, and has a unique, closed-form mean, in contrast to Riemannian distance, so is fast to compute. We demonstrate improved performance over the state of the art in both recognition and registration on a real and challenging dataset, by comparing our distance with others in a mean shift framework, as well as with the commonly used Hough voting approach. © 2011 IEEE.

Achieving robust face recognition from video by combining a weak photometric model and a learnt generic face invariant

In spite of over two decades of intense research, illumination and pose invariance remain prohibitively challenging aspects of face recognition for most practical applications. The objective of this work is to recognize faces using video sequences both for training and recognition input, in a realistic, unconstrained setup in which lighting, pose and user motion pattern have a wide variability and face images are of low resolution. The central contribution is an illumination invariant, which we show to be suitable for recognition from video of loosely constrained head motion. In particular there are three contributions: (i) we show how a photometric model of image formation can be combined with a statistical model of generic face appearance variation to exploit the proposed invariant and generalize in the presence of extreme illumination changes; (ii) we introduce a video sequence re-illumination algorithm to achieve fine alignment of two video sequences; and (iii) we use the smoothness of geodesically local appearance manifold structure and a robust same-identity likelihood to achieve robustness to unseen head poses. We describe a fully automatic recognition system based on the proposed method and an extensive evaluation on 323 individuals and 1474 video sequences with extreme illumination, pose and head motion variation. Our system consistently achieved a nearly perfect recognition rate (over 99.7% on all four databases). © 2012 Elsevier Ltd All rights reserved.

Scale-invariant vote-based 3D recognition and registration from point clouds

This chapter presents a method for vote-based 3D shape recognition and registration, in particular using mean shift on 3D pose votes in the space of direct similarity transformations for the first time. We introduce a new distance between poses in this spacethe SRT distance. It is left-invariant, unlike Euclidean distance, and has a unique, closed-form mean, in contrast to Riemannian distance, so is fast to compute. We demonstrate improved performance over the state of the art in both recognition and registration on a (real and) challenging dataset, by comparing our distance with others in a mean shift framework, as well as with the commonly used Hough voting approach. © 2013 Springer-Verlag Berlin Heidelberg.

Topologically invariant reaction coordinates for simulating multistate chemical reactions.

Evaluating free energy profiles of chemical reactions in complex environments such as solvents and enzymes requires extensive sampling, which is usually performed by potential of mean force (PMF) techniques. The reliability of the sampling depends not only on the applied PMF method but also the reaction coordinate space within the dynamics is biased. In contrast to simple geometrical collective variables that depend only on the positions of the atomic coordinates of the reactants, the E(gap) reaction coordinate (the energy difference obtained by evaluating a suitable force field using reactant and product state topologies) has the unique property that it is able to take environmental effects into account leading to better convergence, a more faithful description of the transition state ensemble and therefore more accurate free energy profiles. However, E(gap) requires predefined topologies and is therefore inapplicable for multistate reactions, in which the barrier between the chemically equivalent topologies is comparable to the reaction activation barrier, because undesired "side reactions" occur. In this article, we introduce a new energy-based collective variable by generalizing the E(gap) reaction coordinate such that it becomes invariant to equivalent topologies and show that it yields more well behaved free energy profiles than simpler geometrical reaction coordinates.

Shape vs. volume: Invariant shape descriptors for 3D region of interest characterization in MRI

We propose a new approach for quantifying regions of interest (ROIs) in medical image data. Rotationally invariant shape descriptors (ISDs) were applied to 3D brain regions extracted from MRI scans of 5 Parkinson's patients and 10 control subjects. We concentrated on the thalamus and the caudate nucleus since prior studies have suggested they are affected in Parkinson's disease (PD). In the caudate, both the ISD and volumetric analyses found significant differences between control and PD subjects. The ISD analysis however revealed additional differences between the left and right caudate nuclei in both control and PD subjects. In the thalamus, the volumetric analysis showed significant differences between PD and control subjects, while ISD analysis found significant differences between the left and right thalami in control subjects but not in PD patients, implying disease-induced shape changes. These results suggest that employing ISDs for ROI characterization both complements and extends traditional volumetric analyses. © 2006 IEEE.

Cubically convergent iterations for invariant subspace computation

We propose a Newton-like iteration that evolves on the set of fixed dimensional subspaces of ℝ n and converges locally cubically to the invariant subspaces of a symmetric matrix. This iteration is compared in terms of numerical cost and global behavior with three other methods that display the same property of cubic convergence. Moreover, we consider heuristics that greatly improve the global behavior of the iterations.

A Newton algorithm for invariant subspace computation with large basins of attraction

We study the global behaviour of a Newton algorithm on the Grassmann manifold for invariant subspace computation. It is shown that the basins of attraction of the invariant subspaces may collapse in case of small eigenvalue gaps. A Levenberg-Marquardt-like modification of the algorithm with low numerical cost is proposed. A simple strategy for choosing the parameter is shown to dramatically enlarge the basins of attraction of the invariant subspaces while preserving the fast local convergence.

A Grassmann-Rayleigh quotient iteration for computing invariant subspaces

The classical Rayleigh quotient iteration (RQI) allows one to compute a one-dimensional invariant subspace of a symmetric matrix A. Here we propose a generalization of the RQI which computes a p-dimensional invariant subspace of A. Cubic convergence is preserved and the cost per iteration is low compared to other methods proposed in the literature.

A Grassman-Rayleigh quotient iteration for computing invariant subspaces

The classical Rayleigh Quotient Iteration (RQI) computes a 1-dimensional invariant subspace of a symmetric matrix A with cubic convergence. We propose a generalization of the RQI which computes a p-dimensional invariant subspace of A. The geometry of the algorithm on the Grassmann manifold Gr(p,n) is developed to show cubic convergence and to draw connections with recently proposed Newton algorithms on Riemannian manifolds.