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.

Riemannian geometry of Grassmann manifolds with a view on algorithmic computation

We give simple formulas for the canonical metric, gradient, Lie derivative, Riemannian connection, parallel translation, geodesics and distance on the Grassmann manifold of p-planes in ℝn. In these formulas, p-planes are represented as the column space of n × p matrices. The Newton method on abstract Riemannian manifolds proposed by Smith is made explicit on the Grassmann manifold. Two applications - computing an invariant subspace of a matrix and the mean of subspaces - are worked out.

Optimized logarithmic phase masks used to generate defocus invariant modulation transfer function for wavefront coding system

In a previous Letter [Opt. Lett. 33, 1171 (2008)], we proposed an improved logarithmic phase mask by making modifications to the original one designed by Sherif. However, further studies in another paper [Appl. Opt. 49, 229 (2010)] show that even when the Sherif mask and the improved one are optimized, their corresponding defocused modulation transfer functions (MTFs) are still not stable with respect to focus errors. So, by further modifying their phase profiles, we design another two logarithmic phase masks that exhibit more stable defocused MTF. However, with the defocus-induced phase effect considered, we find that the performance of the two masks proposed in this Letter is better than the Sherif mask, but worse than our previously proposed phase mask, according to the Hilbert space angle. (C) 2010 Optical Society of America

Knotted wave dislocation with the hopf invariant

We study the wave dislocations with an induced gauge potential. The topological current characterized the wave dislocations is constructed with the dual of Abelian gauge field. And the topological charges and locations of the wave dislocations are determined by the phi-mapping topological current theory. Furthermore, it is shown that the knotted wave dislocations can be described with a Hopf invariant in the wave field. At last we discussed the evolution of the knotted wave dislocations.

BRST invariant theory of a generalized 1+1 Dimensional nonlinear sigma model with topological term

We give a generalized Lagrangian density of 1 + 1 Dimensional O( 3) nonlinear sigma model with subsidiary constraints, different Lagrange multiplier fields and topological term, find a lost intrinsic constraint condition, convert the subsidiary constraints into inner constraints in the nonlinear sigma model, give the example of not introducing the lost constraint. N = 0, by comparing the example with the case of introducing the lost constraint, we obtain that when not introducing the lost constraint, one has to obtain a lot of various non-intrinsic constraints. We further deduce the gauge generator, give general BRST transformation of the model under the general conditions. It is discovered that there exists a gauge parameter beta originating from the freedom degree of BRST transformation in a general O( 3) nonlinear sigma model, and we gain the general commutation relations of ghost field.

Local histogram based geometric invariant image watermarking

Compared with other existing methods, the feature point-based image watermarking schemes can resist to global geometric attacks and local geometric attacks, especially cropping and random bending attacks (RBAs), by binding watermark synchronization with salient image characteristics. However, the watermark detection rate remains low in the current feature point-based watermarking schemes. The main reason is that both of feature point extraction and watermark embedding are more or less related to the pixel position, which is seriously distorted by the interpolation error and the shift problem during geometric attacks. In view of these facts, this paper proposes a geometrically robust image watermarking scheme based on local histogram. Our scheme mainly consists of three components: (1) feature points extraction and local circular regions (LCRs) construction are conducted by using Harris-Laplace detector; (2) a mechanism of grapy theoretical clustering-based feature selection is used to choose a set of non-overlapped LCRs, then geometrically invariant LCRs are completely formed through dominant orientation normalization; and (3) the histogram and mean statistically independent of the pixel position are calculated over the selected LCRs and utilized to embed watermarks. Experimental results demonstrate that the proposed scheme can provide sufficient robustness against geometric attacks as well as common image processing operations. (C) 2010 Elsevier B.V. All rights reserved.

A novel invariant and sequence comparison for DNA

We consider numerical characterization of DNA primary sequence based on the positions of bases (a, t, c, g) and the pairs of bases X, Y in DNA (X, Y=a, t, c, g). This leads to a representation of DNA by a numerical sequence. Then, we extract a novel invariant (molecular connectivity index) from the derived numerical sequences. The suitable invariant can offer a characterization of DNA primary sequence. Finally, we provide an illustration of its utility by making a comparison between ten DNA sequences belonging to beta-globin gene in different species. The evolutionary relationships of ten species we have revealed in this contribution accord with phylogenetic tree properly.

Object Recognition By Alignment Using Invariant Projections of Planar Surfaces

In order to recognize an object in an image, we must determine the best transformation from object model to the image. In this paper, we show that for features from coplanar surfaces which undergo linear transformations in space, there exist projections invariant to the surface motions up to rotations in the image field. To use this property, we propose a new alignment approach to object recognition based on centroid alignment of corresponding feature groups. This method uses only a single pair of 2D model and data. Experimental results show the robustness of the proposed method against perturbations of feature positions.