Multilinear Wavelets: A Statistical Shape Space for Human Faces

We present a statistical model for $3$D human faces in varying expression, which decomposes the surface of the face using a wavelet transform, and learns many localized, decorrelated multilinear models on the resulting coefficients. Using this model we are able to reconstruct faces from noisy and occluded $3$D face scans, and facial motion sequences. Accurate reconstruction of face shape is important for applications such as tele-presence and gaming. The localized and multi-scale nature of our model allows for recovery of fine-scale detail while retaining robustness to severe noise and occlusion, and is computationally efficient and scalable. We validate these properties experimentally on challenging data in the form of static scans and motion sequences. We show that in comparison to a global multilinear model, our model better preserves fine detail and is computationally faster, while in comparison to a localized PCA model, our model better handles variation in expression, is faster, and allows us to fix identity parameters for a given subject.Comment: 10 pages, 7 figures; accepted to ECCV 201

Intersubject Regularity in the Intrinsic Shape of Human V1

Previous studies have reported considerable intersubject variability in the three-dimensional geometry of the human primary visual cortex (V1). Here we demonstrate that much of this variability is due to extrinsic geometric features of the cortical folds, and that the intrinsic shape of V1 is similar across individuals. V1 was imaged in ten ex vivo human hemispheres using high-resolution (200 μm) structural magnetic resonance imaging at high field strength (7 T). Manual tracings of the stria of Gennari were used to construct a surface representation, which was computationally flattened into the plane with minimal metric distortion. The instrinsic shape of V1 was determined from the boundary of the planar representation of the stria. An ellipse provided a simple parametric shape model that was a good approximation to the boundary of flattened V1. The aspect ration of the best-fitting ellipse was found to be consistent across subject, with a mean of 1.85 and standard deviation of 0.12. Optimal rigid alignment of size-normalized V1 produced greater overlap than that achieved by previous studies using different registration methods. A shape analysis of published macaque data indicated that the intrinsic shape of macaque V1 is also stereotyped, and similar to the human V1 shape. Previoud measurements of the functional boundary of V1 in human and macaque are in close agreement with these results

The Power Spectrum of Mass Fluctuations Measured from the Lyman-alpha Forest at Redshift z=2.5

We measure the linear power spectrum of mass density fluctuations at redshift z=2.5 from the \lya forest absorption in a sample of 19 QSO spectra, using the method introduced by Croft et al. (1998). The P(k) measurement covers the range 2\pi/k ~ 450-2350 km/s (2-12 comoving \hmpc for \Omega=1). We examine a number of possible sources of systematic error and find none that are significant on these scales. In particular, we show that spatial variations in the UV background caused by the discreteness of the source population should have negligible effect on our P(k) measurement. We obtain consistent results from the high and low redshift halves of the data set and from an entirely independent sample of nine QSO spectra with mean redshift z=2.1. A power law fit to our measured P(k) yields a logarithmic slope n=-2.25 +/- 0.18 and an amplitude \Delta^2(k_p) = 0.57^{+0.26}_{-0.18}, where $\Delta^2$ is the contribution to the density variance from a unit interval of lnk and k_p=0.008 (km/s)^{-1}. Direct comparison of our mass P(k) to the measured clustering of Lyman Break Galaxies shows that they are a highly biased population, with a bias factor b~2-5. The slope of the linear P(k), never previously measured on these scales, is close to that predicted by models based on inflation and Cold Dark Matter (CDM). The P(k) amplitude is consistent with some scale-invariant, COBE-normalized CDM models (e.g., an open model with \Omega_0=0.4) and inconsistent with others (e.g., \Omega=1). Even with limited dynamic range and substantial statistical uncertainty, a measurement of P(k) that has no unknown ``bias factors'' offers many opportunities for testing theories of structure formation and constraining cosmological parameters. (Shortened)Comment: Submitted to ApJ, 27 emulateapj pages w/ 19 postscript fig

A Bayesian Approach to Manifold Topology Reconstruction

In this paper, we investigate the problem of statistical reconstruction of piecewise linear manifold topology. Given a noisy, probably undersampled point cloud from a one- or two-manifold, the algorithm reconstructs an approximated most likely mesh in a Bayesian sense from which the sample might have been taken. We incorporate statistical priors on the object geometry to improve the reconstruction quality if additional knowledge about the class of original shapes is available. The priors can be formulated analytically or learned from example geometry with known manifold tessellation. The statistical objective function is approximated by a linear programming / integer programming problem, for which a globally optimal solution is found. We apply the algorithm to a set of 2D and 3D reconstruction examples, demon-strating that a statistics-based manifold reconstruction is feasible, and still yields plausible results in situations where sampling conditions are violated