Second-order Democratic Aggregation

Aggregated second-order features extracted from deep convolutional networks have been shown to be effective for texture generation, fine-grained recognition, material classification, and scene understanding. In this paper, we study a class of orderless aggregation functions designed to minimize interference or equalize contributions in the context of second-order features and we show that they can be computed just as efficiently as their first-order counterparts and they have favorable properties over aggregation by summation. Another line of work has shown that matrix power normalization after aggregation can significantly improve the generalization of second-order representations. We show that matrix power normalization implicitly equalizes contributions during aggregation thus establishing a connection between matrix normalization techniques and prior work on minimizing interference. Based on the analysis we present {\gamma}-democratic aggregators that interpolate between sum ({\gamma}=1) and democratic pooling ({\gamma}=0) outperforming both on several classification tasks. Moreover, unlike power normalization, the {\gamma}-democratic aggregations can be computed in a low dimensional space by sketching that allows the use of very high-dimensional second-order features. This results in a state-of-the-art performance on several datasets

Developmental and evolutionary significance of the zygomatic bone

International audienc

Detecting the direction of a signal on high-dimensional spheres: Non-null and Le Cam optimality results

We consider one of the most important problems in directional statistics, namely the problem of testing the null hypothesis that the spike direction $\theta$ of a Fisher-von Mises-Langevin distribution on the $p$-dimensional unit hypersphere is equal to a given direction $\theta_0$. After a reduction through invariance arguments, we derive local asymptotic normality (LAN) results in a general high-dimensional framework where the dimension $p_n$ goes to infinity at an arbitrary rate with the sample size $n$, and where the concentration $\kappa_n$ behaves in a completely free way with $n$, which offers a spectrum of problems ranging from arbitrarily easy to arbitrarily challenging ones. We identify various asymptotic regimes, depending on the convergence/divergence properties of $(\kappa_n)$, that yield different contiguity rates and different limiting experiments. In each regime, we derive Le Cam optimal tests under specified $\kappa_n$ and we compute, from the Le Cam third lemma, asymptotic powers of the classical Watson test under contiguous alternatives. We further establish LAN results with respect to both spike direction and concentration, which allows us to discuss optimality also under unspecified $\kappa_n$. To investigate the non-null behavior of the Watson test outside the parametric framework above, we derive its local asymptotic powers through martingale CLTs in the broader, semiparametric, model of rotationally symmetric distributions. A Monte Carlo study shows that the finite-sample behaviors of the various tests remarkably agree with our asymptotic results.Comment: 47 pages, 4 figure

Rate-invariant analysis of covariance trajectories

Statistical analysis of dynamic systems, such as videos and dynamic functional connectivity, is often translated into a problem of analyzing trajectories of relevant features, particularly covariance matrices. As an example, in video-based action recognition, a natural mathematical representation of activity videos is as parameterized trajectories on the set of symmetric, positive-definite matrices (SPDMs). The variable execution-rates of actions, implying arbitrary parameterizations of trajectories, complicates their analysis and classification. To handle this challenge, we represent covariance trajectories using transported square-root vector fields (TSRVFs), constructed by parallel translating scaled-velocity vectors of trajectories to their starting points. The space of such representations forms a vector bundle on the SPDM manifold. Using a natural Riemannian metric on this vector bundle, we approximate geodesic paths and geodesic distances between trajectories in the quotient space of this vector bundle. This metric is invariant to the action of the reparameterization group, and leads to a rate-invariant analysis of trajectories. In the process, we remove the parameterization variability and temporally register trajectories during analysis. We demonstrate this framework in multiple contexts, using both generative statistical models and discriminative data analysis. The latter is illustrated using several applications involving video-based action recognition and dynamic functional connectivity analysis

Bayesian linear size-and-shape regression with applications to face data

Regression models for size-and-shape analysis are developed, where the model is specified in the Euclidean space of the landmark coordinates. Statistical models in this space (which is known as the top space or ambient space) are often easier for practitioners to understand than alternative models in the quotient space of size-and-shapes. We consider a Bayesian linear size-and-shape regression model in which the response variable is given by labelled configuration matrix, and the covariates represent quantities such as gender and age. It is important to parameterize the model so that it is identifiable, and we use the LQ decomposition in the intercept term in the model for this purpose. Gamma priors for the inverse variance of the error term, matrix Fisher priors for the random rotation matrix, and flat priors for the regression coefficients are used. Markov chain Monte Carlo algorithms are used for sampling from the posterior distribution, in particular by using combinations of Metropolis-Hastings updates and a Gibbs sampler.The proposed Bayesian methodology is illustrated with an application to forensic facial data in three dimensions, where we investigate the main changes in growth by describing relative movements of landmarks for each gender over time

Persistent homology to analyse 3D faces and assess body weight gain

In this paper, we analyse patterns in face shape variation due to weight gain. We propose the use of persistent homology descriptors to get geometric and topological information about the configuration of anthropometric 3D face landmarks. In this way, evaluating face changes boils down to comparing the descriptors computed on 3D face scans taken at different times. By applying dimensionality reduction techniques to the dissimilarity matrix of descriptors, we get a space in which each face is a point and face shape variations are encoded as trajectories in that space. Our results show that persistent homology is able to identify features which are well related to overweight and may help assessing individual weight trends. The research was carried out in the context of the European project SEMEOTICONS, which developed a multisensory platform which detects and monitors over time facial signs of cardio-metabolic risk

A three-dimensional comparison of a morphometric and conventional cephalometric midsagittal planes for craniofacial asymmetry

Morphometric methods are used in biology to study object symmetry in living organisms and to determine the true plane of symmetry. The aim of this study was to determine if there are clinical differences between three-dimensional (3D) cephalometric midsagittal planes used to describe craniofacial asymmetry and a true symmetry plane derived from a morphometric method based on visible facial features. The sample consisted of 14 dry skulls (9 symmetric and 5 asymmetric) with metallic markers which were imaged with cone-beam computed tomography. An error study and statistical analysis were performed to validate the morphometric method. The morphometric and conventional cephalometric planes were constructed and compared. The 3D cephalometric planes constructed as perpendiculars to the Frankfort horizontal plane resembled the morphometric plane the most in both the symmetric and asymmetric groups with mean differences of less than 1.00 mm for most variables. However, the standard deviations were often large and clinically significant for these variables. There were clinically relevant differences (>1.00 mm) between the different 3D cephalometric midsagittal planes and the true plane of symmetry determined by the visible facial features. The difference between 3D cephalometric midsagittal planes and the true plane of symmetry determined by the visible facial features were clinically relevant. Care has to be taken using cephalometric midsagittal planes for diagnosis and treatment planning of craniofacial asymmetry as they might differ from the true plane of symmetry as determined by morphometrics

Nasal Bone Shape Is under Complex Epistatic Genetic Control in Mouse Interspecific Recombinant Congenic Strains

Genetic determinism of cranial morphology in the mouse is still largely unknown, despite the localization of putative QTLs and the identification of genes associated with Mendelian skull malformations. To approach the dissection of this multigenic control, we have used a set of interspecific recombinant congenic strains (IRCS) produced between C57BL/6 and mice of the distant species Mus spretus (SEG/Pas). Each strain has inherited 1.3% of its genome from SEG/Pas under the form of few, small-sized, chromosomal segments.The shape of the nasal bone was studied using outline analysis combined with Fourier descriptors, and differential features were identified between IRCS BcG-66H and C57BL/6. An F2 cross between BcG-66H and C57BL/6 revealed that, out of the three SEG/Pas-derived chromosomal regions present in BcG-66H, two were involved. Segments on chromosomes 1 (∼32 Mb) and 18 (∼13 Mb) showed additive effect on nasal bone shape. The three chromosomal regions present in BcG-66H were isolated in congenic strains to study their individual effect. Epistatic interactions were assessed in bicongenic strains.Our results show that, besides a strong individual effect, the QTL on chromosome 1 interacts with genes on chromosomes 13 and 18. This study demonstrates that nasal bone shape is under complex genetic control but can be efficiently dissected in the mouse using appropriate genetic tools and shape descriptors

Geometric morphometrics defines shape differences in the cortical area map of C57BL/6J and DBA/2J inbred mice

BACKGROUND: We previously described planar areal differences in adult mouse visual, somatosensory, and neocortex that collectively discriminated C57BL/6J and DBA/2J inbred strain identity. Here we use a novel application of established methods of two-dimensional geometric morphometrics to examine shape differences in the cortical area maps of these inbred strains. RESULTS: We used Procrustes superimposition to align a reliable set of landmarks in the plane of the cortical sheet from tangential sections stained for the cytochrome oxidase enzyme. Procrustes superimposition translates landmark configurations to a common origin, scales them to a common size, and rotates them to minimize an estimate of error. Remaining variation represents shape differences. We compared the variation in shape between C57BL/6J and DBA/2J relative to that within each strain using a permutation test of Goodall's F statistic. Significant differences in shape in the posterior medial barrel subfield (PMBSF), as well as differences in shape across primary sensory areas, characterize the cortical area maps of these common inbred, isogenic strains. CONCLUSION: C57BL/6J and DBA/2J have markedly different cortical area maps, in both size and shape. These differences suggest polymorphism in genetic factors underlying cortical specification, even between common isogenic strains. Comparing cortical phenotypes between normally varying inbred mice or between genetically modified mice can identify genetic contributions to cortical specification. Geometric morphometric analysis of shape represents an additional quantitative tool for the study of cortical development, regardless of whether it is studied from phenotype to gene or gene to phenotype