Bayesian data assimilation in shape registration

In this paper we apply a Bayesian framework to the problem of geodesic curve matching. Given a template curve, the geodesic equations provide a mapping from initial conditions\ud for the conjugate momentum onto topologically equivalent shapes. Here, we aim to recover the well defined posterior distribution on the initial momentum which gives rise to observed points on the target curve; this is achieved by explicitly including a reparameterisation in the formulation. Appropriate priors are chosen for the functions which together determine this field and the positions of the observation points, the initial momentum p0 and the reparameterisation vector field v, informed by regularity results about the forward model. Having done this, we illustrate how Maximum Likelihood Estimators (MLEs) can be used to find regions of high posterior density, but also how we can apply recently developed MCMC methods on function spaces to characterise the whole of the posterior density. These illustrative examples also include scenarios where the posterior distribution is multimodal and irregular, leading us to the conclusion that knowledge of a state of global maximal posterior density does not always give us the whole picture, and full posterior sampling can give better quantification of likely states and the overall uncertainty inherent in the problem

Mixture of Kernels and Iterated Semidirect Product of Diffeomorphisms Groups

In the framework of large deformation diffeomorphic metric mapping (LDDMM), we develop a multi-scale theory for the diffeomorphism group based on previous works. The purpose of the paper is (1) to develop in details a variational approach for multi-scale analysis of diffeomorphisms, (2) to generalise to several scales the semidirect product representation and (3) to illustrate the resulting diffeomorphic decomposition on synthetic and real images. We also show that the approaches presented in other papers and the mixture of kernels are equivalent.Comment: 21 pages, revised version without section on evaluatio

Fast Predictive Image Registration

We present a method to predict image deformations based on patch-wise image appearance. Specifically, we design a patch-based deep encoder-decoder network which learns the pixel/voxel-wise mapping between image appearance and registration parameters. Our approach can predict general deformation parameterizations, however, we focus on the large deformation diffeomorphic metric mapping (LDDMM) registration model. By predicting the LDDMM momentum-parameterization we retain the desirable theoretical properties of LDDMM, while reducing computation time by orders of magnitude: combined with patch pruning, we achieve a 1500x/66x speed up compared to GPU-based optimization for 2D/3D image registration. Our approach has better prediction accuracy than predicting deformation or velocity fields and results in diffeomorphic transformations. Additionally, we create a Bayesian probabilistic version of our network, which allows evaluation of deformation field uncertainty through Monte Carlo sampling using dropout at test time. We show that deformation uncertainty highlights areas of ambiguous deformations. We test our method on the OASIS brain image dataset in 2D and 3D

A reduced-order strategy for 4D-Var data assimilation

This paper presents a reduced-order approach for four-dimensional variational data assimilation, based on a prior EO F analysis of a model trajectory. This method implies two main advantages: a natural model-based definition of a mul tivariate background error covariance matrix $\textbf{B}_r$, and an important decrease of the computational burden o f the method, due to the drastic reduction of the dimension of the control space. % An illustration of the feasibility and the effectiveness of this method is given in the academic framework of twin experiments for a model of the equatorial Pacific ocean. It is shown that the multivariate aspect of $\textbf{B}_r$ brings additional information which substantially improves the identification procedure. Moreover the computational cost can be decreased by one order of magnitude with regard to the full-space 4D-Var method

Salinity Measurements Collected by Fishermen Reveal a “River in the Sea” Flowing Along the Eastern Coast of India

Being the only tropical ocean bounded by a continent to the north, the Indian Ocean is home to the most powerful monsoon system on Earth. Monsoonal rains and winds induce huge river discharges and strong coastal currents in the northern Bay of Bengal. To date, the paucity of salinity data has prevented a thorough description of the spreading of this freshwater into the bay. The potential impact of the salinity on cyclones and regional climate in the Bay of Bengal is, however, a strong incentive for a better description of the water cycle in this region. Since May 2005, the National Institute of Oceanography conducts a program in which fishermen collect seawater samples in knee-deep water at eight stations along the Indian coastline every 5 days. Comparison with open-ocean samples shows that this cost-effective sampling strategy is representative of offshore salinity evolution. This new dataset reveals a salinity drop exceeding 10 g kg−1 in the northern part of the bay at the end of the summer monsoon. This freshening signal propagates southward in a narrow (~100 km wide) strip along the eastern coast of India, and reaches its southern tip after 2.5 months. Satellite-derived alongshore-current data shows that the southward propagation of this “river in the sea” is consistent with transport by seasonal coastal currents, while other processes are responsible for the ensuing erosion of this coastal freshening. This simple procedure of coastal seawater samples collection could further be used to monitor phytoplankton concentration, bacterial content, and isotopic composition of seawater along the Indian coastlin

Invariant higher-order variational problems II

Motivated by applications in computational anatomy, we consider a second-order problem in the calculus of variations on object manifolds that are acted upon by Lie groups of smooth invertible transformations. This problem leads to solution curves known as Riemannian cubics on object manifolds that are endowed with normal metrics. The prime examples of such object manifolds are the symmetric spaces. We characterize the class of cubics on object manifolds that can be lifted horizontally to cubics on the group of transformations. Conversely, we show that certain types of non-horizontal geodesics on the group of transformations project to cubics. Finally, we apply second-order Lagrange--Poincar\'e reduction to the problem of Riemannian cubics on the group of transformations. This leads to a reduced form of the equations that reveals the obstruction for the projection of a cubic on a transformation group to again be a cubic on its object manifold.Comment: 40 pages, 1 figure. First version -- comments welcome

Cirene : air-sea iInteractions in the Seychelles-Chagos thermocline ridge region

Author Posting. © American Meteorological Society, 2009. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Bulletin of the American Meteorological Society 90 (2009): 1337-1350, doi:10.1175/2008BAMS2499.1.The Vasco—Cirene program ex-plores how strong air—sea inter-actions promoted by the shallow thermocline and high sea surface temperature in the Seychelles—Chagos thermocline ridge results in marked variability at synoptic, intraseasonal, and interannual time scales. The Cirene oceano-graphic cruise collected oceanic, atmospheric, and air—sea flux observations in this region in Jan-uary—February 2007. The contem-poraneous Vasco field experiment complemented these measure-ments with balloon deployments from the Seychelles. Cirene also contributed to the development of the Indian Ocean observing system via deployment of a moor-ing and 12 Argo profilers. Unusual conditions prevailed in the Indian Ocean during Janu-ary and February 2007, following the Indian Ocean dipole climate anomaly of late 2006. Cirene measurements show that the Seychelles—Chagos thermocline ridge had higher-than-usual heat content with subsurface anomalies up to 7°C. The ocean surface was warmer and fresher than average, and unusual eastward currents prevailed down to 800 m. These anomalous conditions had a major impact on tuna fishing in early 2007. Our dataset also sampled the genesis and maturation of Tropical Cyclone Dora, including high surface temperatures and a strong diurnal cycle before the cyclone, followed by a 1.5°C cool-ing over 10 days. Balloonborne instruments sampled the surface and boundary layer dynamics of Dora. We observed small-scale structures like dry-air layers in the atmosphere and diurnal warm layers in the near-surface ocean. The Cirene data will quantify the impact of these finescale features on the upper-ocean heat budget and atmospheric deep convection.CNES funded the Vasco part of the experiment; INSU funded the Cirene part. R/V Suroît is an Ifremer ship. The contributions from ODU, WHOI, and FOI (Sweden) are supported by the National Science Foundation under Grant Number 0525657. The participation of the University of Miami group was funded though NASA (NNG04HZ33C). PMEL participation was supported through NOAA’s Office of Climate Observation

Climate change initiative+ (CCI+) phase 1 sea surface salinity: Product validation and intercomparison report (PVIR)

The purpose of this document (D4.1 Product Validation and Intercomparison Report, PVIR, document version v3.0) is to describe the results of the validation of the Sea Surface Salinity (SSS) products obtained during the ESA CCI+ SSS project when compared with other data sources. The PVIR is a requirement of the Statement of Work (Task 3 SoW ref. ESA-CCI-PRGM-EOPS-SW-17- 0032). The PVIR contains a list of all reference datasets used for validation of each SSS product. This report contains an assessment of both the level 4 and level 3 (ascending, descending and combined ascending plus descending) products for weekly and monthly time periods. The products are based on a temporal optimal interpolation of SSS data measured by SMOS, Aquarius-SAC and SMAP satellite missions. All products are gridded on an equal area EASE-2 grid with a grid resolution of ~25 km

COOK (Polinesia Francesa) (Morea) (Bahía). Cartas náuticas. 1878 (1876). 1:10175

Carta náutica de la Bahía de Cook, en la que se determina la batimetría, sondas y veriles, así como la calidad del fondoEscala gráfica en millas marinas, estando orientada de forma nominalPresenta gráfico de declinación magnética y mención de localización respecto a un meridiano sin determinarRepresentación del relieve con orografía de normalesLos ángulos superior e inferior derecho recogen un número referencial y el precio del documento respectivamenteCopia digital. Madrid : Ministerio de Cultura. Dirección General del Libro, Archivos y Bibliotecas, 201