Comparison of climate field reconstruction techniques: Application to Europe

This paper presents a comparison of principal component (PC) regression and regularized expectation maximization (RegEM) to reconstruct European summer and winter surface air temperature over the past millennium. Reconstruction is performed within a surrogate climate using the National Center for Atmospheric Research (NCAR) Climate System Model (CSM) 1.4 and the climate model ECHO-G 4, assuming different white and red noise scenarios to define the distortion of pseudoproxy series. We show how sensitivity tests lead to valuable “a priori” information that provides a basis for improving real world proxy reconstructions. Our results emphasize the need to carefully test and evaluate reconstruction techniques with respect to the temporal resolution and the spatial scale they are applied to. Furthermore, we demonstrate that uncertainties inherent to the predictand and predictor data have to be more rigorously taken into account. The comparison of the two statistical techniques, in the specific experimental setting presented here, indicates that more skilful results are achieved with RegEM as low frequency variability is better preserved. We further detect seasonal differences in reconstruction skill for the continental scale, as e.g. the target temperature average is more adequately reconstructed for summer than for winter. For the specific predictor network given in this paper, both techniques underestimate the target temperature variations to an increasing extent as more noise is added to the signal, albeit RegEM less than with PC regression. We conclude that climate field reconstruction techniques can be improved and need to be further optimized in future applications.

Hierarchical segmentation-assisted multimodal registration for MR brain images

Information theory-based metric such as mutual information (MI) is widely used as similarity measurement for multimodal registration. Nevertheless, this metric may lead to matching ambiguity for non-rigid registration. Moreover, maximization of MI alone does not necessarily produce an optimal solution. In this paper, we propose a segmentation-assisted similarity metric based on point-wise mutual information (PMI). This similarity metric, termed SPMI, enhances the registration accuracy by considering tissue classification probabilities as prior information, which is generated from an expectation maximization (EM) algorithm. Diffeomorphic demons is then adopted as the registration model and is optimized in a hierarchical framework (H-SPMI) based on different levels of anatomical structure as prior knowledge. The proposed method is evaluated using Brainweb synthetic data and clinical fMRI images. Both qualitative and quantitative assessment were performed as well as a sensitivity analysis to the segmentation error. Compared to the pure intensity-based approaches which only maximize mutual information, we show that the proposed algorithm provides significantly better accuracy on both synthetic and clinical data.

Expectation Conditional Maximization-Based Deformable Shape Registration

This paper addresses the issue of matching statistical and non-rigid shapes, and introduces an Expectation Conditional Maximization-based deformable shape registration (ECM-DSR) algorithm. Similar to previous works, we cast the statistical and non-rigid shape registration problem into a missing data framework and handle the unknown correspondences with Gaussian Mixture Models (GMM). The registration problem is then solved by fitting the GMM centroids to the data. But unlike previous works where equal isotropic covariances are used, our new algorithm uses heteroscedastic covariances whose values are iteratively estimated from the data. A previously introduced virtual observation concept is adopted here to simplify the estimation of the registration parameters. Based on this concept, we derive closed-form solutions to estimate parameters for statistical or non-rigid shape registrations in each iteration. Our experiments conducted on synthesized and real data demonstrate that the ECM-DSR algorithm has various advantages over existing algorithms.

Unifying energy minimization and mutual information maximization for robust 2D/3D registration of X-ray and CT images

Similarity measure is one of the main factors that affect the accuracy of intensity-based 2D/3D registration of X-ray fluoroscopy to CT images. Information theory has been used to derive similarity measure for image registration leading to the introduction of mutual information, an accurate similarity measure for multi-modal and mono-modal image registration tasks. However, it is known that the standard mutual information measure only takes intensity values into account without considering spatial information and its robustness is questionable. Previous attempt to incorporate spatial information into mutual information either requires computing the entropy of higher dimensional probability distributions, or is not robust to outliers. In this paper, we show how to incorporate spatial information into mutual information without suffering from these problems. Using a variational approximation derived from the Kullback-Leibler bound, spatial information can be effectively incorporated into mutual information via energy minimization. The resulting similarity measure has a least-squares form and can be effectively minimized by a multi-resolution Levenberg-Marquardt optimizer. Experimental results are presented on datasets of two applications: (a) intra-operative patient pose estimation from a few (e.g. 2) calibrated fluoroscopic images, and (b) post-operative cup alignment estimation from single X-ray radiograph with gonadal shielding.

Estimating and quantifying uncertainties on level sets using the Vorob'ev expectation and deviation with Gaussian process models

Several methods based on Kriging have recently been proposed for calculating a probability of failure involving costly-to-evaluate functions. A closely related problem is to estimate the set of inputs leading to a response exceeding a given threshold. Now, estimating such a level set—and not solely its volume—and quantifying uncertainties on it are not straightforward. Here we use notions from random set theory to obtain an estimate of the level set, together with a quantification of estimation uncertainty. We give explicit formulae in the Gaussian process set-up and provide a consistency result. We then illustrate how space-filling versus adaptive design strategies may sequentially reduce level set estimation uncertainty.

Disentangling mental imagery and perceptual expectation

Mental imagery and perception are thought to rely on similar neural circuits, and many recent behavioral studies have attempted to demonstrate interactions between actual physical stimulation and sensory imagery in the corresponding sensory modality. However, there has been a lack of theoretical understanding of the nature of these interactions, and both interferential and facilitatory effects have been found. Facilitatory effects appear strikingly similar to those that arise due to experimental manipulations of expectation. Using a self-motion discrimination task, we try to disentangle the effects of mental imagery from those of expectation by using a hierarchical drift diffusion model to investigate both choice data and response times. Manipulations of expectation are reasonably well understood in terms of their selective influence on parameters of the drift diffusion model, and in this study, we make the first attempt to similarly characterize the effects of mental imagery. We investigate mental imagery within the computational framework of control theory and state estimation. • Mental imagery and perception are thought to rely on similar neural circuits; however, on more theoretical grounds, imagery seems to be closely related to the output of forward models (sensory predictions). • We reanalyzed data from a study of imagined self-motion. • Bayesian modeling of response times may allow us to disentangle the effects of mental imagery on behavior from other cognitive (top-down) effects, such as expectation.