Kernel density correlation based non-rigid point set matching for statistical model-based 2D/3D reconstruction

This paper presents a kernel density correlation based nonrigid point set matching method and shows its application in statistical model based 2D/3D reconstruction of a scaled, patient-specific model from an un-calibrated x-ray radiograph. In this method, both the reference point set and the floating point set are first represented using kernel density estimates. A correlation measure between these two kernel density estimates is then optimized to find a displacement field such that the floating point set is moved to the reference point set. Regularizations based on the overall deformation energy and the motion smoothness energy are used to constraint the displacement field for a robust point set matching. Incorporating this non-rigid point set matching method into a statistical model based 2D/3D reconstruction framework, we can reconstruct a scaled, patient-specific model from noisy edge points that are extracted directly from the x-ray radiograph by an edge detector. Our experiment conducted on datasets of two patients and six cadavers demonstrates a mean reconstruction error of 1.9 mm

Personalized X-Ray Reconstruction of the Proximal Femur via Intensity-Based Non-rigid 2D-3D Registration

This paper presents a new approach for reconstructing a patient-specific shape model and internal relative intensity distribution of the proximal femur from a limited number (e.g., 2) of calibrated C-arm images or X-ray radiographs. Our approach uses independent shape and appearance models that are learned from a set of training data to encode the a priori information about the proximal femur. An intensity-based non-rigid 2D-3D registration algorithm is then proposed to deformably fit the learned models to the input images. The fitting is conducted iteratively by minimizing the dissimilarity between the input images and the associated digitally reconstructed radiographs of the learned models together with regularization terms encoding the strain energy of the forward deformation and the smoothness of the inverse deformation. Comprehensive experiments conducted on images of cadaveric femurs and on clinical datasets demonstrate the efficacy of the present approach.

From EEG dependency multichannel matching pursuit to sparse topographic EEG decomposition

In this work, we present a multichannel EEG decomposition model based on an adaptive topographic time-frequency approximation technique. It is an extension of the Matching Pursuit algorithm and called dependency multichannel matching pursuit (DMMP). It takes the physiologically explainable and statistically observable topographic dependencies between the channels into account, namely the spatial smoothness of neighboring electrodes that is implied by the electric leadfield. DMMP decomposes a multichannel signal as a weighted sum of atoms from a given dictionary where the single channels are represented from exactly the same subset of a complete dictionary. The decomposition is illustrated on topographical EEG data during different physiological conditions using a complete Gabor dictionary. Further the extension of the single-channel time-frequency distribution to a multichannel time-frequency distribution is given. This can be used for the visualization of the decomposition structure of multichannel EEG. A clustering procedure applied to the topographies, the vectors of the corresponding contribution of an atom to the signal in each channel produced by DMMP, leads to an extremely sparse topographic decomposition of the EEG.

Topographic time-frequency decomposition of the EEG

Frequency-transformed EEG resting data has been widely used to describe normal and abnormal brain functional states as function of the spectral power in different frequency bands. This has yielded a series of clinically relevant findings. However, by transforming the EEG into the frequency domain, the initially excellent time resolution of time-domain EEG is lost. The topographic time-frequency decomposition is a novel computerized EEG analysis method that combines previously available techniques from time-domain spatial EEG analysis and time-frequency decomposition of single-channel time series. It yields a new, physiologically and statistically plausible topographic time-frequency representation of human multichannel EEG. The original EEG is accounted by the coefficients of a large set of user defined EEG like time-series, which are optimized for maximal spatial smoothness and minimal norm. These coefficients are then reduced to a small number of model scalp field configurations, which vary in intensity as a function of time and frequency. The result is thus a small number of EEG field configurations, each with a corresponding time-frequency (Wigner) plot. The method has several advantages: It does not assume that the data is composed of orthogonal elements, it does not assume stationarity, it produces topographical maps and it allows to include user-defined, specific EEG elements, such as spike and wave patterns. After a formal introduction of the method, several examples are given, which include artificial data and multichannel EEG during different physiological and pathological conditions.

A new Bayesian approach to the reconstruction of spectral functions

We present a novel approach for the reconstruction of spectra from Euclidean correlator data that makes close contact to modern Bayesian concepts. It is based upon an axiomatically justified dimensionless prior distribution, which in the case of constant prior function m(ω) only imprints smoothness on the reconstructed spectrum. In addition we are able to analytically integrate out the only relevant overall hyper-parameter α in the prior, removing the necessity for Gaussian approximations found e.g. in the Maximum Entropy Method. Using a quasi-Newton minimizer and high-precision arithmetic, we are then able to find the unique global extremum of P[ρ|D] in the full Nω » Nτ dimensional search space. The method actually yields gradually improving reconstruction results if the quality of the supplied input data increases, without introducing artificial peak structures, often encountered in the MEM. To support these statements we present mock data analyses for the case of zero width delta peaks and more realistic scenarios, based on the perturbative Euclidean Wilson Loop as well as the Wilson Line correlator in Coulomb gauge.

The hp-adaptive FEM based on continuous Sobolev embeddings: isotropic refinements

The aim of this paper is to present a new class of smoothness testing strategies in the context of hp-adaptive refinements based on continuous Sobolev embeddings. In addition to deriving a modified form of the 1d smoothness indicators introduced in [26], they will be extended and applied to a higher dimensional framework. A few numerical experiments in the context of the hp-adaptive FEM for a linear elliptic PDE will be performed.

Localization and Segmentation of 3D Intervertebral Discs in MR Images by Data Driven Estimation

This paper addresses the problem of fully-automatic localization and segmentation of 3D intervertebral discs (IVDs) from MR images. Our method contains two steps, where we first localize the center of each IVD, and then segment IVDs by classifying image pixels around each disc center as foreground (disc) or background. The disc localization is done by estimating the image displacements from a set of randomly sampled 3D image patches to the disc center. The image displacements are estimated by jointly optimizing the training and test displacement values in a data-driven way, where we take into consideration both the training data and the geometric constraint on the test image. After the disc centers are localized, we segment the discs by classifying image pixels around disc centers as background or foreground. The classification is done in a similar data-driven approach as we used for localization, but in this segmentation case we are aiming to estimate the foreground/background probability of each pixel instead of the image displacements. In addition, an extra neighborhood smooth constraint is introduced to enforce the local smoothness of the label field. Our method is validated on 3D T2-weighted turbo spin echo MR images of 35 patients from two different studies. Experiments show that compared to state of the art, our method achieves better or comparable results. Specifically, we achieve for localization a mean error of 1.6-2.0 mm, and for segmentation a mean Dice metric of 85%-88% and a mean surface distance of 1.3-1.4 mm.

Temporally Coherent Disparity Maps Using CRFs with Fast 4D Filtering

State of the art methods for disparity estimation achieve good results for single stereo frames, but temporal coherence in stereo videos is often neglected. In this paper we present a method to compute temporally coherent disparity maps. We define an energy over whole stereo sequences and optimize their Conditional Random Field (CRF) distributions using mean-field approximation. We introduce novel terms for smoothness and consistency between the left and right views, and perform CRF optimization by fast, iterative spatio-temporal filtering with linear complexity in the total number of pixels. Our results rank among the state of the art while having significantly less flickering artifacts in stereo sequences.