Real-Time Joint Coupling of the Spine for Inverse Kinematics

In this paper we propose a simple model for the coupling behavior of the human spine for an inverse kinematics framework. Our spine model exhibits anatomically correct motions of the vertebrae of virtual mannequins by coupling standard swing and revolute joint models. The adjustement of the joints is made with several simple (in)equality constraints, resulting in a reduction of the solution space dimensionality for the inverse kinematics solver. By reducing the solution space dimensionality to feasible spine shapes, we prevent the inverse kinematics algorithm from providing infeasible postures for the spine.In this paper, we exploit how to apply these simple constraints to the human spine by a strict decoupling of the swing and torsion motion of the vertebrae. We demonstrate the validity of our approach on various experiments.

Distance-based kriging relying on proxy simulations for inverse conditioning

Let us consider a large set of candidate parameter fields, such as hydraulic conductivity maps, on which we can run an accurate forward flow and transport simulation. We address the issue of rapidly identifying a subset of candidates whose response best match a reference response curve. In order to keep the number of calls to the accurate flow simulator computationally tractable, a recent distance-based approach relying on fast proxy simulations is revisited, and turned into a non-stationary kriging method where the covariance kernel is obtained by combining a classical kernel with the proxy. Once the accurate simulator has been run for an initial subset of parameter fields and a kriging metamodel has been inferred, the predictive distributions of misfits for the remaining parameter fields can be used as a guide to select candidate parameter fields in a sequential way. The proposed algorithm, Proxy-based Kriging for Sequential Inversion (ProKSI), relies on a variant of the Expected Improvement, a popular criterion for kriging-based global optimization. A statistical benchmark of ProKSI’s performances illustrates the efficiency and the robustness of the approach when using different kinds of proxies.

Inverse relationship between fractionated electrograms and atrial fibrosis in persistent atrial fibrillation: combined magnetic resonance imaging and high-density mapping

OBJECTIVES This study sought to evaluate the relationship between fibrosis imaged by delayed-enhancement (DE) magnetic resonance imaging (MRI) and atrial electrograms (Egms) in persistent atrial fibrillation (AF). BACKGROUND Atrial fractionated Egms are strongly related to slow anisotropic conduction. Their relationship to atrial fibrosis has not yet been investigated. METHODS Atrial high-resolution MRI of 18 patients with persistent AF (11 long-lasting persistent AF) was registered with mapping geometry (NavX electro-anatomical system (version 8.0, St. Jude Medical, St. Paul, Minnesota)). DE areas were categorized as dense or patchy, depending on their DE content. Left atrial Egms during AF were acquired using a high-density, 20-pole catheter (514 ± 77 sites/map). Fractionation, organization/regularity, local mean cycle length (CL), and voltage were analyzed with regard to DE. RESULTS Patients with long-lasting persistent versus persistent AF had larger left atrial (LA) surface area (134 ± 38 cm(2) vs. 98 ± 9 cm(2), p = 0.02), a higher amount of atrial DE (70 ± 16 cm(2) vs. 49 ± 10 cm(2), p = 0.01), more complex fractionated atrial Egm (CFAE) extent (54 ± 16 cm(2) vs. 28 ± 15 cm(2), p = 0.02), and a shorter baseline AF CL (147 ± 10 ms vs. 182 ± 14 ms, p = 0.01). Continuous CFAE (CFEmean [NavX algorithm that quantifies Egm fractionation] <80 ms) occupied 38 ± 19% of total LA surface area. Dense DE was detected at the left posterior left atrium. In contrast, the right posterior left atrium contained predominantly patchy DE. Most CFAE (48 ± 14%) occurred at non-DE LA sites, followed by 41 ± 12% CFAE at patchy DE and 11 ± 6% at dense DE regions (p = 0.005 and p = 0.008, respectively); 19 ± 6% CFAE sites occurred at border zones of dense DE. Egms were less fractionated, with longer CL and lower voltage at dense DE versus non-DE regions: CFEmean: 97 ms versus 76 ms, p < 0.0001; local CL: 153 ms versus 143 ms, p < 0.0001; mean voltage: 0.63 mV versus 0.86 mV, p < 0.0001. CONCLUSIONS Atrial fibrosis as defined by DE MRI is associated with slower and more organized electrical activity but with lower voltage than healthy atrial areas. Ninety percent of continuous CFAE sites occur at non-DE and patchy DE LA sites. These findings are important when choosing the ablation strategy in persistent AF.

Symmetric inverse consistent nonlinear registration driven by mutual information.

A nonlinear viscoelastic image registration algorithm based on the demons paradigm and incorporating inverse consistent constraint (ICC) is implemented. An inverse consistent and symmetric cost function using mutual information (MI) as a similarity measure is employed. The cost function also includes regularization of transformation and inverse consistent error (ICE). The uncertainties in balancing various terms in the cost function are avoided by alternatively minimizing the similarity measure, the regularization of the transformation, and the ICE terms. The diffeomorphism of registration for preventing folding and/or tearing in the deformation is achieved by the composition scheme. The quality of image registration is first demonstrated by constructing brain atlas from 20 adult brains (age range 30-60). It is shown that with this registration technique: (1) the Jacobian determinant is positive for all voxels and (2) the average ICE is around 0.004 voxels with a maximum value below 0.1 voxels. Further, the deformation-based segmentation on Internet Brain Segmentation Repository, a publicly available dataset, has yielded high Dice similarity index (DSI) of 94.7% for the cerebellum and 74.7% for the hippocampus, attesting to the quality of our registration method.

An evolutionary algorithm for the surface structure problem

Many macroscopic properties: hardness, corrosion, catalytic activity, etc. are directly related to the surface structure, that is, to the position and chemical identity of the outermost atoms of the material. Current experimental techniques for its determination produce a “signature” from which the structure must be inferred by solving an inverse problem: a solution is proposed, its corresponding signature computed and then compared to the experiment. This is a challenging optimization problem where the search space and the number of local minima grows exponentially with the number of atoms, hence its solution cannot be achieved for arbitrarily large structures. Nowadays, it is solved by using a mixture of human knowledge and local search techniques: an expert proposes a solution that is refined using a local minimizer. If the outcome does not fit the experiment, a new solution must be proposed again. Solving a small surface can take from days to weeks of this trial and error method. Here we describe our ongoing work in its solution. We use an hybrid algorithm that mixes evolutionary techniques with trusted region methods and reuses knowledge gained during the execution to avoid repeated search of structures. Its parallelization produces good results even when not requiring the gathering of the full population, hence it can be used in loosely coupled environments such as grids. With this algorithm, the solution of test cases that previously took weeks of expert time can be automatically solved in a day or two of uniprocessor time.

A guided heuristic approach to the MEG inverse problem.

There is general agreement within the scientific community in considering Biology as the science with more potential to develop in the XXI century. This is due to several reasons, but probably the most important one is the state of development of the rest of experimental and technological sciences. In this context, there are a very rich variety of mathematical tools, physical techniques and computer resources that permit to do biological experiments that were unbelievable only a few years ago. Biology is nowadays taking advantage of all these newly developed technologies, which are been applied to life sciences opening new research fields and helping to give new insights in many biological problems. Consequently, biologists have improved a lot their knowledge in many key areas as human function and human diseases. However there is one human organ that is still barely understood compared with the rest: The human brain. The understanding of the human brain is one of the main challenges of the XXI century. In this regard, it is considered a strategic research field for the European Union and the USA. Thus, there is a big interest in applying new experimental techniques for the study of brain function. Magnetoencephalography (MEG) is one of these novel techniques that are currently applied for mapping the brain activity1. This technique has important advantages compared to the metabolic-based brain imagining techniques like Functional Magneto Resonance Imaging2 (fMRI). The main advantage is that MEG has a higher time resolution than fMRI. Another benefit of MEG is that it is a patient friendly clinical technique. The measure is performed with a wireless set up and the patient is not exposed to any radiation. Although MEG is widely applied in clinical studies, there are still open issues regarding data analysis. The present work deals with the solution of the inverse problem in MEG, which is the most controversial and uncertain part of the analysis process3. This question is addressed using several variations of a new solving algorithm based in a heuristic method. The performance of those methods is analyzed by applying them to several test cases with known solutions and comparing those solutions with the ones provided by our methods.

Novel fast random search clustering approach for mixing matrix identification in MIMO linear blind inverse problems with sparse inputs

In this paper we propose a novel fast random search clustering (RSC) algorithm for mixing matrix identification in multiple input multiple output (MIMO) linear blind inverse problems with sparse inputs. The proposed approach is based on the clustering of the observations around the directions given by the columns of the mixing matrix that occurs typically for sparse inputs. Exploiting this fact, the RSC algorithm proceeds by parameterizing the mixing matrix using hyperspherical coordinates, randomly selecting candidate basis vectors (i.e. clustering directions) from the observations, and accepting or rejecting them according to a binary hypothesis test based on the Neyman–Pearson criterion. The RSC algorithm is not tailored to any specific distribution for the sources, can deal with an arbitrary number of inputs and outputs (thus solving the difficult under-determined problem), and is applicable to both instantaneous and convolutive mixtures. Extensive simulations for synthetic and real data with different number of inputs and outputs, data size, sparsity factors of the inputs and signal to noise ratios confirm the good performance of the proposed approach under moderate/high signal to noise ratios. RESUMEN. Método de separación ciega de fuentes para señales dispersas basado en la identificación de la matriz de mezcla mediante técnicas de "clustering" aleatorio.

Integration of robotic inverse kinematic routines in an algorithmic 3D modeling software

An industrial manipulator equipped with an automatic clay extruder is used to realize a machine that can manufacture additively clay objects. The desired geometries are designed by means of a 3D modeling software and then sliced in a sequence of layers with the same thickness of the extruded clay section. The profiles of each layer are transformed in trajectories for the extruder and therefore for the end-effector of the manipulator. The goal of this thesis is to improve the algorithm for the inverse kinematic resolution and the integration of the routine within the development software that controls the machine (Rhino/Grasshopper). The kinematic model is described by homogeneous transformations, adopting the Denavit-Hartenberg standard convention. The function is implemented in C# and it has been preliminarily tested in Matlab. The outcome of this work is a substantial reduction of the computation time relative to the execution of the algorithm, which is halved.

A verifiable solution to the MEG inverse problem

Magnetoencephalography (MEG) is a non-invasive brain imaging technique with the potential for very high temporal and spatial resolution of neuronal activity. The main stumbling block for the technique has been that the estimation of a neuronal current distribution, based on sensor data outside the head, is an inverse problem with an infinity of possible solutions. Many inversion techniques exist, all using different a-priori assumptions in order to reduce the number of possible solutions. Although all techniques can be thoroughly tested in simulation, implicit in the simulations are the experimenter's own assumptions about realistic brain function. To date, the only way to test the validity of inversions based on real MEG data has been through direct surgical validation, or through comparison with invasive primate data. In this work, we constructed a null hypothesis that the reconstruction of neuronal activity contains no information on the distribution of the cortical grey matter. To test this, we repeatedly compared rotated sections of grey matter with a beamformer estimate of neuronal activity to generate a distribution of mutual information values. The significance of the comparison between the un-rotated anatomical information and the electrical estimate was subsequently assessed against this distribution. We found that there was significant (P < 0.05) anatomical information contained in the beamformer images across a number of frequency bands. Based on the limited data presented here, we can say that the assumptions behind the beamformer algorithm are not unreasonable for the visual-motor task investigated.

Bayesian analysis of the scatterometer wind retrieval inverse problem:Some new approaches

The retrieval of wind vectors from satellite scatterometer observations is a non-linear inverse problem. A common approach to solving inverse problems is to adopt a Bayesian framework and to infer the posterior distribution of the parameters of interest given the observations by using a likelihood model relating the observations to the parameters, and a prior distribution over the parameters. We show how Gaussian process priors can be used efficiently with a variety of likelihood models, using local forward (observation) models and direct inverse models for the scatterometer. We present an enhanced Markov chain Monte Carlo method to sample from the resulting multimodal posterior distribution. We go on to show how the computational complexity of the inference can be controlled by using a sparse, sequential Bayes algorithm for estimation with Gaussian processes. This helps to overcome the most serious barrier to the use of probabilistic, Gaussian process methods in remote sensing inverse problems, which is the prohibitively large size of the data sets. We contrast the sampling results with the approximations that are found by using the sparse, sequential Bayes algorithm.

On a Direct Approach to the Solution of Inverse Optical Problems

The evaluation from experimental data, of physical quantities, which enter into the electromagnetic Maxwell equations, is described as inverse optical problem. The functional relations between the dependent and independent variables are of transcendental character and numeric procedures for evaluation of the unknowns are largely used. Herein, we discuss a direct approach to the solution, illustrated by a specific example of determination of thin films optical constants from spectrophotometric data. New algorithm is proposed for the parameters evaluation, which does not need an initial guess of the unknowns and does not use iterative procedures. Thus we overcome the intrinsic deficiency of minimization techniques, such as gradient search methods, Simplex methods, etc. The price of it is a need of more computing power, but our algorithm is easily implemented in structures such as grid clusters. We show the advantages of this approach and its potential for generalization to other inverse optical problems.

Self-tuning algorithm for dsp-based motion control in cnc applications

This thesis describes the development of an adaptive control algorithm for Computerized Numerical Control (CNC) machines implemented in a multi-axis motion control board based on the TMS320C31 DSP chip. The adaptive process involves two stages: Plant Modeling and Inverse Control Application. The first stage builds a non-recursive model of the CNC system (plant) using the Least-Mean-Square (LMS) algorithm. The second stage consists of the definition of a recursive structure (the controller) that implements an inverse model of the plant by using the coefficients of the model in an algorithm called Forward-Time Calculation (FTC). In this way, when the inverse controller is implemented in series with the plant, it will pre-compensate for the modification that the original plant introduces in the input signal. The performance of this solution was verified at three different levels: Software simulation, implementation in a set of isolated motor-encoder pairs and implementation in a real CNC machine. The use of the adaptive inverse controller effectively improved the step response of the system in all three levels. In the simulation, an ideal response was obtained. In the motor-encoder test, the rise time was reduced by as much as 80%, without overshoot, in some cases. Even with the larger mass of the actual CNC machine, decrease of the rise time and elimination of the overshoot were obtained in most cases. These results lead to the conclusion that the adaptive inverse controller is a viable approach to position control in CNC machinery.

Tensor Completion for Multidimensional Inverse Problems with Applications to Magnetic Resonance Relaxometry

This thesis deals with tensor completion for the solution of multidimensional inverse problems. We study the problem of reconstructing an approximately low rank tensor from a small number of noisy linear measurements. New recovery guarantees, numerical algorithms, non-uniform sampling strategies, and parameter selection algorithms are developed. We derive a fixed point continuation algorithm for tensor completion and prove its convergence. A restricted isometry property (RIP) based tensor recovery guarantee is proved. Probabilistic recovery guarantees are obtained for sub-Gaussian measurement operators and for measurements obtained by non-uniform sampling from a Parseval tight frame. We show how tensor completion can be used to solve multidimensional inverse problems arising in NMR relaxometry. Algorithms are developed for regularization parameter selection, including accelerated k-fold cross-validation and generalized cross-validation. These methods are validated on experimental and simulated data. We also derive condition number estimates for nonnegative least squares problems. Tensor recovery promises to significantly accelerate N-dimensional NMR relaxometry and related experiments, enabling previously impractical experiments. Our methods could also be applied to other inverse problems arising in machine learning, image processing, signal processing, computer vision, and other fields.

Inverse identification of the bending stiffness of a braided polyethylene twine subject to large deformation: application to the identification of the mesh opening rigidity of fishing nets.

The evaluation of the mesh opening stiffness of fishing nets is an important issue in assessing the selectivity of trawls. It appeared that a larger bending rigidity of twines decreases the mesh opening and could reduce the escapement of fish. Nevertheless, netting structure is complex. A netting is made up of braided twines made of polyethylene or polyamide. These twines are tied with non-symmetrical knots. Thus, these assemblies develop contact-friction interactions. Moreover, the netting can be subject to large deformation. In this study, we investigate the responses of netting samples to different types of solicitations. Samples are loaded and unloaded with creep and relaxation stages, with different boundary conditions. Then, two models have been developed: an analytical model and a finite element model. The last one was used to assess, with an inverse identification algorithm, the bending stiffness of twines. In this paper, experimental results and a model for netting structures made up of braided twines are presented. During dry forming of a composite, for example, the matrix is not present or not active, and relative sliding can occur between constitutive fibres. So an accurate modelling of the mechanical behaviour of fibrous material is necessary. This study offers experimental data which could permit to improve current models of contact-friction interactions [4], to validate models for large deformation analysis of fibrous materials [1] on a new experimental case, then to improve the evaluation of the mesh opening stiffness of a fishing net

Geological realism in hydrogeological and geophysical inverse modeling: A review

Scientific curiosity, exploration of georesources and environmental concerns are pushing the geoscientific research community toward subsurface investigations of ever-increasing complexity. This review explores various approaches to formulate and solve inverse problems in ways that effectively integrate geological concepts with geophysical and hydrogeological data. Modern geostatistical simulation algorithms can produce multiple subsurface realizations that are in agreement with conceptual geological models and statistical rock physics can be used to map these realizations into physical properties that are sensed by the geophysical or hydrogeological data. The inverse problem consists of finding one or an ensemble of such subsurface realizations that are in agreement with the data. The most general inversion frameworks are presently often computationally intractable when applied to large-scale problems and it is necessary to better understand the implications of simplifying (1) the conceptual geological model (e.g., using model compression); (2) the physical forward problem (e.g., using proxy models); and (3) the algorithm used to solve the inverse problem (e.g., Markov chain Monte Carlo or local optimization methods) to reach practical and robust solutions given today's computer resources and knowledge. We also highlight the need to not only use geophysical and hydrogeological data for parameter estimation purposes, but also to use them to falsify or corroborate alternative geological scenarios.