Header logo is


2022


Reconstructing Expressive {3D} Humans from {RGB} Images
Reconstructing Expressive 3D Humans from RGB Images

Choutas, V.

ETH Zurich, Max Planck Institute for Intelligent Systems and ETH Zurich, December 2022 (thesis)

Abstract
To interact with our environment, we need to adapt our body posture and grasp objects with our hands. During a conversation our facial expressions and hand gestures convey important non-verbal cues about our emotional state and intentions towards our fellow speakers. Thus, modeling and capturing 3D full-body shape and pose, hand articulation and facial expressions are necessary to create realistic human avatars for augmented and virtual reality. This is a complex task, due to the large number of degrees of freedom for articulation, body shape variance, occlusions from objects and self-occlusions from body parts, e.g. crossing our hands, and subject appearance. The community has thus far relied on expensive and cumbersome equipment, such as multi-view cameras or motion capture markers, to capture the 3D human body. While this approach is effective, it is limited to a small number of subjects and indoor scenarios. Using monocular RGB cameras would greatly simplify the avatar creation process, thanks to their lower cost and ease of use. These advantages come at a price though, since RGB capture methods need to deal with occlusions, perspective ambiguity and large variations in subject appearance, in addition to all the challenges posed by full-body capture. In an attempt to simplify the problem, researchers generally adopt a divide-and-conquer strategy, estimating the body, face and hands with distinct methods using part-specific datasets and benchmarks. However, the hands and face constrain the body and vice-versa, e.g. the position of the wrist depends on the elbow, shoulder, etc.; the divide-and-conquer approach can not utilize this constraint. In this thesis, we aim to reconstruct the full 3D human body, using only readily accessible monocular RGB images. In a first step, we introduce a parametric 3D body model, called SMPL-X, that can represent full-body shape and pose, hand articulation and facial expression. Next, we present an iterative optimization method, named SMPLify-X, that fits SMPL-X to 2D image keypoints. While SMPLify-X can produce plausible results if the 2D observations are sufficiently reliable, it is slow and susceptible to initialization. To overcome these limitations, we introduce ExPose, a neural network regressor, that predicts SMPL-X parameters from an image using body-driven attention, i.e. by zooming in on the hands and face, after predicting the body. From the zoomed-in part images, dedicated part networks predict the hand and face parameters. ExPose combines the independent body, hand, and face estimates by trusting them equally. This approach though does not fully exploit the correlation between parts and fails in the presence of challenges such as occlusion or motion blur. Thus, we need a better mechanism to aggregate information from the full body and part images. PIXIE uses neural networks called moderators that learn to fuse information from these two image sets before predicting the final part parameters. Overall, the addition of the hands and face leads to noticeably more natural and expressive reconstructions. Creating high fidelity avatars from RGB images requires accurate estimation of 3D body shape. Although existing methods are effective at predicting body pose, they struggle with body shape. We identify the lack of proper training data as the cause. To overcome this obstacle, we propose to collect internet images from fashion models websites, together with anthropometric measurements. At the same time, we ask human annotators to rate images and meshes according to a pre-defined set of linguistic attributes. We then define mappings between measurements, linguistic shape attributes and 3D body shape. Equipped with these mappings, we train a neural network regressor, SHAPY, that predicts accurate 3D body shapes from a single RGB image. We observe that existing 3D shape benchmarks lack subject variety and/or ground-truth shape. Thus, we introduce a new benchmark, Human Bodies in the Wild (HBW), which contains images of humans and their corresponding 3D ground-truth body shape. SHAPY shows how we can overcome the lack of in-the-wild images with 3D shape annotations through easy-to-obtain anthropometric measurements and linguistic shape attributes. Regressors that estimate 3D model parameters are robust and accurate, but often fail to tightly fit the observations. Optimization-based approaches tightly fit the data, by minimizing an energy function composed of a data term that penalizes deviations from the observations and priors that encode our knowledge of the problem. Finding the balance between these terms and implementing a performant version of the solver is a time-consuming and non-trivial task. Machine-learned continuous optimizers combine the benefits of both regression and optimization approaches. They learn the priors directly from data, avoiding the need for hand-crafted heuristics and loss term balancing, and benefit from optimized neural network frameworks for fast inference. Inspired from the classic Levenberg-Marquardt algorithm, we propose a neural optimizer that outperforms classic optimization, regression and hybrid optimization-regression approaches. Our proposed update rule uses a weighted combination of gradient descent and a network-predicted update. To show the versatility of the proposed method, we apply it on three other problems, namely full body estimation from (i) 2D keypoints, (ii) head and hand location from a head-mounted device and (iii) face tracking from dense 2D landmarks. Our method can easily be applied to new model fitting problems and offers a competitive alternative to well-tuned traditional model fitting pipelines, both in terms of accuracy and speed. To summarize, we propose a new and richer representation of the human body, SMPL-X, that is able to jointly model the 3D human body pose and shape, facial expressions and hand articulation. We propose methods, SMPLify-X, ExPose and PIXIE that estimate SMPL-X parameters from monocular RGB images, progressively improving the accuracy and realism of the predictions. To further improve reconstruction fidelity, we demonstrate how we can use easy-to-collect internet data and human annotations to overcome the lack of 3D shape data and train a model, SHAPY, that predicts accurate 3D body shape from a single RGB image. Finally, we propose a flexible learnable update rule for parametric human model fitting that outperforms both classic optimization and neural network approaches. This approach is easily applicable to a variety of problems, unlocking new applications in AR/VR scenarios.

ps

pdf [BibTex]

2022


pdf [BibTex]


no image
Proceedings of the First Conference on Causal Learning and Reasoning (CLeaR 2022)

Schölkopf, B., Uhler, C., Zhang, K.

177, Proceedings of Machine Learning Research, PMLR, April 2022 (proceedings)

ei

link (url) [BibTex]

link (url) [BibTex]

2021


no image
Proceedings of the 1st Workshop on NLP for Positive Impact

Field, A., Prabhumoye, S., Sap, M., Jin, Z., Zhao, J., Brockett, C.

Association for Computational Linguistics, August 2021 (proceedings)

ei

link (url) [BibTex]

2021


link (url) [BibTex]

2020


no image
Voltage dependent interfacial magnetism in multilayer systems

Nacke, R.

Universität Stuttgart, Stuttgart, December 2020 (thesis)

mms

[BibTex]

2020


[BibTex]


Excursion Search for Constrained Bayesian Optimization under a Limited Budget of Failures
Excursion Search for Constrained Bayesian Optimization under a Limited Budget of Failures

Marco, A., Rohr, A. V., Baumann, D., Hernández-Lobato, J. M., Trimpe, S.

2020 (proceedings) In revision

Abstract
When learning to ride a bike, a child falls down a number of times before achieving the first success. As falling down usually has only mild consequences, it can be seen as a tolerable failure in exchange for a faster learning process, as it provides rich information about an undesired behavior. In the context of Bayesian optimization under unknown constraints (BOC), typical strategies for safe learning explore conservatively and avoid failures by all means. On the other side of the spectrum, non conservative BOC algorithms that allow failing may fail an unbounded number of times before reaching the optimum. In this work, we propose a novel decision maker grounded in control theory that controls the amount of risk we allow in the search as a function of a given budget of failures. Empirical validation shows that our algorithm uses the failures budget more efficiently in a variety of optimization experiments, and generally achieves lower regret, than state-of-the-art methods. In addition, we propose an original algorithm for unconstrained Bayesian optimization inspired by the notion of excursion sets in stochastic processes, upon which the failures-aware algorithm is built.

am ics

arXiv code (python) PDF [BibTex]

2016


no image
Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence (UAI)

Ihler, A. T., Janzing, D.

pages: 869 pages, AUAI Press, June 2016 (proceedings)

ei

link (url) [BibTex]

2016


link (url) [BibTex]

2015


Proceedings of the 37th German Conference on Pattern Recognition
Proceedings of the 37th German Conference on Pattern Recognition

Gall, J., Gehler, P., Leibe, B.

Springer, German Conference on Pattern Recognition, October 2015 (proceedings)

ps

GCPR conference website [BibTex]

2015


GCPR conference website [BibTex]


no image
Policy Search for Imitation Learning

Doerr, A.

University of Stuttgart, January 2015 (thesis)

am ics

link (url) Project Page [BibTex]

link (url) Project Page [BibTex]

2014


no image
Development of advanced methods for improving astronomical images

Schmeißer, N.

Eberhard Karls Universität Tübingen, Germany, Eberhard Karls Universität Tübingen, Germany, 2014 (diplomathesis)

ei

[BibTex]

2014


[BibTex]

2013


no image
Camera-specific Image Denoising

Schober, M.

Eberhard Karls Universität Tübingen, Germany, October 2013 (diplomathesis)

ei pn

PDF [BibTex]

2013


PDF [BibTex]


no image
Proceedings of the 10th European Workshop on Reinforcement Learning, Volume 24

Deisenroth, M., Szepesvári, C., Peters, J.

pages: 173, JMLR, European Workshop On Reinforcement Learning, EWRL, 2013 (proceedings)

ei

Web [BibTex]

Web [BibTex]

2012


no image
Machine Learning and Interpretation in Neuroimaging - Revised Selected and Invited Contributions

Langs, G., Rish, I., Grosse-Wentrup, M., Murphy, B.

pages: 266, Springer, Heidelberg, Germany, International Workshop, MLINI, Held at NIPS, 2012, Lecture Notes in Computer Science, Vol. 7263 (proceedings)

ei

DOI [BibTex]

2012


DOI [BibTex]


no image
MICCAI, Workshop on Computational Diffusion MRI, 2012 (electronic publication)

Panagiotaki, E., O’Donnell, L., Schultz, T., Zhang, G.

15th International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), Workshop on Computational Diffusion MRI , 2012 (proceedings)

ei

PDF [BibTex]

PDF [BibTex]

2011


no image
JMLR Workshop and Conference Proceedings Volume 19: COLT 2011

Kakade, S., von Luxburg, U.

pages: 834, MIT Press, Cambridge, MA, USA, 24th Annual Conference on Learning Theory , June 2011 (proceedings)

ei

Web [BibTex]

2011


Web [BibTex]

2010


no image
Inferring High-Dimensional Causal Relations using Free Probability Theory

Zscheischler, J.

Humboldt Universität Berlin, Germany, August 2010 (diplomathesis)

ei

PDF [BibTex]

2010


PDF [BibTex]


no image
Semi-supervised Subspace Learning and Application to Human Functional Magnetic Brain Resonance Imaging Data

Shelton, J.

Biologische Kybernetik, Eberhard Karls Universität, Tübingen, Germany, July 2010 (diplomathesis)

ei

PDF [BibTex]

PDF [BibTex]


no image
Quantitative Evaluation of MR-based Attenuation Correction for Positron Emission Tomography (PET)

Mantlik, F.

Biologische Kybernetik, Universität Mannheim, Germany, March 2010 (diplomathesis)

ei

[BibTex]

[BibTex]


no image
JMLR Workshop and Conference Proceedings: Volume 6

Guyon, I., Janzing, D., Schölkopf, B.

pages: 288, MIT Press, Cambridge, MA, USA, Causality: Objectives and Assessment (NIPS Workshop) , February 2010 (proceedings)

ei

Web [BibTex]

Web [BibTex]


no image
Finding Gene-Gene Interactions using Support Vector Machines

Rakitsch, B.

Eberhard Karls Universität Tübingen, Germany, 2010 (diplomathesis)

ei

[BibTex]

[BibTex]


no image
Detecting the mincut in sparse random graphs

Köhler, R.

Eberhard Karls Universität Tübingen, Germany, 2010 (diplomathesis)

ei

[BibTex]

[BibTex]

2009


no image
Motor Control and Learning in Table Tennis

Mülling, K.

Eberhard Karls Universität Tübingen, Gerrmany, 2009 (diplomathesis)

ei

[BibTex]

2009


[BibTex]


no image
Hierarchical Clustering and Density Estimation Based on k-nearest-neighbor graphs

Drewe, P.

Eberhard Karls Universität Tübingen, Germany, 2009 (diplomathesis)

ei

[BibTex]

[BibTex]

2008


no image
Reinforcement Learning for Motor Primitives

Kober, J.

Biologische Kybernetik, University of Stuttgart, Stuttgart, Germany, August 2008 (diplomathesis)

ei

PDF [BibTex]

2008


PDF [BibTex]


no image
Asymmetries of Time Series under Inverting their Direction

Peters, J.

Biologische Kybernetik, University of Heidelberg, August 2008 (diplomathesis)

ei

PDF [BibTex]

PDF [BibTex]


no image
CogRob 2008: The 6th International Cognitive Robotics Workshop

Lespérance, Y., Lakemeyer, G., Peters, J., Pirri, F.

Proceedings of the 6th International Cognitive Robotics Workshop (CogRob 2008), pages: 35, Patras University Press, Patras, Greece, 6th International Cognitive Robotics Workshop (CogRob), July 2008 (proceedings)

ei

Web [BibTex]

Web [BibTex]


no image
Pairwise Correlations and Multineuronal Firing Patterns in Primary Visual Cortex

Berens, P.

Biologische Kybernetik, Eberhard Karls Universität Tübingen, Tübingen, Germany, April 2008 (diplomathesis)

ei

[BibTex]

[BibTex]


no image
Development and Application of a Python Scripting Framework for BCI2000

Schreiner, T.

Biologische Kybernetik, Eberhard-Karls-Universität Tübingen, Tübingen, Germany, January 2008 (diplomathesis)

ei

[BibTex]

[BibTex]

2007


no image
Statistical Learning Theory Approaches to Clustering

Jegelka, S.

Biologische Kybernetik, Eberhard-Karls-Universität Tübingen, Tübingen, Germany, November 2007 (diplomathesis)

ei

PDF [BibTex]

2007


PDF [BibTex]


no image
Advances in Neural Information Processing Systems 19: Proceedings of the 2006 Conference

Schölkopf, B., Platt, J., Hofmann, T.

Proceedings of the Twentieth Annual Conference on Neural Information Processing Systems (NIPS 2006), pages: 1690, MIT Press, Cambridge, MA, USA, 20th Annual Conference on Neural Information Processing Systems (NIPS), September 2007 (proceedings)

Abstract
The annual Neural Information Processing Systems (NIPS) conference is the flagship meeting on neural computation and machine learning. It draws a diverse group of attendees--physicists, neuroscientists, mathematicians, statisticians, and computer scientists--interested in theoretical and applied aspects of modeling, simulating, and building neural-like or intelligent systems. The presentations are interdisciplinary, with contributions in algorithms, learning theory, cognitive science, neuroscience, brain imaging, vision, speech and signal processing, reinforcement learning, and applications. Only twenty-five percent of the papers submitted are accepted for presentation at NIPS, so the quality is exceptionally high. This volume contains the papers presented at the December 2006 meeting, held in Vancouver.

ei

Web [BibTex]

Web [BibTex]


no image
Error Correcting Codes for the P300 Visual Speller

Biessmann, F.

Biologische Kybernetik, Eberhard-Karls-Universität Tübingen, Tübingen, Germany, July 2007 (diplomathesis)

Abstract
The aim of brain-computer interface (BCI) research is to establish a communication system based on intentional modulation of brain activity. This is accomplished by classifying patterns of brain ac- tivity, volitionally induced by the user. The BCI presented in this study is based on a classical paradigm as proposed by (Farwell and Donchin, 1988), the P300 visual speller. Recording electroencephalo- grams (EEG) from the scalp while presenting letters successively to the user, the speller can infer from the brain signal which letter the user was focussing on. Since EEG recordings are noisy, usually many repetitions are needed to detect the correct letter. The focus of this study was to improve the accuracy of the visual speller applying some basic principles from information theory: Stimulus sequences of the speller have been modified into error-correcting codes. Additionally a language model was incorporated into the probabilistic letter de- coder. Classification of single EEG epochs was less accurate using error correcting codes. However, the novel code could compensate for that such that overall, letter accuracies were as high as or even higher than for classical stimulus codes. In particular at high noise levels, error-correcting decoding achieved higher letter accuracies.

ei

PDF [BibTex]

PDF [BibTex]


no image
A priori Knowledge from Non-Examples

Sinz, FH.

Biologische Kybernetik, Eberhard-Karls-Universität Tübingen, Tübingen, Germany, March 2007 (diplomathesis)

ei

PDF Web [BibTex]

PDF Web [BibTex]


no image
Development of a Brain-Computer Interface Approach Based on Covert Attention to Tactile Stimuli

Raths, C.

University of Tübingen, Germany, University of Tübingen, Germany, January 2007 (diplomathesis)

ei

[BibTex]

[BibTex]


no image
A Machine Learning Approach for Estimating the Attenuation Map for a Combined PET/MR Scanner

Hofmann, M.

Biologische Kybernetik, Max-Planck Institute for Biological Cybernetics, Tübingen, Germany, 2007 (diplomathesis)

ei

[BibTex]

[BibTex]

2006


no image
Advances in Neural Information Processing Systems 18: Proceedings of the 2005 Conference

Weiss, Y., Schölkopf, B., Platt, J.

Proceedings of the 19th Annual Conference on Neural Information Processing Systems (NIPS 2005), pages: 1676, MIT Press, Cambridge, MA, USA, 19th Annual Conference on Neural Information Processing Systems (NIPS), May 2006 (proceedings)

Abstract
The annual Neural Information Processing Systems (NIPS) conference is the flagship meeting on neural computation. It draws a diverse group of attendees--physicists, neuroscientists, mathematicians, statisticians, and computer scientists. The presentations are interdisciplinary, with contributions in algorithms, learning theory, cognitive science, neuroscience, brain imaging, vision, speech and signal processing, reinforcement learning and control, emerging technologies, and applications. Only twenty-five percent of the papers submitted are accepted for presentation at NIPS, so the quality is exceptionally high. This volume contains the papers presented at the December 2005 meeting, held in Vancouver.

ei

Web [BibTex]

2006


Web [BibTex]


no image
Kernel PCA for Image Compression

Huhle, B.

Biologische Kybernetik, Eberhard-Karls-Universität, Tübingen, Germany, April 2006 (diplomathesis)

ei

PDF [BibTex]

PDF [BibTex]


no image
Machine Learning Challenges: evaluating predictive uncertainty, visual object classification and recognising textual entailment

Quinonero Candela, J., Dagan, I., Magnini, B., Lauria, F.

Proceedings of the First Pascal Machine Learning Challenges Workshop on Machine Learning Challenges, Evaluating Predictive Uncertainty, Visual Object Classification and Recognizing Textual Entailment (MLCW 2005), pages: 462, Lecture Notes in Computer Science, Springer, Heidelberg, Germany, First Pascal Machine Learning Challenges Workshop (MLCW), 2006 (proceedings)

Abstract
This book constitutes the thoroughly refereed post-proceedings of the First PASCAL (pattern analysis, statistical modelling and computational learning) Machine Learning Challenges Workshop, MLCW 2005, held in Southampton, UK in April 2005. The 25 revised full papers presented were carefully selected during two rounds of reviewing and improvement from about 50 submissions. The papers reflect the concepts of three challenges dealt with in the workshop: finding an assessment base on the uncertainty of predictions using classical statistics, Bayesian inference, and statistical learning theory; the second challenge was to recognize objects from a number of visual object classes in realistic scenes; the third challenge of recognizing textual entailment addresses semantic analysis of language to form a generic framework for applied semantic inference in text understanding.

ei

Web DOI [BibTex]

Web DOI [BibTex]

2005


no image
Implicit Surfaces For Modelling Human Heads

Steinke, F.

Biologische Kybernetik, Eberhard-Karls-Universität, Tübingen, September 2005 (diplomathesis)

ei

[BibTex]

2005


[BibTex]


no image
Efficient Adaptive Sampling of the Psychometric Function by Maximizing Information Gain

Tanner, TG.

Biologische Kybernetik, Eberhard-Karls University Tübingen, Tübingen, Germany, May 2005 (diplomathesis)

Abstract
A common task in psychophysics is to measure the psychometric function. A psychometric function can be described by its shape and four parameters: offset or threshold, slope or width, false alarm rate or chance level and miss or lapse rate. Depending on the parameters of interest some points on the psychometric function may be more informative than others. Adaptive methods attempt to place trials on the most informative points based on the data collected in previous trials. A new Bayesian adaptive psychometric method placing trials by minimising the expected entropy of the posterior probabilty dis- tribution over a set of possible stimuli is introduced. The method is more flexible, faster and at least as efficient as the established method (Kontsevich and Tyler, 1999). Comparably accurate (2dB) threshold and slope estimates can be obtained after about 30 and 500 trials, respectively. By using a dynamic termination criterion the efficiency can be further improved. The method can be applied to all experimental designs including yes/no designs and allows acquisition of any set of free parameters. By weighting the importance of parameters one can include nuisance parameters and adjust the relative expected errors. Use of nuisance parameters may lead to more accurate estimates than assuming a guessed fixed value. Block designs are supported and do not harm the performance if a sufficient number of trials are performed. The method was evaluated by computer simulations in which the role of parametric assumptions, its robustness, the quality of different point estimates, the effect of dynamic termination criteria and many other settings were investigated.

ei

[BibTex]

[BibTex]

2004


no image
Advanced Lectures on Machine Learning

Bousquet, O., von Luxburg, U., Rätsch, G.

ML Summer Schools 2003, LNAI 3176, pages: 240, Springer, Berlin, Germany, ML Summer Schools, September 2004 (proceedings)

Abstract
Machine Learning has become a key enabling technology for many engineering applications, investigating scientific questions and theoretical problems alike. To stimulate discussions and to disseminate new results, a summer school series was started in February 2002, the documentation of which is published as LNAI 2600. This book presents revised lectures of two subsequent summer schools held in 2003 in Canberra, Australia, and in T{\"u}bingen, Germany. The tutorial lectures included are devoted to statistical learning theory, unsupervised learning, Bayesian inference, and applications in pattern recognition; they provide in-depth overviews of exciting new developments and contain a large number of references. Graduate students, lecturers, researchers and professionals alike will find this book a useful resource in learning and teaching machine learning.

ei

Web [BibTex]

2004


Web [BibTex]


no image
Pattern Recognition: 26th DAGM Symposium, LNCS, Vol. 3175

Rasmussen, C., Bülthoff, H., Giese, M., Schölkopf, B.

Proceedings of the 26th Pattern Recognition Symposium (DAGM‘04), pages: 581, Springer, Berlin, Germany, 26th Pattern Recognition Symposium, August 2004 (proceedings)

ei

Web DOI [BibTex]

Web DOI [BibTex]


no image
Advances in Neural Information Processing Systems 16: Proceedings of the 2003 Conference

Thrun, S., Saul, L., Schölkopf, B.

Proceedings of the Seventeenth Annual Conference on Neural Information Processing Systems (NIPS 2003), pages: 1621, MIT Press, Cambridge, MA, USA, 17th Annual Conference on Neural Information Processing Systems (NIPS), June 2004 (proceedings)

Abstract
The annual Neural Information Processing (NIPS) conference is the flagship meeting on neural computation. It draws a diverse group of attendees—physicists, neuroscientists, mathematicians, statisticians, and computer scientists. The presentations are interdisciplinary, with contributions in algorithms, learning theory, cognitive science, neuroscience, brain imaging, vision, speech and signal processing, reinforcement learning and control, emerging technologies, and applications. Only thirty percent of the papers submitted are accepted for presentation at NIPS, so the quality is exceptionally high. This volume contains all the papers presented at the 2003 conference.

ei

Web [BibTex]

Web [BibTex]

2003


no image
Learning Theory and Kernel Machines: 16th Annual Conference on Learning Theory and 7th Kernel Workshop (COLT/Kernel 2003), LNCS Vol. 2777

Schölkopf, B., Warmuth, M.

Proceedings of the 16th Annual Conference on Learning Theory and 7th Kernel Workshop (COLT/Kernel 2003), COLT/Kernel 2003, pages: 746, Springer, Berlin, Germany, 16th Annual Conference on Learning Theory and 7th Kernel Workshop, November 2003, Lecture Notes in Computer Science ; 2777 (proceedings)

ei

DOI [BibTex]

2003


DOI [BibTex]


no image
Real-Time Face Detection

Kienzle, W.

Biologische Kybernetik, Eberhard-Karls-Universitaet Tuebingen, Tuebingen, Germany, October 2003 (diplomathesis)

ei

[BibTex]

[BibTex]


no image
m-Alternative Forced Choice—Improving the Efficiency of the Method of Constant Stimuli

Jäkel, F.

Biologische Kybernetik, Graduate School for Neural and Behavioural Sciences, Tübingen, 2003 (diplomathesis)

ei

[BibTex]

[BibTex]

2001


no image
Variationsverfahren zur Untersuchung von Grundzustandseigenschaften des Ein-Band Hubbard-Modells

Eichhorn, J.

Biologische Kybernetik, Technische Universität Dresden, Dresden/Germany, May 2001 (diplomathesis)

Abstract
Using different modifications of a new variational approach, statical groundstate properties of the one-band Hubbard model such as energy and staggered magnetisation are calculated. By taking into account additional fluctuations, the method ist gradually improved so that a very good description of the energy in one and two dimensions can be achieved. After a detailed discussion of the application in one dimension, extensions for two dimensions are introduced. By use of a modified version of the variational ansatz in particular a description of the quantum phase transition for the magnetisation should be possible.

ei

PostScript [BibTex]

2001


PostScript [BibTex]