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51 results (View BibTeX file of all listed publications)

2017

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Improving performance of linear field generation with multi-coil setup by optimizing coils position

Aghaeifar, A., Loktyushin, A., Eschelbach, M., Scheffler, K.

Magnetic Resonance Materials in Physics, Biology and Medicine, 30(Supplement 1):S259, 34th Annual Scientific Meeting of the European Society for Magnetic Resonance in Medicine and Biology (ESMRMB), October 2017 (poster)

link (url) DOI [BibTex]

2017

Aghaeifar, A., Loktyushin, A., Eschelbach, M., Scheffler, K. Improving performance of linear field generation with multi-coil setup by optimizing coils position Magnetic Resonance Materials in Physics, Biology and Medicine, 30(Supplement 1):S259, 34th Annual Scientific Meeting of the European Society for Magnetic Resonance in Medicine and Biology (ESMRMB), October 2017 (poster)

link (url) DOI [BibTex]

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Estimating B0 inhomogeneities with projection FID navigator readouts

Loktyushin, A., Ehses, P., Schölkopf, B., Scheffler, K.

25th Annual Meeting and Exhibition of the International Society for Magnetic Resonance in Medicine (ISMRM), April 2017 (poster)

link (url) [BibTex]

Loktyushin, A., Ehses, P., Schölkopf, B., Scheffler, K. Estimating B0 inhomogeneities with projection FID navigator readouts 25th Annual Meeting and Exhibition of the International Society for Magnetic Resonance in Medicine (ISMRM), April 2017 (poster)

link (url) [BibTex]

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Image Quality Improvement by Applying Retrospective Motion Correction on Quantitative Susceptibility Mapping and R2*

Feng, X., Loktyushin, A., Deistung, A., Reichenbach, J.

25th Annual Meeting and Exhibition of the International Society for Magnetic Resonance in Medicine (ISMRM), April 2017 (poster)

link (url) [BibTex]

Feng, X., Loktyushin, A., Deistung, A., Reichenbach, J. Image Quality Improvement by Applying Retrospective Motion Correction on Quantitative Susceptibility Mapping and R2* 25th Annual Meeting and Exhibition of the International Society for Magnetic Resonance in Medicine (ISMRM), April 2017 (poster)

link (url) [BibTex]

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Elements of Causal Inference - Foundations and Learning Algorithms

Peters, J., Janzing, D., Schölkopf, B.

Adaptive Computation and Machine Learning Series, The MIT Press, Cambridge, MA, USA, 2017 (book)

PDF [BibTex]

Peters, J., Janzing, D., Schölkopf, B. Elements of Causal Inference - Foundations and Learning Algorithms Adaptive Computation and Machine Learning Series, The MIT Press, Cambridge, MA, USA, 2017 (book)

PDF [BibTex]

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New Directions for Learning with Kernels and Gaussian Processes (Dagstuhl Seminar 16481)

Gretton, A., Hennig, P., Rasmussen, C., Schölkopf, B.

Dagstuhl Reports, 6(11):142-167, 2017 (book)

DOI [BibTex]

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Generalized phase locking analysis of electrophysiology data

Safavi, S., Panagiotaropoulos, T., Kapoor, V., Logothetis, N. K., Besserve, M.

ESI Systems Neuroscience Conference (ESI-SyNC 2017): Principles of Structural and Functional Connectivity, 2017 (poster)

[BibTex]

Safavi, S., Panagiotaropoulos, T., Kapoor, V., Logothetis, N. K., Besserve, M. Generalized phase locking analysis of electrophysiology data ESI Systems Neuroscience Conference (ESI-SyNC 2017): Principles of Structural and Functional Connectivity, 2017 (poster)

[BibTex]

2015

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Diversity of sharp wave-ripples in the CA1 of the macaque hippocampus and their brain wide signatures

Ramirez-Villegas, J. F., Logothetis, N. K., Besserve, M.

45th Annual Meeting of the Society for Neuroscience (Neuroscience 2015), October 2015 (poster)

link (url) [BibTex]

2015

Ramirez-Villegas, J. F., Logothetis, N. K., Besserve, M. Diversity of sharp wave-ripples in the CA1 of the macaque hippocampus and their brain wide signatures 45th Annual Meeting of the Society for Neuroscience (Neuroscience 2015), October 2015 (poster)

link (url) [BibTex]

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Retrospective rigid motion correction of undersampled MRI data

Loktyushin, A., Babayeva, M., Gallichan, D., Krueger, G., Scheffler, K., Kober, T.

23rd Annual Meeting and Exhibition of the International Society for Magnetic Resonance in Medicine, ISMRM, June 2015 (poster)

[BibTex]

Loktyushin, A., Babayeva, M., Gallichan, D., Krueger, G., Scheffler, K., Kober, T. Retrospective rigid motion correction of undersampled MRI data 23rd Annual Meeting and Exhibition of the International Society for Magnetic Resonance in Medicine, ISMRM, June 2015 (poster)

[BibTex]

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Improving Quantitative Susceptibility and R2* Mapping by Applying Retrospective Motion Correction

Feng, X., Loktyushin, A., Deistung, A., Reichenbach, J. R.

23rd Annual Meeting and Exhibition of the International Society for Magnetic Resonance in Medicine, ISMRM, June 2015 (poster)

[BibTex]

Feng, X., Loktyushin, A., Deistung, A., Reichenbach, J. R. Improving Quantitative Susceptibility and R2* Mapping by Applying Retrospective Motion Correction 23rd Annual Meeting and Exhibition of the International Society for Magnetic Resonance in Medicine, ISMRM, June 2015 (poster)

[BibTex]

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Increasing the sensitivity of Kepler to Earth-like exoplanets

Foreman-Mackey, D., Hogg, D., Schölkopf, B., Wang, D.

Workshop: 225th American Astronomical Society Meeting 2015 , pages: 105.01D, 2015 (poster)

Web link (url) [BibTex]

Foreman-Mackey, D., Hogg, D., Schölkopf, B., Wang, D. Increasing the sensitivity of Kepler to Earth-like exoplanets Workshop: 225th American Astronomical Society Meeting 2015 , pages: 105.01D, 2015 (poster)

Web link (url) [BibTex]

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Calibrating the pixel-level Kepler imaging data with a causal data-driven model

Wang, D., Foreman-Mackey, D., Hogg, D., Schölkopf, B.

Workshop: 225th American Astronomical Society Meeting 2015 , pages: 258.08, 2015 (poster)

Web link (url) [BibTex]

Wang, D., Foreman-Mackey, D., Hogg, D., Schölkopf, B. Calibrating the pixel-level Kepler imaging data with a causal data-driven model Workshop: 225th American Astronomical Society Meeting 2015 , pages: 258.08, 2015 (poster)

Web link (url) [BibTex]

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Disparity estimation from a generative light field model

Köhler, R., Schölkopf, B., Hirsch, M.

IEEE International Conference on Computer Vision (ICCV 2015), Workshop on Inverse Rendering, 2015, Note: This work has been presented as a poster and is not included in the workshop proceedings. (poster)

[BibTex]

Köhler, R., Schölkopf, B., Hirsch, M. Disparity estimation from a generative light field model IEEE International Conference on Computer Vision (ICCV 2015), Workshop on Inverse Rendering, 2015, Note: This work has been presented as a poster and is not included in the workshop proceedings. (poster)

[BibTex]

2013

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Coupling between spiking activity and beta band spatio-temporal patterns in the macaque PFC

Safavi, S., Panagiotaropoulos, T., Kapoor, V., Logothetis, N., Besserve, M.

43rd Annual Meeting of the Society for Neuroscience (Neuroscience), 2013 (poster)

[BibTex]

2013

Safavi, S., Panagiotaropoulos, T., Kapoor, V., Logothetis, N., Besserve, M. Coupling between spiking activity and beta band spatio-temporal patterns in the macaque PFC 43rd Annual Meeting of the Society for Neuroscience (Neuroscience), 2013 (poster)

[BibTex]

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Gaussian Process Vine Copulas for Multivariate Dependence

Lopez-Paz, D., Hernandez-Lobato, J., Ghahramani, Z.

International Conference on Machine Learning (ICML), 2013 (poster)

PDF [BibTex]

Lopez-Paz, D., Hernandez-Lobato, J., Ghahramani, Z. Gaussian Process Vine Copulas for Multivariate Dependence International Conference on Machine Learning (ICML), 2013 (poster)

PDF [BibTex]

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Domain Generalization via Invariant Feature Representation

Muandet, K., Balduzzi, D., Schölkopf, B.

30th International Conference on Machine Learning (ICML2013), 2013 (poster)

PDF [BibTex]

Muandet, K., Balduzzi, D., Schölkopf, B. Domain Generalization via Invariant Feature Representation 30th International Conference on Machine Learning (ICML2013), 2013 (poster)

PDF [BibTex]

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Analyzing locking of spikes to spatio-temporal patterns in the macaque prefrontal cortex

Safavi, S., Panagiotaropoulos, T., Kapoor, V., Logothetis, N., Besserve, M.

Bernstein Conference, 2013 (poster)

DOI [BibTex]

Safavi, S., Panagiotaropoulos, T., Kapoor, V., Logothetis, N., Besserve, M. Analyzing locking of spikes to spatio-temporal patterns in the macaque prefrontal cortex Bernstein Conference, 2013 (poster)

DOI [BibTex]

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One-class Support Measure Machines for Group Anomaly Detection

Muandet, K., Schölkopf, B.

29th Conference on Uncertainty in Artificial Intelligence (UAI), 2013 (poster)

PDF [BibTex]

Muandet, K., Schölkopf, B. One-class Support Measure Machines for Group Anomaly Detection 29th Conference on Uncertainty in Artificial Intelligence (UAI), 2013 (poster)

PDF [BibTex]

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The Randomized Dependence Coefficient

Lopez-Paz, D., Hennig, P., Schölkopf, B.

Neural Information Processing Systems (NIPS), 2013 (poster)

PDF [BibTex]

Lopez-Paz, D., Hennig, P., Schölkopf, B. The Randomized Dependence Coefficient Neural Information Processing Systems (NIPS), 2013 (poster)

PDF [BibTex]

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Characterization of different types of sharp-wave ripple signatures in the CA1 of the macaque hippocampus

Ramirez-Villegas, J., Logothetis, N., Besserve, M.

4th German Neurophysiology PhD Meeting Networks, 2013 (poster)

Web [BibTex]

Ramirez-Villegas, J., Logothetis, N., Besserve, M. Characterization of different types of sharp-wave ripple signatures in the CA1 of the macaque hippocampus 4th German Neurophysiology PhD Meeting Networks, 2013 (poster)

Web [BibTex]

2006

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Some observations on the pedestal effect or dipper function

Henning, B., Wichmann, F.

Journal of Vision, 6(13):50, 2006 Fall Vision Meeting of the Optical Society of America, December 2006 (poster)

Abstract
The pedestal effect is the large improvement in the detectabilty of a sinusoidal “signal” grating observed when the signal is added to a masking or “pedestal” grating of the same spatial frequency, orientation, and phase. We measured the pedestal effect in both broadband and notched noise - noise from which a 1.5-octave band centred on the signal frequency had been removed. Although the pedestal effect persists in broadband noise, it almost disappears in the notched noise. Furthermore, the pedestal effect is substantial when either high- or low-pass masking noise is used. We conclude that the pedestal effect in the absence of notched noise results principally from the use of information derived from channels with peak sensitivities at spatial frequencies different from that of the signal and pedestal. The spatial-frequency components of the notched noise above and below the spatial frequency of the signal and pedestal prevent the use of information about changes in contrast carried in channels tuned to spatial frequencies that are very much different from that of the signal and pedestal. Thus the pedestal or dipper effect measured without notched noise is not a characteristic of individual spatial-frequency tuned channels.

Web DOI [BibTex]

2006

Henning, B., Wichmann, F. Some observations on the pedestal effect or dipper function Journal of Vision, 6(13):50, 2006 Fall Vision Meeting of the Optical Society of America, December 2006 (poster)

Web DOI [BibTex]

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Optimizing Spatial Filters for BCI: Margin- and Evidence-Maximization Approaches

Farquhar, J., Hill, N., Schölkopf, B.

Challenging Brain-Computer Interfaces: MAIA Workshop 2006, pages: 1, November 2006 (poster)

Abstract
We present easy-to-use alternatives to the often-used two-stage Common Spatial Pattern + classifier approach for spatial filtering and classification of Event-Related Desychnronization signals in BCI. We report two algorithms that aim to optimize the spatial filters according to a criterion more directly related to the ability of the algorithms to generalize to unseen data. Both are based upon the idea of treating the spatial filter coefficients as hyperparameters of a kernel or covariance function. We then optimize these hyper-parameters directly along side the normal classifier parameters with respect to our chosen learning objective function. The two objectives considered are margin maximization as used in Support-Vector Machines and the evidence maximization framework used in Gaussian Processes. Our experiments assessed generalization error as a function of the number of training points used, on 9 BCI competition data sets and 5 offline motor imagery data sets measured in Tubingen. Both our approaches sho w consistent improvements relative to the commonly used CSP+linear classifier combination. Strikingly, the improvement is most significant in the higher noise cases, when either few trails are used for training, or with the most poorly performing subjects. This a reversal of the usual "rich get richer" effect in the development of CSP extensions, which tend to perform best when the signal is strong enough to accurately find their additional parameters. This makes our approach particularly suitable for clinical application where high levels of noise are to be expected.

PDF PDF [BibTex]

Farquhar, J., Hill, N., Schölkopf, B. Optimizing Spatial Filters for BCI: Margin- and Evidence-Maximization Approaches Challenging Brain-Computer Interfaces: MAIA Workshop 2006, pages: 1, November 2006 (poster)

PDF PDF [BibTex]

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Learning Eye Movements

Kienzle, W., Wichmann, F., Schölkopf, B., Franz, M.

Sensory Coding And The Natural Environment, 2006, pages: 1, September 2006 (poster)

Abstract
The human visual system samples images through saccadic eye movements which rapidly change the point of fixation. Although the selection of eye movement targets depends on numerous top-down mechanisms, a number of recent studies have shown that low-level image features such as local contrast or edges play an important role. These studies typically used predefined image features which were afterwards experimentally verified. Here, we follow a complementary approach: instead of testing a set of candidate image features, we infer these hypotheses from the data, using methods from statistical learning. To this end, we train a non-linear classifier on fixated vs. randomly selected image patches without making any physiological assumptions. The resulting classifier can be essentially characterized by a nonlinear combination of two center-surround receptive fields. We find that the prediction performance of this simple model on our eye movement data is indistinguishable from the physiologically motivated model of Itti & Koch (2000) which is far more complex. In particular, we obtain a comparable performance without using any multi-scale representations, long-range interactions or oriented image features.

Web [BibTex]

Kienzle, W., Wichmann, F., Schölkopf, B., Franz, M. Learning Eye Movements Sensory Coding And The Natural Environment, 2006, pages: 1, September 2006 (poster)

Web [BibTex]

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Semi-Supervised Learning

Chapelle, O., Schölkopf, B., Zien, A.

pages: 508, Adaptive computation and machine learning, MIT Press, Cambridge, MA, USA, September 2006 (book)

Abstract
In the field of machine learning, semi-supervised learning (SSL) occupies the middle ground, between supervised learning (in which all training examples are labeled) and unsupervised learning (in which no label data are given). Interest in SSL has increased in recent years, particularly because of application domains in which unlabeled data are plentiful, such as images, text, and bioinformatics. This first comprehensive overview of SSL presents state-of-the-art algorithms, a taxonomy of the field, selected applications, benchmark experiments, and perspectives on ongoing and future research. Semi-Supervised Learning first presents the key assumptions and ideas underlying the field: smoothness, cluster or low-density separation, manifold structure, and transduction. The core of the book is the presentation of SSL methods, organized according to algorithmic strategies. After an examination of generative models, the book describes algorithms that implement the low-density separation assumption, graph-based methods, and algorithms that perform two-step learning. The book then discusses SSL applications and offers guidelines for SSL practitioners by analyzing the results of extensive benchmark experiments. Finally, the book looks at interesting directions for SSL research. The book closes with a discussion of the relationship between semi-supervised learning and transduction.

Web [BibTex]

Chapelle, O., Schölkopf, B., Zien, A. Semi-Supervised Learning pages: 508, Adaptive computation and machine learning, MIT Press, Cambridge, MA, USA, September 2006 (book)

Web [BibTex]

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Classification of natural scenes: Critical features revisited

Drewes, J., Wichmann, F., Gegenfurtner, K.

Journal of Vision, 6(6):561, 6th Annual Meeting of the Vision Sciences Society (VSS), June 2006 (poster)

Abstract
Human observers are capable of detecting animals within novel natural scenes with remarkable speed and accuracy. Despite the seeming complexity of such decisions it has been hypothesized that a simple global image feature, the relative abundance of high spatial frequencies at certain orientations, could underly such fast image classification (A. Torralba & A. Oliva, Network: Comput. Neural Syst., 2003). We successfully used linear discriminant analysis to classify a set of 11.000 images into “animal” and “non-animal” images based on their individual amplitude spectra only (Drewes, Wichmann, Gegenfurtner VSS 2005). We proceeded to sort the images based on the performance of our classifier, retaining only the best and worst classified 400 images (“best animals”, “best distractors” and “worst animals”, “worst distractors”). We used a Go/No-go paradigm to evaluate human performance on this subset of our images. Both reaction time and proportion of correctly classified images showed a significant effect of classification difficulty. Images more easily classified by our algorithm were also classified faster and better by humans, as predicted by the Torralba & Oliva hypothesis. We then equated the amplitude spectra of the 400 images, which, by design, reduced algorithmic performance to chance whereas human performance was only slightly reduced (cf. Wichmann, Rosas, Gegenfurtner, VSS 2005). Most importantly, the same images as before were still classified better and faster, suggesting that even in the original condition features other than specifics of the amplitude spectrum made particular images easy to classify, clearly at odds with the Torralba & Oliva hypothesis.

Web DOI [BibTex]

Drewes, J., Wichmann, F., Gegenfurtner, K. Classification of natural scenes: Critical features revisited Journal of Vision, 6(6):561, 6th Annual Meeting of the Vision Sciences Society (VSS), June 2006 (poster)

Web DOI [BibTex]

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The pedestal effect is caused by off-frequency looking, not nonlinear transduction or contrast gain-control

Wichmann, F., Henning, B.

Journal of Vision, 6(6):194, 6th Annual Meeting of the Vision Sciences Society (VSS), June 2006 (poster)

Abstract
The pedestal or dipper effect is the large improvement in the detectabilty of a sinusoidal grating observed when the signal is added to a pedestal or masking grating having the signal‘s spatial frequency, orientation, and phase. The effect is largest with pedestal contrasts just above the ‘threshold‘ in the absence of a pedestal. We measured the pedestal effect in both broadband and notched masking noise---noise from which a 1.5- octave band centered on the signal and pedestal frequency had been removed. The pedestal effect persists in broadband noise, but almost disappears with notched noise. The spatial-frequency components of the notched noise that lie above and below the spatial frequency of the signal and pedestal prevent the use of information about changes in contrast carried in channels tuned to spatial frequencies that are very much different from that of the signal and pedestal. We conclude that the pedestal effect in the absence of notched noise results principally from the use of information derived from channels with peak sensitivities at spatial frequencies that are different from that of the signal and pedestal. Thus the pedestal or dipper effect is not a characteristic of individual spatial-frequency tuned channels.

Web DOI [BibTex]

Wichmann, F., Henning, B. The pedestal effect is caused by off-frequency looking, not nonlinear transduction or contrast gain-control Journal of Vision, 6(6):194, 6th Annual Meeting of the Vision Sciences Society (VSS), June 2006 (poster)

Web DOI [BibTex]

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The Pedestal Effect is Caused by Off-Frequency Looking, not Nonlinear Transduction or Contrast Gain-Control

Wichmann, F., Henning, G.

9, pages: 174, 9th T{\"u}bingen Perception Conference (TWK), March 2006 (poster)

Abstract
The pedestal or dipper effect is the large improvement in the detectability of a sinusoidal grating observed when the signal is added to a pedestal or masking grating having the signal‘s spatial frequency, orientation, and phase. The effect is largest with pedestal contrasts just above the ‘threshold’ in the absence of a pedestal. We measured the pedestal effect in both broadband and notched masking noise---noise from which a 1.5-octave band centered on the signal and pedestal frequency had been removed. The pedestal effect persists in broadband noise, but almost disappears with notched noise. The spatial-frequency components of the notched noise that lie above and below the spatial frequency of the signal and pedestal prevent the use of information about changes in contrast carried in channels tuned to spatial frequencies that are very much different from that of the signal and pedestal. We conclude that the pedestal effect in the absence of notched noise results principally from the use of information derived from channels with peak sensitivities at spatial frequencies that are different from that of the signal and pedestal. Thus the pedestal or dipper effect is not a characteristic of individual spatial-frequency tuned channels.

Web [BibTex]

Wichmann, F., Henning, G. The Pedestal Effect is Caused by Off-Frequency Looking, not Nonlinear Transduction or Contrast Gain-Control 9, pages: 174, 9th T{\"u}bingen Perception Conference (TWK), March 2006 (poster)

Web [BibTex]

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Classification of Natural Scenes: Critical Features Revisited

Drewes, J., Wichmann, F., Gegenfurtner, K.

9, pages: 92, 9th T{\"u}bingen Perception Conference (TWK), March 2006 (poster)

Abstract
Human observers are capable of detecting animals within novel natural scenes with remarkable speed and accuracy. Despite the seeming complexity of such decisions it has been hypothesized that a simple global image feature, the relative abundance of high spatial frequencies at certain orientations, could underly such fast image classification [1]. We successfully used linear discriminant analysis to classify a set of 11.000 images into “animal” and “non-animal” images based on their individual amplitude spectra only [2]. We proceeded to sort the images based on the performance of our classifier, retaining only the best and worst classified 400 images ("best animals", "best distractors" and "worst animals", "worst distractors"). We used a Go/No-go paradigm to evaluate human performance on this subset of our images. Both reaction time and proportion of correctly classified images showed a significant effect of classification difficulty. Images more easily classified by our algorithm were also classified faster and better by humans, as predicted by the Torralba & Oliva hypothesis. We then equated the amplitude spectra of the 400 images, which, by design, reduced algorithmic performance to chance whereas human performance was only slightly reduced [3]. Most importantly, the same images as before were still classified better and faster, suggesting that even in the original condition features other than specifics of the amplitude spectrum made particular images easy to classify, clearly at odds with the Torralba & Oliva hypothesis.

Web [BibTex]

Drewes, J., Wichmann, F., Gegenfurtner, K. Classification of Natural Scenes: Critical Features Revisited 9, pages: 92, 9th T{\"u}bingen Perception Conference (TWK), March 2006 (poster)

Web [BibTex]

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Factorial Coding of Natural Images: How Effective are Linear Models in Removing Higher-Order Dependencies?

Bethge, M.

9, pages: 90, 9th T{\"u}bingen Perception Conference (TWK), March 2006 (poster)

Abstract
The performance of unsupervised learning models for natural images is evaluated quantitatively by means of information theory. We estimate the gain in statistical independence (the multi-information reduction) achieved with independent component analysis (ICA), principal component analysis (PCA), zero-phase whitening, and predictive coding. Predictive coding is translated into the transform coding framework, where it can be characterized by the constraint of a triangular filter matrix. A randomly sampled whitening basis and the Haar wavelet are included into the comparison as well. The comparison of all these methods is carried out for different patch sizes, ranging from 2x2 to 16x16 pixels. In spite of large differences in the shape of the basis functions, we find only small differences in the multi-information between all decorrelation transforms (5% or less) for all patch sizes. Among the second-order methods, PCA is optimal for small patch sizes and predictive coding performs best for large patch sizes. The extra gain achieved with ICA is always less than 2%. In conclusion, the `edge filters‘ found with ICA lead only to a surprisingly small improvement in terms of its actual objective.

Web [BibTex]

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Gaussian Processes for Machine Learning

Rasmussen, CE., Williams, CKI.

pages: 248, Adaptive Computation and Machine Learning, MIT Press, Cambridge, MA, USA, January 2006 (book)

Abstract
Gaussian processes (GPs) provide a principled, practical, probabilistic approach to learning in kernel machines. GPs have received increased attention in the machine-learning community over the past decade, and this book provides a long-needed systematic and unified treatment of theoretical and practical aspects of GPs in machine learning. The treatment is comprehensive and self-contained, targeted at researchers and students in machine learning and applied statistics. The book deals with the supervised-learning problem for both regression and classification, and includes detailed algorithms. A wide variety of covariance (kernel) functions are presented and their properties discussed. Model selection is discussed both from a Bayesian and a classical perspective. Many connections to other well-known techniques from machine learning and statistics are discussed, including support-vector machines, neural networks, splines, regularization networks, relevance vector machines and others. Theoretical issues including learning curves and the PAC-Bayesian framework are treated, and several approximation methods for learning with large datasets are discussed. The book contains illustrative examples and exercises, and code and datasets are available on the Web. Appendixes provide mathematical background and a discussion of Gaussian Markov processes.

Web [BibTex]

Rasmussen, CE., Williams, CKI. Gaussian Processes for Machine Learning pages: 248, Adaptive Computation and Machine Learning, MIT Press, Cambridge, MA, USA, January 2006 (book)

Web [BibTex]

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Classification of natural scenes: critical features revisited

Drewes, J., Wichmann, F., Gegenfurtner, K.

Experimentelle Psychologie: Beitr{\"a}ge zur 48. Tagung experimentell arbeitender Psychologen, 48, pages: 251, 2006 (poster)

[BibTex]

Drewes, J., Wichmann, F., Gegenfurtner, K. Classification of natural scenes: critical features revisited Experimentelle Psychologie: Beitr{\"a}ge zur 48. Tagung experimentell arbeitender Psychologen, 48, pages: 251, 2006 (poster)

[BibTex]

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Texture and haptic cues in slant discrimination: combination is sensitive to reliability but not statistically optimal

Rosas, P., Wagemans, J., Ernst, M., Wichmann, F.

Beitr{\"a}ge zur 48. Tagung experimentell arbeitender Psychologen (TeaP 2006), 48, pages: 80, 2006 (poster)

[BibTex]

Rosas, P., Wagemans, J., Ernst, M., Wichmann, F. Texture and haptic cues in slant discrimination: combination is sensitive to reliability but not statistically optimal Beitr{\"a}ge zur 48. Tagung experimentell arbeitender Psychologen (TeaP 2006), 48, pages: 80, 2006 (poster)

[BibTex]

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Ähnlichkeitsmasse in Modellen zur Kategorienbildung

Jäkel, F., Wichmann, F.

Experimentelle Psychologie: Beitr{\"a}ge zur 48. Tagung experimentell arbeitender Psychologen, 48, pages: 223, 2006 (poster)

[BibTex]

Jäkel, F., Wichmann, F. Ähnlichkeitsmasse in Modellen zur Kategorienbildung Experimentelle Psychologie: Beitr{\"a}ge zur 48. Tagung experimentell arbeitender Psychologen, 48, pages: 223, 2006 (poster)

[BibTex]

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The pedestal effect is caused by off-frequency looking, not nonlinear transduction or contrast gain-control

Wichmann, F., Henning, B.

Experimentelle Psychologie: Beitr{\"a}ge zur 48. Tagung experimentell arbeitender Psychologen, 48, pages: 205, 2006 (poster)

[BibTex]

Wichmann, F., Henning, B. The pedestal effect is caused by off-frequency looking, not nonlinear transduction or contrast gain-control Experimentelle Psychologie: Beitr{\"a}ge zur 48. Tagung experimentell arbeitender Psychologen, 48, pages: 205, 2006 (poster)

[BibTex]

2003

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Texture and haptic cues in slant discrimination: Measuring the effect of texture type on cue combination

Rosas, P., Wichmann, F., Ernst, M., Wagemans, J.

Journal of Vision, 3(12):26, 2003 Fall Vision Meeting of the Optical Society of America, December 2003 (poster)

Abstract
In a number of models of depth cue combination the depth percept is constructed via a weighted average combination of independent depth estimations. The influence of each cue in such average depends on the reliability of the source of information. (Young, Landy, & Maloney, 1993; Ernst & Banks, 2002.) In particular, Ernst & Banks (2002) formulate the combination performed by the human brain as that of the minimum variance unbiased estimator that can be constructed from the available cues. Using slant discrimination and slant judgment via probe adjustment as tasks, we have observed systematic differences in performance of human observers when a number of different types of textures were used as cue to slant (Rosas, Wichmann & Wagemans, 2003). If the depth percept behaves as described above, our measurements of the slopes of the psychometric functions provide the predicted weights for the texture cue for the ranked texture types. We have combined these texture types with object motion but the obtained results are difficult to reconcile with the unbiased minimum variance estimator model (Rosas & Wagemans, 2003). This apparent failure of such model might be explained by the existence of a coupling of texture and motion, violating the assumption of independence of cues. Hillis, Ernst, Banks, & Landy (2002) have shown that while for between-modality combination the human visual system has access to the single-cue information, for within-modality combination (visual cues: disparity and texture) the single-cue information is lost, suggesting a coupling between these cues. Then, in the present study we combine the different texture types with haptic information in a slant discrimination task, to test whether in the between-modality condition the texture cue and the haptic cue to slant are combined as predicted by an unbiased, minimum variance estimator model.

Web DOI [BibTex]

2003

Rosas, P., Wichmann, F., Ernst, M., Wagemans, J. Texture and haptic cues in slant discrimination: Measuring the effect of texture type on cue combination Journal of Vision, 3(12):26, 2003 Fall Vision Meeting of the Optical Society of America, December 2003 (poster)

Web DOI [BibTex]

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Phase Information and the Recognition of Natural Images

Braun, D., Wichmann, F., Gegenfurtner, K.

6, pages: 138, (Editors: H.H. Bülthoff, K.R. Gegenfurtner, H.A. Mallot, R. Ulrich, F.A. Wichmann), 6. T{\"u}binger Wahrnehmungskonferenz (TWK), February 2003 (poster)

Abstract
Fourier phase plays an important role in determining image structure. For example, when the phase spectrum of an image showing a ower is swapped with the phase spectrum of an image showing a tank, then we will usually perceive a tank in the resulting image, even though the amplitude spectrum is still that of the ower. Also, when the phases of an image are randomly swapped across frequencies, the resulting image becomes impossible to recognize. Our goal was to evaluate the e ect of phase manipulations in a more quantitative manner. On each trial subjects viewed two images of natural scenes. The subject had to indicate which one of the two images contained an animal. The spectra of the images were manipulated by adding random phase noise at each frequency. The phase noise was uniformly distributed in the interval [;+], where  was varied between 0 degree and 180 degrees. Image pairs were displayed for 100 msec. Subjects were remarkably resistant to the addition of phase noise. Even with [120; 120] degree noise, subjects still were at a level of 75% correct. The introduction of phase noise leads to a reduction of image contrast. Subjects were slightly better than a simple prediction based on this contrast reduction. However, when contrast response functions were measured in the same experimental paradigm, we found that performance in the phase noise experiment was signi cantly lower than that predicted by the corresponding contrast reduction.

Web [BibTex]

Braun, D., Wichmann, F., Gegenfurtner, K. Phase Information and the Recognition of Natural Images 6, pages: 138, (Editors: H.H. Bülthoff, K.R. Gegenfurtner, H.A. Mallot, R. Ulrich, F.A. Wichmann), 6. T{\"u}binger Wahrnehmungskonferenz (TWK), February 2003 (poster)

Web [BibTex]

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Constraints measures and reproduction of style in robot imitation learning

Bakir, GH., Ilg, W., Franz, MO., Giese, M.

6, pages: 70, (Editors: H.H. Bülthoff, K.R. Gegenfurtner, H.A. Mallot, R. Ulrich, F.A. Wichmann), 6. T{\"u}binger Wahrnehmungskonferenz (TWK), February 2003 (poster)

Abstract
Imitation learning is frequently discussed as a method for generating complex behaviors in robots by imitating human actors. The kinematic and the dynamic properties of humans and robots are typically quite di erent, however. For this reason observed human trajectories cannot be directly transferred to robots, even if their geometry is humanoid. Instead the human trajectory must be approximated by trajectories that can be realized by the robot. During this approximation deviations from the human trajectory may arise that change the style of the executed movement. Alternatively, the style of the movement might be well reproduced, but the imitated trajectory might be suboptimal with respect to di erent constraint measures from robotics control, leading to non-robust behavior. Goal of the presented work is to quantify this trade-o between \imitation quality" and constraint compatibility for the imitation of complex writing movements. In our experiment, we used trajectory data from human writing movements (see the abstract of Ilg et al. in this volume). The human trajectories were mapped onto robot trajectories by minimizing an error measure that integrates constraints that are important for the imitation of movement style and a regularizing constraint that ensures smooth joint trajectories with low velocities. In a rst experiment, both the end-e ector position and the shoulder angle of the robot were optimized in order to achieve good imitation together with accurate control of the end-e ector position. In a second experiment only the end-e ector trajectory was imitated whereas the motion of the elbow joint was determined using the optimal inverse kinematic solution for the robot. For both conditions di erent constraint measures (dexterity and relative jointlimit distances) and a measure for imitation quality were assessed. By controling the weight of the regularization term we can vary continuously between robot behavior optimizing imitation quality, and behavior minimizing joint velocities.

PDF Web [BibTex]

Bakir, GH., Ilg, W., Franz, MO., Giese, M. Constraints measures and reproduction of style in robot imitation learning 6, pages: 70, (Editors: H.H. Bülthoff, K.R. Gegenfurtner, H.A. Mallot, R. Ulrich, F.A. Wichmann), 6. T{\"u}binger Wahrnehmungskonferenz (TWK), February 2003 (poster)

PDF Web [BibTex]

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Study of Human Classification using Psychophysics and Machine Learning

Graf, A., Wichmann, F., Bülthoff, H., Schölkopf, B.

6, pages: 149, (Editors: H.H. Bülthoff, K.R. Gegenfurtner, H.A. Mallot, R. Ulrich, F.A. Wichmann), 6. T{\"u}binger Wahrnehmungskonferenz (TWK), Febuary 2003 (poster)

Abstract
We attempt to reach a better understanding of classi cation in humans using both psychophysical and machine learning techniques. In our psychophysical paradigm the stimuli presented to the human subjects are modi ed using machine learning algorithms according to their responses. Frontal views of human faces taken from a processed version of the MPI face database are employed for a gender classi cation task. The processing assures that all heads have same mean intensity, same pixel-surface area and are centered. This processing stage is followed by a smoothing of the database in order to eliminate, as much as possible, scanning artifacts. Principal Component Analysis is used to obtain a low-dimensional representation of the faces in the database. A subject is asked to classify the faces and experimental parameters such as class (i.e. female/male), con dence ratings and reaction times are recorded. A mean classi cation error of 14.5% is measured and, on average, 0.5 males are classi ed as females and 21.3females as males. The mean reaction time for the correctly classi ed faces is 1229 +- 252 [ms] whereas the incorrectly classi ed faces have a mean reaction time of 1769 +- 304 [ms] showing that the reaction times increase with the subject's classi- cation error. Reaction times are also shown to decrease with increasing con dence, both for the correct and incorrect classi cations. Classi cation errors, reaction times and con dence ratings are then correlated to concepts of machine learning such as separating hyperplane obtained when considering Support Vector Machines, Relevance Vector Machines, boosted Prototype and K-means Learners. Elements near the separating hyperplane are found to be classi ed with more errors than those away from it. In addition, the subject's con dence increases when moving away from the hyperplane. A preliminary analysis on the available small number of subjects indicates that K-means classi cation seems to re ect the subject's classi cation behavior best. The above learnersare then used to generate \special" elements, or representations, of the low-dimensional database according to the labels given by the subject. A memory experiment follows where the representations are shown together with faces seen or unseen during the classi cation experiment. This experiment aims to assess the representations by investigating whether some representations, or special elements, are classi ed as \seen before" despite that they never appeared in the classi cation experiment, possibly hinting at their use during human classi cation.

PDF Web [BibTex]

Graf, A., Wichmann, F., Bülthoff, H., Schölkopf, B. Study of Human Classification using Psychophysics and Machine Learning 6, pages: 149, (Editors: H.H. Bülthoff, K.R. Gegenfurtner, H.A. Mallot, R. Ulrich, F.A. Wichmann), 6. T{\"u}binger Wahrnehmungskonferenz (TWK), Febuary 2003 (poster)

PDF Web [BibTex]

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A Representation of Complex Movement Sequences Based on Hierarchical Spatio-Temporal Correspondence for Imitation Learning in Robotics

Ilg, W., Bakir, GH., Franz, MO., Giese, M.

6, pages: 74, (Editors: H.H. Bülthoff, K.R. Gegenfurtner, H.A. Mallot, R. Ulrich, F.A. Wichmann), 6. T{\"u}binger Wahrnehmungskonferenz (TWK), February 2003 (poster)

Abstract
Imitation learning of complex movements has become a popular topic in neuroscience, as well as in robotics. A number of conceptual as well as practical problems are still unsolved. One example is the determination of the aspects of movements which are relevant for imitation. Problems concerning the movement representation are twofold: (1) The movement characteristics of observed movements have to be transferred from the perceptual level to the level of generated actions. (2) Continuous spaces of movements with variable styles have to be approximated based on a limited number of learned example sequences. Therefore, one has to use representation with a high generalisation capability. We present methods for the representation of complex movement sequences that addresses these questions in the context of the imitation learning of writing movements using a robot arm with human-like geometry. For the transfer of complex movements from perception to action we exploit a learning-based method that represents complex action sequences by linear combination of prototypical examples (Ilg and Giese, BMCV 2002). The method of hierarchical spatio-temporal morphable models (HSTMM) decomposes action sequences automatically into movement primitives. These primitives are modeled by linear combinations of a small number of learned example trajectories. The learned spatio-temporal models are suitable for the analysis and synthesis of long action sequences, which consist of movement primitives with varying style parameters. The proposed method is illustrated by imitation learning of complex writing movements. Human trajectories were recorded using a commercial motion capture system (VICON). In the rst step the recorded writing sequences are decomposed into movement primitives. These movement primitives can be analyzed and changed in style by de ning linear combinations of prototypes with di erent linear weight combinations. Our system can imitate writing movements of di erent actors, synthesize new writing styles and can even exaggerate the writing movements of individual actors. Words and writing movements of the robot look very natural, and closely match the natural styles. These preliminary results makes the proposed method promising for further applications in learning-based robotics. In this poster we focus on the acquisition of the movement representation (identi cation and segmentation of movement primitives, generation of new writing styles by spatio-temporal morphing). The transfer of the generated writing movements to the robot considering the given kinematic and dynamic constraints is discussed in Bakir et al (this volume).

PDF Web [BibTex]

Ilg, W., Bakir, GH., Franz, MO., Giese, M. A Representation of Complex Movement Sequences Based on Hierarchical Spatio-Temporal Correspondence for Imitation Learning in Robotics 6, pages: 74, (Editors: H.H. Bülthoff, K.R. Gegenfurtner, H.A. Mallot, R. Ulrich, F.A. Wichmann), 6. T{\"u}binger Wahrnehmungskonferenz (TWK), February 2003 (poster)

PDF Web [BibTex]

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Models of contrast transfer as a function of presentation time and spatial frequency.

Wichmann, F.

2003 (poster)

Abstract
Understanding contrast transduction is essential for understanding spatial vision. Using standard 2AFC contrast discrimination experiments conducted using a carefully calibrated display we previously showed that the shape of the threshold versus (pedestal) contrast (TvC) curve changes with presentation time and the performance level defined as threshold (Wichmann, 1999; Wichmann & Henning, 1999). Additional experiments looked at the change of the TvC curve with spatial frequency (Bird, Henning & Wichmann, 2002), and at how to constrain the parameters of models of contrast processing (Wichmann, 2002). Here I report modelling results both across spatial frequency and presentation time. An extensive model-selection exploration was performed using Bayesian confidence regions for the fitted parameters as well as cross-validation methods. Bird, C.M., G.B. Henning and F.A. Wichmann (2002). Contrast discrimination with sinusoidal gratings of different spatial frequency. Journal of the Optical Society of America A, 19, 1267-1273. Wichmann, F.A. (1999). Some aspects of modelling human spatial vision: contrast discrimination. Unpublished doctoral dissertation, The University of Oxford. Wichmann, F.A. & Henning, G.B. (1999). Implications of the Pedestal Effect for Models of Contrast-Processing and Gain-Control. OSA Annual Meeting Program, 62. Wichmann, F.A. (2002). Modelling Contrast Transfer in Spatial Vision [Abstract]. Journal of Vision, 2, 7a.

[BibTex]

2002

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Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond

Schölkopf, B., Smola, A.

pages: 644, Adaptive Computation and Machine Learning, MIT Press, Cambridge, MA, USA, December 2002, Parts of this book, including an introduction to kernel methods, can be downloaded here. (book)

Abstract
In the 1990s, a new type of learning algorithm was developed, based on results from statistical learning theory: the Support Vector Machine (SVM). This gave rise to a new class of theoretically elegant learning machines that use a central concept of SVMs-kernels—for a number of learning tasks. Kernel machines provide a modular framework that can be adapted to different tasks and domains by the choice of the kernel function and the base algorithm. They are replacing neural networks in a variety of fields, including engineering, information retrieval, and bioinformatics. Learning with Kernels provides an introduction to SVMs and related kernel methods. Although the book begins with the basics, it also includes the latest research. It provides all of the concepts necessary to enable a reader equipped with some basic mathematical knowledge to enter the world of machine learning using theoretically well-founded yet easy-to-use kernel algorithms and to understand and apply the powerful algorithms that have been developed over the last few years.

Web [BibTex]

2002

Schölkopf, B., Smola, A. Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond pages: 644, Adaptive Computation and Machine Learning, MIT Press, Cambridge, MA, USA, December 2002, Parts of this book, including an introduction to kernel methods, can be downloaded here. (book)

Web [BibTex]

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Surface-slant-from-texture discrimination: Effects of slant level and texture type

Rosas, P., Wichmann, F., Wagemans, J.

Journal of Vision, 2(7):300, Second Annual Meeting of the Vision Sciences Society (VSS), November 2002 (poster)

Abstract
The problem of surface-slant-from-texture was studied psychophysically by measuring the performances of five human subjects in a slant-discrimination task with a number of different types of textures: uniform lattices, randomly displaced lattices, polka dots, Voronoi tessellations, orthogonal sinusoidal plaid patterns, fractal or 1/f noise, “coherent” noise and a “diffusion-based” texture (leopard skin-like). The results show: (1) Improving performance with larger slants for all textures. (2) A “non-symmetrical” performance around a particular slant characterized by a psychometric function that is steeper in the direction of the more slanted orientation. (3) For sufficiently large slants (66 deg) there are no major differences in performance between any of the different textures. (4) For slants at 26, 37 and 53 degrees, however, there are marked differences between the different textures. (5) The observed differences in performance across textures for slants up to 53 degrees are systematic within subjects, and nearly so across them. This allows a rank-order of textures to be formed according to their “helpfulness” — that is, how easy the discrimination task is when a particular texture is mapped on the surface. Polka dots tended to allow the best slant discrimination performance, noise patterns the worst up to the large slant of 66 degrees at which performance was almost independent of the particular texture chosen. Finally, our large number of 2AFC trials (approximately 2800 trials per texture across subjects) and associated tight confidence intervals may enable us to find out about which statistical properties of the textures could be responsible for surface-slant-from-texture estimation, with the ultimate goal of being able to predict observer performance for any arbitrary texture.

Web DOI [BibTex]

Rosas, P., Wichmann, F., Wagemans, J. Surface-slant-from-texture discrimination: Effects of slant level and texture type Journal of Vision, 2(7):300, Second Annual Meeting of the Vision Sciences Society (VSS), November 2002 (poster)

Web DOI [BibTex]

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Modelling Contrast Transfer in Spatial Vision

Wichmann, F.

Journal of Vision, 2(10):7, Second Annual Meeting of the Vision Sciences Society (VSS), November 2002 (poster)

Abstract
Much of our information about spatial vision comes from detection experiments involving low-contrast stimuli. Contrast discrimination experiments provide one way to explore the visual system's response to stimuli of higher contrast, the results of which allow different models of contrast processing (e.g. energy versus gain-control models) to be critically assessed (Wichmann & Henning, 1999). Studies of detection and discrimination using pulse train stimuli in noise, on the other hand, make predictions about the number, position and properties of noise sources within the processing stream (Henning, Bird & Wichmann, 2002). Here I report modelling results combining data from both sinusoidal and pulse train experiments in and without noise to arrive at a more tightly constrained model of early spatial vision.

Web DOI [BibTex]

Wichmann, F. Modelling Contrast Transfer in Spatial Vision Journal of Vision, 2(10):7, Second Annual Meeting of the Vision Sciences Society (VSS), November 2002 (poster)

Web DOI [BibTex]

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Pulse train detection and discrimination in pink noise

Henning, G., Wichmann, F., Bird, C.

Journal of Vision, 2(7):229, Second Annual Meeting of the Vision Sciences Society (VSS), November 2002 (poster)

Abstract
Much of our information about spatial vision comes from detection experiments involving low-contrast stimuli. Contrast discrimination experiments provide one way to explore the visual system's response to stimuli of higher contrast. We explored both detection and contrast discrimination performance with sinusoidal and "pulse-train" (or line) gratings. Both types of grating had a fundamental spatial frequency of 2.09-c/deg but the pulse-train, ideally, contains, in addition to its fundamental component, all the harmonics of the fundamental. Although the 2.09-c/deg pulse-train produced on the display was measured and shown to contain at least 8 harmonics at equal contrast, it was no more detectable than its most detectable component; no benefit from having additional information at the harmonics was measurable. The addition of broadband "pink" noise, designed to equalize the detectability of the components of the pulse train, made it about a factor of four more detectable than any of its components. However, in contrast-discrimination experiments, with an in-phase pedestal or masking grating of the same form and phase as the signal and 15% contrast, the noise did not improve the discrimination performance of the pulse train relative to that of its sinusoidal components. In contrast, a 2.09-c/deg "super train," constructed to have 8 equally detectable harmonics, was a factor of five more detectable than any of its components. We discuss the implications of these observations for models of early vision in particular the implications for possible sources of internal noise.

Web DOI [BibTex]

Henning, G., Wichmann, F., Bird, C. Pulse train detection and discrimination in pink noise Journal of Vision, 2(7):229, Second Annual Meeting of the Vision Sciences Society (VSS), November 2002 (poster)

Web DOI [BibTex]

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Phase information in the recognition of natural images

Braun, D., Wichmann, F., Gegenfurtner, K.

Perception, 31(ECVP Abstract Supplement):133, 25th European Conference on Visual Perception, August 2002 (poster)

Abstract
Fourier phase plays an important role in determining global image structure. For example, when the phase spectrum of an image of a flower is swapped with that of a tank, we usually perceive a tank, even though the amplitude spectrum is still that of the flower. Similarly, when the phase spectrum of an image is randomly swapped across frequencies, that is its Fourier energy is randomly distributed over the image, the resulting image becomes impossible to recognise. Our goal was to evaluate the effect of phase manipulations in a quantitative manner. Subjects viewed two images of natural scenes, one of which contained an animal (the target) embedded in the background. The spectra of the images were manipulated by adding random phase noise at each frequency. The phase noise was the independent variable, uniformly distributed between 0° and ±180°. Subjects were remarkably resistant to phase noise. Even with ±120° noise, subjects were still 75% correct. The proportion of correct answers closely followed the correlation between original and noise-distorted images. Thus it appears as if it was not the global phase information per se that determines our percept of natural images, but rather the effect of phase on local image features.

Web [BibTex]

Braun, D., Wichmann, F., Gegenfurtner, K. Phase information in the recognition of natural images Perception, 31(ECVP Abstract Supplement):133, 25th European Conference on Visual Perception, August 2002 (poster)

Web [BibTex]

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Detection and discrimination in pink noise

Wichmann, F., Henning, G.

5, pages: 100, 5. T{\"u}binger Wahrnehmungskonferenz (TWK), February 2002 (poster)

Abstract
Much of our information about early spatial vision comes from detection experiments involving low-contrast stimuli, which are not, perhaps, particularly "natural" stimuli. Contrast discrimination experiments provide one way to explore the visual system's response to stimuli of higher contrast whilst keeping the number of unknown parameters comparatively small. We explored both detection and contrast discrimination performance with sinusoidal and "pulse-train" (or line) gratings. Both types of grating had a fundamental spatial frequency of 2.09-c/deg but the pulse-train, ideally, contains, in addition to its fundamental component, all the harmonics of the fundamental. Although the 2.09-c/deg pulse-train produced on our display was measured using a high-performance digital camera (Photometrics) and shown to contain at least 8 harmonics at equal contrast, it was no more detectable than its most detectable component; no benefit from having additional information at the harmonics was measurable. The addition of broadband 1-D "pink" noise made it about a factor of four more detectable than any of its components. However, in contrast-discrimination experiments, with an in-phase pedestal or masking grating of the same form and phase as the signal and 15% contrast, the noise did not improve the discrimination performance of the pulse train relative to that of its sinusoidal components. We discuss the implications of these observations for models of early vision in particular the implications for possible sources of internal noise.

Web [BibTex]

Wichmann, F., Henning, G. Detection and discrimination in pink noise 5, pages: 100, 5. T{\"u}binger Wahrnehmungskonferenz (TWK), February 2002 (poster)

Web [BibTex]

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Application of Monte Carlo Methods to Psychometric Function Fitting

Wichmann, F.

Proceedings of the 33rd European Conference on Mathematical Psychology, pages: 44, 2002 (poster)

Abstract
The psychometric function relates an observer's performance to an independent variable, usually some physical quantity of a stimulus in a psychophysical task. Here I describe methods to (1) fitting psychometric functions, (2) assessing goodness-of-fit, and (3) providing confidence intervals for the function's parameters and other estimates derived from them. First I describe a constrained maximum-likelihood method for parameter estimation. Using Monte-Carlo simulations I demonstrate that it is important to have a fitting method that takes stimulus-independent errors (or "lapses") into account. Second, a number of goodness-of-fit tests are introduced. Because psychophysical data sets are usually rather small I advocate the use of Monte Carlo resampling techniques that do not rely on asymptotic theory for goodness-of-fit assessment. Third, a parametric bootstrap is employed to estimate the variability of fitted parameters and derived quantities such as thresholds and slopes. I describe how the bootstrap bridging assumption, on which the validity of the procedure depends, can be tested without incurring too high a cost in computation time. Finally I describe how the methods can be extended to test hypotheses concerning the form and shape of several psychometric functions. Software describing the methods is available (http://www.bootstrap-software.com/psignifit/), as well as articles describing the methods in detail (Wichmann&Hill, Perception&Psychophysics, 2001a,b).

[BibTex]

Wichmann, F. Application of Monte Carlo Methods to Psychometric Function Fitting Proceedings of the 33rd European Conference on Mathematical Psychology, pages: 44, 2002 (poster)

[BibTex]