Michael J. Black received his B.Sc. from the University of British Columbia (1985), his M.S. from Stanford (1989), and his Ph.D. in computer science from Yale University (1992). After research at NASA Ames and post-doctoral research at the University of Toronto, he joined the Xerox Palo Alto Research Center in 1993 where he later managed the Image Understanding Area and founded the Digital Video Analysis group. From 2000 to 2010 he was on the faculty of Brown University in the Department of Computer Science (Assoc. Prof. 2000-2004, Prof. 2004-2010). He is a founding director at the Max Planck Institute for Intelligent Systems in Tübingen, Germany, where he leads the Perceiving Systems department. He is an honorary professor at the University of Tübingen, a visiting professor at ETH Zürich, and an adjunct professor (research) at Brown University.
Black is a foreign member of the Royal Swedish Academy of Sciences. He is a recipient of the 2010 Koenderink Prize for Fundamental Contributions in Computer Vision and the 2013 Helmholtz Prize for work that has stood the test of time. His work has won several paper awards including the IEEE Computer Society Outstanding Paper Award (CVPR'91). His work received Honorable Mention for the Marr Prize in 1999 and 2005. His early work on optical flow has been widely used in Hollywood films including for the Academy-Award-winning effects in “What Dreams May Come” and “The Matrix Reloaded.” He has contributed to several influential datasets including the Middlebury Flow dataset, HumanEva, and the Sintel dataset. He is a co-founder, science advisor, and member of the board of directors of Body Labs Inc., which is commercializing his team’s research on 3D human body shape.
Prof. Black's research interests in machine vision include optical flow estimation, 3D shape models, human shape and motion analysis, robust statistical methods, and probabilistic models of the visual world. In computational neuroscience his work focuses on probabilistic models of the neural code and applications of neural decoding in neural prosthetics.
Michael Black received his B.Sc. from the University of British Columbia (1985), his M.S. from Stanford (1989), and his Ph.D. from Yale University (1992). After post-doctoral research at the University of Toronto, he worked at Xerox PARC as a member of research staff and an area manager. From 2000 to 2010 he was on the faculty of Brown University in the Department of Computer Science (Assoc. Prof. 2000-2004, Prof. 2004-2010). He is one of the founding directors at the Max Planck Institute for Intelligent Systems in Tübingen, Germany, where he leads the Perceiving Systems department. He is an Honorarprofessor at the University of Tuebingen, Visiting Professor at ETH Zürich, and Adjunct Professor (Research) at Brown University. His work has won several awards including the IEEE Computer Society Outstanding Paper Award (1991), Honorable Mention for the Marr Prize (1999 and 2005), the 2010 Koenderink Prize for Fundamental Contributions in Computer Vision, and the 2013 Helmholtz Prize for work that has stood the test of time. He is a foreign member of the Royal Swedish Academy of Sciences. He is also a co-founder, science advisor, and board member of Body Labs Inc.
Royal Swedish Academy of Sciences
Foreign member, Class for Engineering Sciences, since June 2015.
for the paper: Black, M. J., and Anandan, P., "A framework for the robust estimation of optical flow,'' IEEE International Conference on Computer Vision, ICCV, pages 231-236, Berlin, Germany. May 1993.
2010Koenderink Prize for Fundamental Contributions in Computer Vision,
with Sidenbladh, H. and Fleet, D. J. for the paper "Stochastic tracking of 3D human figures using 2D image motion,'' European Conference on Computer Vision, 2000.
Best Paper Award, Eurographics 2017, for the paper "Sparse Inertial Poser: Automatic 3D Human Pose Estimation from Sparse IMUs", by von Marcard, T., Rosenhahn, B., Black, M. J., Pons-Moll, G.
"Dataset Award" at the Eurographics Symposium on Geometry Processing 2016, with F. Bogo, J. Romero, and M. Loper, for the paper "FAUST: Dataset and evaluation for 3D mesh registration," CVPR 2014.
Best Paper Award, International Conference on 3D Vision (3DV), 2015, with A. O. Ulusoy and A. Geiger, for the paper "Towards Probabilistic Volumetric Reconstruction using Ray Potentials."
Best Paper Award, INI-Graphics Net, 2008, First Prize Winner of Category Research,
with S. Roth for the paper "Steerable random fields."
Best Paper Award, Fourth International Conference on Articulated Motion and Deformable Objects (AMDO-e 2006), with L. Sigal for the paper "Predicting 3D people from 2D pictures.''
Marr Prize, Honorable Mention, Int. Conf. on Computer Vision, ICCV-2005, Beijing, China, Oct. 2005 with S. Roth for the paper "On the spatial statistics of optical flow.''
Marr Prize, Honorable Mention, Int. Conf. on Computer Vision, ICCV-99, Corfu, Greece, Sept. 1999 with D. J. Fleet for the paper "Probabilistic detection and tracking of motion discontinuities.''
IEEE Computer Society, Outstanding Paper Award, Conference on Computer Vision and Pattern Recognition, Maui, Hawaii, June 1991 with P. Anandan for the paper "Robust dynamic motion estimation over time.''
Commendation and Chief's Award, Henrico County Division of Police,
County of Henrico, Virginia, April 19, 2007.
University of Maryland, Invention of the Year, 1995, "Tracking and Recognizing Facial Expressions,'' with Y. Yacoob.
University of Toronto, Computer Science Students' Union Teaching Award for 1992-1993.
My research addressed the problem of estimating and explaining motion in image sequences. I developed methods detecting and tracking 2D and 3D human motion including the introduction of particle filtering for 3D human tracking and belief propagation for 3D human pose estimation. I worked on probabilistic models of images include the high-order Field of Experts model. I worked on 3D human shape estimation from images and video and developed applications of this technology. I also developed mathematical models for decoding neural signals. This included the first uses of particle filtering and Kalman filtering for decoding motor cortical neural activity and the first point-and-click cortical neural brain-machine-interface for people with paralysis.
Research included modeling image changes (motion, illumination, specularity, occlusion, etc.) in video as a mixture of causes. I developed methods of motion explanation; that is, the extraction of mid-level or high-level concepts from motion.This included the modeling and recognition of motion "features" (occlusion boundaries, moving bars, etc.), human facial expressions and gestures, and motion "texture" (plants, fire, water, etc.). I applied these methods to problems in video indexing, motion for video annotation, teleconferencing, and gestural user interfaces. Other research included robust learning of image-based models, regularization with transparency, anisotropic diffusion, and the recovery of multiple shapes from transparent textures.
Research included the application of mixture models to optical flow, detection and tracking of surface discontinuities using motion information, and robust surface recovery in dynamic environments.
Yale University, (9/89-8/92) New Haven, CT
Research Assistant, Department of Computer Science.
Research in the recovery of optical flow, incremental estimation, temporal continuity, applications of robust statistics to optical flow, the relationship between robust statistics and line processes, the early detection of motion discontinuities, and the role of representation in computer vision.
Developed motion estimation algorithms in the context of an autonomous Mars landing and nap-of-the-earth helicopter flight and studied the psychophysical implications of a temporal continuity assumption.
Research on spatial reasoning for robotic vehicle route planning and terrain analysis. Vision research including perceptual grouping, object-based translational motion processing, the integration of vision and control for an autonomous vehicle, object modeling using generalized cylinders, and the development of an object-oriented vision environment.
GTE Government Systems, (6/85-12/86) Mountain View, CA
Engineer, Artificial Intelligence Group.
Developed expert systems for multi-source data fusion and fault location.
Summer undergraduate researcher at UBC; park ranger's assistant; volunteer firefighter, busboy; and probably my worst job: cleaning dog kennels.
I am interested in motion. What does motion tell us about the structure of the world and how can we compute this from video? How do humans and animals move? How does the brain control complex movement? My work combines computer vision, graphics and neuroscience to develop new models and algorithms to capture and analyze the motion of the world.
My Computer Vision research addresses:
the estimation of scene structure and physical properties from video;
modeling the neural control of reaching and grasping;
novel neural decoding algorithms;
neural prostheses and cortical brain-machine interfaces;
markless animal motion capture.
What is maybe unique about my work is the combination of the these themes. For example I study human motion from the inside (decoding neural activity in paralyzed humans) and the outside (with novel motion capture techniques).
Frank Wood, Associate Professor, Department of Engineering, Oxford
Thesis: Nonparametric Bayesian modeling of neural data. Department of Computer Science, Brown University
Hulya Yalcin, Assistant Professor, Department of Electronics and Communications Engineering, Istanbul Technical University, Turkey
Thesis: Implicit models of moving and static surfaces, Division of Engineering, Brown University, May 2004
Wei Wu, Associate Professor, Dept. of Statistics, Florida State
Thesis: Statistical models of neural coding in motor cortex, Division of Applied Math, Brown University. Co-supervised with David Mumford. May 2004.
Fernando De la Torre, Research Associate Professor, CMU and Facebook,
Thesis: Robust subspace learning for computer vision, La Salle School of Engineering. Universitat Ramon Llull, Barcelona, Spain. Jan. 2002
My old Brown site has several image sequences used in my older publications. These include some classic sequences such as Yosemite, the Pepsi can, the SRI tree sequence, and the Flower Garden sequence.
A Quantitative Analysis of Current Practices in Optical Flow Estimation and the Principles behind Them
Sun, D., Roth, S., and Black, M.J. International Journal of Computer Vision (IJCV), 106(2):115-137, 2014. (pdf)
Secrets of optical flow estimation and their principles
Sun, D., Roth, S., and Black, M. J., IEEE Conf. on Computer Vision and Pattern Recog., CVPR, June 2010. (pdf)
This method implements many of the currently best known techniques for accurate optical flow and was once ranked #1 on the Middlebury evaluation (June 2010).
The software is made available for research pupropses. Please read the copyright statement and contact me for commerical licensing.
2. Matlab implmentation of the Black and Anandan dense optical flow method
The Matlab flow code is easier to use and more accurate than the original C code. The objective function being optimized is the same but the Matlab version uses more modern optimization methods:
The method in 1 above is more accurate and also implements Black and Anandan plus much more.
3. Original Black and Anandan method implemented in C
The optical flow software here has been used by a number of graphics companies to make special effects for movies. This software is provided for research purposes only; any sale or use for commercial purposes is strictly prohibited.
Contact me for the password to download the software, stating that it is for research purposes.
Please contact me if you wish to use this code for commercial purpose.
If you are a commercial enterprise and would like assistance in using optical flow in your application, please contact me at my consulting address email@example.com.
This is EXPERIMENTAL software. It is provided to illustrate some ideas in the robust estimation of optical flow. Use at your own risk. No warranty is implied by this distribution.
The robust estimation of multiple motions: Parametric and piecewise-smooth flow fields,
Black, M. J. and Anandan, P., Computer Vision and Image Understanding, CVIU, 63(1), pp. 75-104, Jan. 1996. (pdf),(pdf from publisher)
Robust Principal Component Analysis (PCA)
Software is from the ICCV'2001 paper with Fernando De la Torre.
The code below provides a simple Matlab implementation of the Bayesian 3D person tracking system described in ECCV'00 and ICCV'01. It is too slow to be used to track the entire body but can be used to track various limbs and provides a basis for people who want to understand the methods better and extend them.
Stochastic tracking of 3D human figures using 2D image motion,
Sidenbladh, H., Black, M. J., and Fleet, D.J., European Conference on Computer Vision, D. Vernon (Ed.), Springer Verlag, LNCS 1843, Dublin, Ireland, pp. 702-718 June 2000. (postscript)(pdf), (abstract)
Software. (Note: if you uncompress and untar this on a PC using Winzip, the path names may be lost which will cause Matlab to fail when you load the .mat files. Instead uncompress/untar using gunzip and tar.)
In Advances in Neural Information Processing Systems 23 (NIPS), pages: 2226-2234, MIT Press, 2010 (inproceedings)
Layered models are a powerful way of describing natural scenes containing smooth surfaces that may overlap and occlude each other. For image motion estimation, such models have a long history but have not achieved the wide use or accuracy of non-layered methods. We present a new probabilistic model of optical flow in layers that addresses many of the shortcomings of previous approaches. In particular, we define a probabilistic graphical model that explicitly captures: 1) occlusions and disocclusions; 2) depth ordering of the layers; 3) temporal consistency of the layer segmentation. Additionally the optical flow in each layer is modeled by a combination of a parametric model and a smooth deviation based on an MRF with a robust spatial prior; the resulting model allows roughness in
layers. Finally, a key contribution is the formulation of the layers using an image dependent hidden field prior based on recent models for static scene segmentation. The method achieves state-of-the-art results on the Middlebury benchmark and produces meaningful scene segmentations as well as detected occlusion regions.
International Journal of Computer Vision, 87(1):4-27, Springer Netherlands, March 2010 (article)
While research on articulated human motion and pose estimation has progressed rapidly in the last few years, there has been no systematic quantitative evaluation of competing methods to establish the current state of the art. We present data obtained using a hardware system that is able to capture synchronized video and ground-truth 3D motion. The resulting HumanEva datasets contain multiple subjects performing a set of predefined actions with a number of repetitions. On the order of 40,000 frames of synchronized motion capture and multi-view video (resulting in over one quarter million image frames in total) were collected at 60 Hz with an additional 37,000 time instants of pure motion capture data. A standard set of error measures is defined for evaluating both 2D and 3D pose estimation and tracking algorithms. We also describe a baseline algorithm for 3D articulated tracking that uses a relatively standard Bayesian framework with optimization in the form of Sequential Importance Resampling and Annealed Particle Filtering. In the context of this baseline algorithm we explore a variety of likelihood functions, prior models of human motion and the effects of algorithm parameters. Our experiments suggest that image observation models and motion priors play important roles in performance, and that in a multi-view laboratory environment, where initialization is available, Bayesian filtering tends to perform well. The datasets and the software are made available to the research community. This infrastructure will support the development of new articulated motion and pose estimation algorithms, will provide a baseline for the evaluation and comparison of new methods, and will help establish the current state of the art in human pose estimation and tracking.
In European Conf. on Computer Vision, (ECCV), pages: 285-298, Springer-Verlag, September 2010 (inproceedings)
Detection, tracking, segmentation and pose estimation of people in monocular images are widely studied. Two-dimensional models of the human body are extensively used, however, they are typically fairly crude, representing the body either as a rough outline or in terms of articulated geometric primitives. We describe a new 2D model of the human body contour that combines an underlying naked body with a low-dimensional clothing model. The naked body is represented as a Contour Person that can take on a wide variety of poses and body shapes. Clothing is represented as a deformation from the underlying body contour. This deformation is learned from training examples using principal component analysis to produce eigen clothing. We find that the statistics of clothing deformations are skewed and we model the a priori probability of these deformations using a Beta distribution. The resulting generative model captures realistic human forms in monocular images and is used to infer 2D body shape and pose under clothing. We also use the coefficients of the eigen clothing to recognize different categories of clothing on dressed people. The method is evaluated quantitatively on synthetic and real images and achieves better accuracy than previous methods for estimating body shape under clothing.
International Journal of Computer Vision (IJCV), 82(2):205-29, April 2009 (article)
We develop a framework for learning generic, expressive image priors that capture the statistics of natural scenes and can be used for a variety of machine vision tasks. The approach provides a practical method for learning high-order Markov random field (MRF) models with potential functions that extend over large pixel neighborhoods. These clique potentials are modeled using the Product-of-Experts framework that uses non-linear functions of many linear filter responses. In contrast to previous MRF approaches all parameters, including the linear filters themselves, are learned from training data. We demonstrate the capabilities of this Field-of-Experts model with two example applications, image denoising and image inpainting, which are implemented using a simple, approximate inference scheme. While the model is trained on a generic image database and is not tuned toward a specific application, we obtain results that compete with specialized techniques.
(J. Neural Engineering Highlights of 2008 Collection)
Kim, S., Simeral, J., Hochberg, L., Donoghue, J., Black, M. J.
J. Neural Engineering, 5, pages: 455–476, 2008 (article)
Computer-mediated connections between human motor cortical neurons and assistive devices
promise to improve or restore lost function in people with paralysis. Recently, a pilot clinical
study of an intracortical neural interface system demonstrated that a tetraplegic human was
able to obtain continuous two-dimensional control of a computer cursor using neural activity
recorded from his motor cortex. This control, however, was not sufficiently accurate for
reliable use in many common computer control tasks. Here, we studied several central design
choices for such a system including the kinematic representation for cursor movement, the
decoding method that translates neuronal ensemble spiking activity into a control signal and
the cursor control task used during training for optimizing the parameters of the decoding
method. In two tetraplegic participants, we found that controlling a cursor’s velocity resulted
in more accurate closed-loop control than controlling its position directly and that cursor
velocity control was achieved more rapidly than position control. Control quality was further
improved over conventional linear filters by using a probabilistic method, the Kalman filter, to
decode human motor cortical activity. Performance assessment based on standard metrics used
for the evaluation of a wide range of pointing devices demonstrated significantly improved
cursor control with velocity rather than position decoding.
In European Conf. on Computer Vision, ECCV, 5304, pages: 83-97, LNCS, (Editors: Forsyth, D. and Torr, P. and Zisserman, A.), Springer-Verlag, October 2008 (inproceedings)
Assumptions of brightness constancy and spatial smoothness underlie most optical flow estimation methods. In contrast to standard heuristic formulations, we learn a statistical model of both brightness constancy error and the spatial properties of optical flow using image sequences with associated ground truth flow fields. The result is a complete probabilistic model of optical flow. Specifically, the ground truth enables us to model how the assumption of brightness constancy is violated in naturalistic sequences, resulting in a probabilistic model of "brightness inconstancy". We also generalize previous high-order constancy assumptions, such as gradient constancy, by modeling the constancy of responses to various linear filters in a high-order random field framework. These filters are free variables that can be learned from training data. Additionally we study the spatial structure of the optical flow and how motion boundaries are related to image intensity boundaries. Spatial smoothness is modeled using a Steerable Random Field, where spatial derivatives of the optical flow are steered by the image brightness structure. These models provide a statistical motivation for previous methods and enable the learning of all parameters from training data. All proposed models are quantitatively compared on the Middlebury flow dataset.
Sun, D., Roth, S., Lewis, J., Black, M. J.
Learning Optical Flow
In European Conf. on Computer Vision, ECCV, 5304, pages: 83-97, LNCS, (Editors: Forsyth, D. and Torr, P. and Zisserman, A.), Springer-Verlag, October 2008 (inproceedings)
J. Neuroscience Methods, 173(1):1–12, August 2008 (article)
The analysis of extra-cellular neural recordings typically begins with careful spike sorting and all analysis
of the data then rests on the correctness of the resulting spike trains. In many situations this is
unproblematic as experimental and spike sorting procedures often focus on well isolated units. There is
evidence in the literature, however, that errors in spike sorting can occur even with carefully collected
and selected data. Additionally, chronically implanted electrodes and arrays with fixed electrodes cannot
be easily adjusted to provide well isolated units. In these situations, multiple units may be recorded and
the assignment of waveforms to units may be ambiguous. At the same time, analysis of such data may
be both scientifically important and clinically relevant. In this paper we address this issue using a novel
probabilistic model that accounts for several important sources of uncertainty and error in spike sorting.
In lieu of sorting neural data to produce a single best spike train, we estimate a probabilistic model of
spike trains given the observed data. We show how such a distribution over spike sortings can support
standard neuroscientific questions while providing a representation of uncertainty in the analysis. As a
representative illustration of the approach, we analyzed primary motor cortical tuning with respect to
hand movement in data recorded with a chronic multi-electrode array in non-human primates.We found
that the probabilistic analysis generally agrees with human sorters but suggests the presence of tuned
units not detected by humans.
In European Conf. on Computer Vision, ECCV, 5304, pages: 15-29, LNCS, (Editors: D. Forsyth and P. Torr and A. Zisserman), Springer-Verlag, Marseilles, France, October 2008 (inproceedings)
We propose a method to estimate the detailed 3D shape of a person from images of that person wearing clothing. The approach exploits a model of human body shapes that is learned from a database of over 2000 range scans. We show that the parameters of this shape model can be recovered independently of body pose. We further propose a generalization of the visual hull to account for the fact that observed silhouettes of clothed people do not provide a tight bound on the true 3D shape. With clothed subjects, different poses provide different constraints on the possible underlying 3D body shape. We consequently combine constraints across pose to more accurately estimate 3D body shape in the presence of occluding clothing. Finally we use the recovered 3D shape to estimate the gender of subjects and then employ gender-specific body models to refine our shape estimates. Results on a novel database of thousands of images of clothed and "naked" subjects, as well as sequences from the HumanEva dataset, suggest the method may be accurate enough for biometric shape analysis in video.
International Journal of Computer Vision, 74(1):33-50, 2007 (article)
We present an analysis of the spatial and temporal statistics of "natural" optical flow fields and a novel flow algorithm that exploits their spatial statistics. Training flow fields are constructed using range images of natural scenes and 3D camera motions recovered from hand-held and car-mounted video sequences. A detailed analysis of optical flow statistics in natural scenes is presented and machine learning methods are developed to learn a Markov random field model of optical flow. The prior probability of a flow field is formulated as a Field-of-Experts model that captures the spatial statistics in overlapping patches and is trained using contrastive divergence. This new optical flow prior is compared with previous robust priors and is incorporated into a recent, accurate algorithm for dense optical flow computation. Experiments with natural and synthetic sequences illustrate how the learned optical flow prior quantitatively improves flow accuracy and how it captures the rich spatial structure found in natural scene motion.
Journal of Physiology, Special Issue on Brain Computer Interfaces, 579, pages: 603-611, 2007 (article)
This review describes the rationale, early stage development, and initial human application of
neural interface systems (NISs) for humans with paralysis. NISs are emerging medical devices
designed to allowpersonswith paralysis to operate assistive technologies or to reanimatemuscles
based upon a command signal that is obtained directly fromthe brain. Such systems require the
development of sensors to detect brain signals, decoders to transformneural activity signals into
a useful command, and an interface for the user.We review initial pilot trial results of an NIS that
is based on an intracortical microelectrode sensor that derives control signals from the motor
cortex.We review recent findings showing, first, that neurons engaged by movement intentions
persist in motor cortex years after injury or disease to the motor system, and second, that signals
derived from motor cortex can be used by persons with paralysis to operate a range of devices.
We suggest that, with further development, this form of NIS holds promise as a useful new
neurotechnology for those with limited motor function or communication.We also discuss the
additional potential for neural sensors to be used in the diagnosis and management of various
neurological conditions and as a new way to learn about human brain function.
Donoghue, J., Hochberg, L., Nurmikko, A., Black, M. J., Simeral, J., Friehs, G.
Medicine & Health Rhode Island, 90(1):12-15, January 2007 (article)
Article describes a neuromotor prosthesis (NMP), in development at Brown University, that records human brain signals, decodes them, and transforms them into movement commands. An NMP is described as a system consisting of a neural interface, a decoding system, and a user interface, also called an effector; a closed-loop system would be completed by a feedback signal from the effector to the brain. The interface is based on neural spiking, a source of information-rich, rapid, complex control signals from the nervous system. The NMP described, named BrainGate, consists of a match-head sized platform with 100 thread-thin electrodes implanted just into the surface of the motor cortex where commands to move the hand emanate. Neural signals are decoded by a rack of computers that displays the resultant output as the motion of a cursor on a computer monitor. While computer cursor motion represents a form of virtual device control, this same command signal could be routed to a device to command motion of paralyzed muscles or the actions of prosthetic limbs. The researchers’ overall goal is the development of a fully implantable, wireless multi-neuron sensor for broad research, neural prosthetic, and human neurodiagnostic applications.
Kim, S., Simeral, J., Hochberg, L., Donoghue, J., Friehs, G., Black, M. J.
In The 3rd International IEEE EMBS Conference on Neural Engineering, pages: 486-489, May 2007 (inproceedings)
Basic neural-prosthetic control of a computer cursor has been recently demonstrated by Hochberg et al. 
using the BrainGate system (Cyberkinetics Neurotechnology Systems, Inc.). While these results demonstrate the feasibility of intracortically-driven prostheses for humans with paralysis, a practical cursor-based computer interface requires more precise cursor control and the ability to “click” on areas of interest. Here we present a practical point and click device that decodes both continuous states (e.g. cursor kinematics) and discrete states (e.g. click state) from single neural population in human motor cortex. We describe a probabilistic multi-state decoder and the necessary training paradigms that enable point and click cursor control by a human with tetraplegia using an
implanted microelectrode array. We present results from multiple recording sessions and quantify the point and click
Wu, W., Gao, Y., Bienenstock, E., Donoghue, J., Black, M. J.
Neural Computation, 18(1):80-118, 2006 (article)
Effective neural motor prostheses require a method for decoding neural activity representing desired movement. In particular, the accurate reconstruction of a continuous motion signal is necessary for the control of devices such as computer cursors, robots, or a patient's own paralyzed limbs. For such applications, we developed a real-time system that uses Bayesian inference techniques to estimate hand motion from the firing rates of multiple neurons. In this study, we used recordings that were previously made in the arm area of primary motor cortex in awake behaving monkeys using a chronically implanted multielectrode microarray. Bayesian inference involves computing the posterior probability of the hand motion conditioned on a sequence of observed firing rates; this is formulated in terms of the product of a likelihood and a prior. The likelihood term models the probability of firing rates given a particular hand motion. We found that a linear gaussian model could be used to approximate this likelihood and could be readily learned from a small amount of training data. The prior term defines a probabilistic model of hand kinematics and was also taken to be a linear gaussian model. Decoding was performed using a Kalman filter, which gives an efficient recursive method for Bayesian inference when the likelihood and prior are linear and gaussian. In off-line experiments, the Kalman filter reconstructions of hand trajectory were more accurate than previously reported results. The resulting decoding algorithm provides a principled probabilistic model of motor-cortical coding, decodes hand motion in real time, provides an estimate of uncertainty, and is straightforward to implement. Additionally the formulation unifies and extends previous models of neural coding while providing insights into the motor-cortical code.
Our goal is to understand the principles of Perception, Action and Learning in autonomous systems that successfully interact with complex environments and to use this understanding to design future systems