Computational Vision
Psychology Department , University of Minnesota
Psy 5036W, Fall 2017, 3 credits #34359

08:15 A.M. - 9:30 A.M. Mondays and Wednesdays
Elliott Hall N668

Instructor: Daniel Kersten. Office: S212 Elliott Hall. Phone: 612 625-2589 email:
Office hours: Mondays 9:30-10:30 am or by appointment.

The visual perception of what is in the world is accomplished continually, instantaneously, and usually without conscious thought. The very effortlessness of perception disguises the underlying richness of the problem. We can gain insight into the processes and functions of human vision by studying the relationship between neural mechanisms and visual behavior through computer analysis and simulation. Students will learn about the anatomy and neurophysiology of vision and how they relate to the phenomona of perception. An underlying theme will be to treat vision as a process of statistical inference. There will be in-class programming exercises using the language Mathematica. No prior programming experience is required; however, some familiarity with probability, vector calculus and linear algebra is helpful.



Additional readings

Math and vision
Functional human vision



Mathematica is the primary programming environment for this course. Students who have registered for the course will have Google Docs access through the Psychology Department's site license.

Alternatives: Mathematica is available in several labs on campus, go to
You may wish to purchase Mathematica for Students see

You can also access Mathematica on the CLA servers:

If you never programmed before go here. If you have programming experience, go here.

For user help on using Mathematica, see:



Grade Requirements

There will be programming assignments and a final project.

The grade weights are:

The programming assignments will use the Mathematica programming environment. No prior experience with Mathematica is necessary.

Assignment due By the midnight on the day due.
Late Policy: Assignments turned in within 24 hours following the due date will have 15% deducted from the assignment score. Assignments turned in between 24 and 48 hours following the due date will have 30% deducted from the score. Assignments more than 48 hours late will receive a score of zero.



Check this section before each class for recent additions and revisions.

(5036W Course material from 2015)

Lecture notes are in Mathematica Notebook and pdf format. You can download the Mathematica notebook files below to view with Mathematica or Wolfram CDF Player (which is free).

University Calendar Date Lecture Main Readings Supplementary Material Assignments
I. Introduction
Sep 6
1. Introduction to Computational Vision


Olshausen, B. A. (2013). Perception as an Inference Problem. In M. Gazzaniga (Ed.), The New Cognitive Neurosciences, 5th Edition (pp. 1–22). MIT Press. (pp. 1–18). MIT Press. (pdf)


Screencast: (WITH AUDIO)

Check out demos under: Life Sciences/Cognitive Science/Perception and Engineering & Technology/Image Processing on the Mathematica Demonstrations site:

Kersten, D., & Yuille, A. (2003). Bayesian models of object perception. Current Opinion in Neurobiology, 13(2), 1-9. (pdf)

EV: Section 1

Sep 11
2.Limits to Vision 2.LimitsToVision.nb

Hecht, S., Shlaer, S., & Pirenne, M. H. (1942). Energy, quanta, and vision. Journal of General Physiology, 25, 819-840. (pdf)

Barlow, H. B. (1981). Critical Limiting Factors in the Design of the Eye and Visual Cortex. Proc. Roy. Soc. Lond. B, 212, 1-34. (pdf)

Baylor, D. A., Lamb, T. D., & Yau, K. W. (1979). Responses of retinal rods to single photons. Journal of Physiology, Lond., 288, 613-634. (pdf)

Tinsley, J. N., Molodtsov, M. I., Prevedel, R., Wartmann, D., Pons, J. E. E., Lauwers, M., & Vaziri, A. (2016). Direct detection of a single photon by humans. Nature Communications, 7, 1–9. (pdf)


Sep 13
3. The Ideal Observer 3.TheIdealObserver.nb


Griffiths, T. L., & Yuille, A. (2008). A primer on probabilistic inference. In M. Oaksford and N. Chater (Eds.). The probabilistic mind: Prospects for rational models of cognition. Oxford: Oxford University Press (pdf).

Try your luck against an ideal discriminator of dot density YesNoDotDiscriminationDemo.nb

Upload Assignment #1 to Moodle


Sep 18

4. Ideal observer analysis: Humans vs. ideals. Neurons vs. ideals

4.IdealObserverAnalysis.nb (pdf)


Kersten and Mamassian (2008), Ideal observer theory. The New Encyclopedia of Neuroscience, Squire et al., editors (pdf).

Geisler, W. S. (2011). Contributions of ideal observer theory to vision research. Vision Research, 51(7), 771781.(pdf)

Burgess, A. E., Wagner, R. F., Jennings, R. J., & Barlow, H. B. (1981). Efficiency of human visual signal discrimination. Science, 214(4516), 93-94. (pdf)

Deneve, S., Latham, P. E., & Pouget, A. (1999). Reading population codes: a neural implementation of ideal observers. Nature Neuroscience, 2(8), 740745. (pdf)

Measure your absolute efficiency to discriminate dot density using a 2AFC task 2AFCDotDiscriminationDemo.nb

II. Image formation,
pattern synthesis
Sep 20
5.Psychophysics: tools & techniques



Farell, B. & Pelli, D. G. (1999) Psychophysical methods, or how to measure a threshold and why. In R. H. S. Carpenter & J. G. Robson (Eds.), Vision Research: A Practical Guide to Laboratory Methods, New York: Oxford University (pdf) Press.

Morgenstern, Y., & Elder, J. H. (2012). Local Visual Energy Mechanisms Revealed by Detection of Global Patterns. Journal of Neuroscience, 32(11), 36793696.

For a free Matlab psychophysics package, see:

For a free Python psychophysics package, see:

Sep 25
6. Bayesian decision theory & perception


Geisler, W. S., & Kersten, D. (2002). Illusions, perception and Bayes. Nat Neurosci, 5(6), 508-510. (pdf)

EV Section 3


Sep 27
7. Limits to spatial resolution, image modeling, introduction to linear systems


Campbell, F. W., & Green, D. (1965). Optical and retinal factors affecting visual resolution. Journal of Physiology (Lond.), 181, 576-593. (pdf)

Williams, D. R. (1986). Seeing through the photoreceptor mosaic. 9(5), 193-197. (pdf)



IPython convolutions notebook

    Upload Assignment #2 to Moodle


(correction 10/4/17)

III. Early visual coding
Oct 2
8. Linear systems analysis 8.LinearSystemsOptics.nb

EV: Section 2



Oct 4
9. Features and filters. Spatial filter models of early human vision


Campbell, F. W., & Robson, J. R. (1968). Application of Fourier Analysis to the Visibility of Gratings. Journal of Physiology 197, 551-566. (pdf)

De Valois, R. L., Albrecht, D. G., & Thorell, L. G. (1982). Spatial frequency selectivity of cells in macaque visual cortex. Vision Res, 22(5), 545-559. (pdf)

Watson, A. B. (1987). Efficiency of a model human image code. J Opt Soc Am A, 4(12), 2401-2417. (pdf)

IPython demo of gabor filtering

Steerable pyramids:

Oct 9
10. Features and filters. Local processing & image analysis 10.ImageProcessing.nb

Gollisch, T., & Meister, M. (2010). Eye Smarter than Scientists Believed: Neural Computations in Circuits of the Retina. Neuron, 65(2), 150164. (pdf)
Albrecht, D. G., De Valois, R. L., & Thorell, L. G. (1980). Visual cortical neurons: are bars or gratings the optimal stimuli? Science, 207(4426), 88-90.(pdf)

Adelson, E. H., & Bergen, J. R. (1991). The plenoptic function and the elements of early vision. In M. S. Landy & J. A. Movshon (Eds.), Computational Models of Visual Processing. Cambridge, MA: The MIT Press: A Bradford Book.(pdf)

ClassificationImage demo (ReverseCorrelation.nb)

Ahumada, A. J., Jr. (2002). Classification image weights and internal noise level estimation. J Vis, 2(1), 121-131. (pdf)

Upload Assignment 3 to Moodle


Oct 11
11. Coding efficiency: Retina


Geisler, W. S. (2008). Visual perception and the statistical properties of natural scenes. Annu Rev Psychol, 59, 167-192. (pdf)

Laughlin, S. (1981). A simple coding procedure enhances a neuron's information capacity. Z Naturforsch [C], 36(9-10), 910-912.(pdf)

Atick, J. J., & Redlich, A. N. (1992). What does the retina know about natural scenes? Neural Computation, 4(2), 196210. Meister, M., & Berry, M. J., 2nd. (1999). The neural code of the retina. Neuron, 22(3), 435-450.(pdf) Srinivasan, M. V., Laughlin, S. B., & Dubs, A. (1982). Predictive coding: a fresh view of inhibition in the retina. Proc R Soc Lond B Biol Sci, 216(1205), 427-459.(pdf)

IPython demo of natural image statistics

Oct 16
12. Coding efficiency: Cortex


Simoncelli, E. P., & Olshausen, B. A. (2001). Natural image statistics and neural representation. Annu Rev Neurosci, 24, 1193-1216.(pdf)


Laughlin, S. B., de Ruyter van Steveninck, R. R., & Anderson, J. C. (1998). The metabolic cost of neural information. Nat Neurosci, 1(1), 36-41.(pdf)

Lennie, P. (2003). The cost of cortical computation. Curr Biol, 13(6), 493-497. (pdf)

Multi-resolution, image pyramids, and efficient coding:

IV. Intermediate-level vision,
integration, grouping
Oct 18
13. Edge detection 13.EdgeDetection.nb

Hubel, D. H., & Wiesel, T. N. (1977). Ferrier lecture. Functional architecture of macaque monkey visual cortex. Proc R Soc Lond B Biol Sci, 198(1130), 1-59. (pdf)

IPython demo of statistical edge detection

Oct 23
14. Objects and scenes from images. The visual cortical pathways and hierarchy.


von der Heydt R (2003) Image parsing mechanisms of the visual cortex. In: The Visual Neurosciences (Werner JS, Chalupa LM, eds.), pp 1139-1150. Cambridge, Mass.: MIT press.(pdf)

Kersten, D. J., & Yuille, A. L. (2014). Inferential Models of the Visual Cortical Hierarchy. In M. S. Gazzaniga & G. R. Mangun (Eds.), The New Cognitive Neurosciences, 5th Edition (pp. 1–22). MIT Press. (pdf)

Zhou H, Friedman HS, von der Heydt R (2000) Coding of border ownership in monkey visual cortex. J Neuroscience 20: 6594-6611. (pdf)  
Oct 25
15. Scene-based generative models


Kersten, D., Mamassian, P., & Yuille, A. (2004). Object perception as Bayesian Inference. Annual Review of Psychology, 55, 271-304. (pdf)



Oct 30
16. Shape-from-X 16.ShapeFromX.nb

Reflectance map: Shape from shading: Horn BKP (1986) Robot Vision. Cambridge MA: MIT Press. Ch 11 (pdf).

Barron, J. T., & Malik, J. (2015). Shape, Illumination, and Reflectance from Shading. IEEE Transactions on Pattern Analysis and Machine Intelligence, 37(8), 1670–1687. (pdf)

Belhumeur, P. N., Kriegman, D. J., & Yuille, A. (1997). The Bas-Relief Ambiguity. (pdf) Johnson, M. K., & Adelson, E. H. (2011). Shape Estimation in Natural Illumination. Computer Vision and Pattern Recognition (CVPR), 2553–2560.

Muryy, A. A., Welchman, A. E., Blake, A., & Fleming, R. W. (2013). Specular reflections and the estimation of shape from binocular disparity. Proceedings of the National Academy of Sciences of the United States of America, 110(6), 2413–2418. (link)

Upload Assignment #4 to Moodle


bluradaptationdemo (Webster et al. pdf)

motion-induced-blindness demo (Bonneh et al. pdf)

Nov 1

17. Shape from shading

Overview of python/ipython for computational vision

17. Shape from shading.nb

Lect_17Intro_Python.ipynb (source)


17. IPython notebook


Demos by Weichao Qiu and Dan Kersten, supplement to Early Vision. Yuille and Kersten. A chapter in From Neuron to Cognition via Computational Neuroscience, M.A. Arbib, James J. Bonaiuto Editors, Cambridge MA: The MIT Press, in 2016

Anaconda python installation recommended. We will use Juypter/IPython, a browser-based notebook interface for python.


See here for illustrations of IPython cell types, and here for a collection of sample notebooks.

Look here for some good tips on installation, as well as the parent directory for excellent ipython-based course material on scientific computing using Monte Carlo methods.

For a quick start to scientific programming, see:

For a comphrensive coverage of scientific python see:

And for a ground-up set of tutorials on python see:

Switching from matlab to python?



Nov 6
18. Motion: optic flow


OpenCV python demo: OpticFlowSparse.ipynb
needs: 648aa10.avi

Horn, B. K. P., & Schunck, B. G. (1981). Determining Optical Flow. Artificial Intelligence, 17, 185-203. (pdf)

Optic Flow (2013) Florian Raudies, Scholarpedia, 8(7):30724. doi:10.4249/scholarpedia.30724 (link) (with available matlab code)

Optic flow matlab code from Michael Black's lab. (link)

Borst, A. (2007). Correlation versus gradient type motion detectors: the pros and cons. Philos Trans R Soc Lond B Biol Sci, 362(1479), 369-374. pdf)

IPython aperture demo

EV: Section 2.4

FV: Chapter 10


Nov 8
19. Motion: biological, human perception


Weiss, Y., Simoncelli, E. P., & Adelson, E. H. (2002). Motion illusions as optimal percepts. Nat Neurosci, 5(6), 598-604.

Heeger, D. J., Simoncelli, E. P., & Movshon, J. A. (1996). Computational models of cortical visual processing. Proc Natl Acad Sci U S A, 93(2), 623-627. (pdf)

EV: Section 4.4
FV: Chapter 10

Nov 13
20. Material perception


V1 and lightness (pdf)

Doerschner, K., Fleming, R. W., Yilmaz, O., Schrater, P. R., Hartung, B., & Kersten, D. (2011). Visual motion and the perception of surface material. Current Biology, 21(23), 2010–2016. (pdf)

Fleming, R. W., Dror, R. O., & Adelson, E. H. (2003). Real-world illumination and the perception of surface reflectance properties. J Vis, 3(5), 347-368. (link)

Adelson, E. H. (1993). Perceptual organization and the judgment of brightness. Science, 262, 2042-2044 (pdf)

Boyaci, H., Fang, F., Murray, S. O., & Kersten, D. (2007). Responses to lightness variations in early human visual cortex. Curr Biol, 17(11), 989-993 (pdf)

Upload Assignment 5 to Moodle




Upload Final project title & paragraph outline to Moodle

Nov 15
21. Texture.


Freeman, J., & Simoncelli, E. P. (2011). Metamers of the ventral stream. Nature Publishing Group, 14(9), 1195-1201. (pdf)

Heeger DJ and Bergen JR, Pyramid Based Texture Analysis/Synthesis, Computer Graphics Proceedings, p. 229-238, 1995. (pdf).




A sample: out2.png

Nov 20
22.Science writing (Thanksgiving week) 22.ScienceWriting.nb

Gopen & Swan, 1990 (pdf)

UM Psychology

Denis Pelli's advice for scientific writing

Nov 22
23.Perceptual integration 23.PerceptualIntegration.nb

McDermott, J., Weiss, Y., & Adelson, E. H. (2001). Beyond junctions: nonlocal form constraints on motion interpretation. Perception, 30(8), 905-923. (pdf)

Hillis, J. M., Ernst, M. O., Banks, M. S., & Landy, M. S. (2002). Combining sensory information: mandatory fusion within, but not between, senses. Science, 298(5598), 1627-1630.(pdf) Ernst, M. O., & Banks, M. S. (2002). Humans integrate visual and haptic information in a statistically optimal fashion. Nature, 415(6870), 429-433. (pdf)

Stocker, A. A., & Simoncelli, E. (2008). A Bayesian model of conditioned perception. Advances in Neural Information Processing Systems, 20, 1409-1416. (pdf)

IPython demo of ideal integration

EV: Section 5

V. High-level vision
Nov 27
24. Object recognition I


DiCarlo, J. J., Zoccolan, D., & Rust, N. C. (2012). How does the brain solve visual object recognition? Neuron, 73(3), 415–434. (pdf)

Liu, Z., Knill, D. C., & Kersten, D. (1995). Object Classification for Human and Ideal Observers. Vision Research, 35(4), 549-568. (pdf)

Tjan, B., Braje, W., Legge, G. E., & Kersten, D. (1995). Human efficiency for recognizing 3-D objects in luminance noise. Vision Research, 35(21), 3053-3069. (pdf)

Tanaka K (2003) Columns for complex visual object features in the inferotemporal cortex: clustering of cells with similar but slightly different stimulus selectivities. Cerebral cortex 13:90-99.(pdf)

Serre, T., Oliva, A., & Poggio, T. (2007). A feedforward architecture accounts for rapid categorization. Proc Natl Acad Sci U S A, 104(15), 6424-6429.

Yamins, D. L. K., Hong, H., Cadieu, C. F., Solomon, E. A., Seibert, D., & DiCarlo, J. J. (2014). Performance-optimized hierarchical models predict neural responses in higher visual cortex. Proceedings of the National Academy of Sciences of the United States of America, 111(23), 8619-8624. (pdf)

Nov 29
25. Object recognition II feeforward architectures 25_Bidirectional_I.key.pdf (pdf)

Ullman, S., Vidal-Naquet, M., & Sali, E. (2002). Visual features of intermediate complexity and their use in classification. Nat Neurosci, 5(7), 682-687. (pdf)

Grill-Spector, K. (2003). The neural basis of object perception. Curr Opin Neurobiol, 13(2), 159-166.(pdf)

Rao, R. P., & Ballard, D. H. (1999). Predictive coding in the visual cortex: a functional interpretation of some extra-classical receptive-field effects. Nat Neurosci, 2(1), 79-87. (pdf)

Bullier, J. (2001). Integrated model of visual processing. Brain Res Brain Res Rev, 36(2-3), 96-107. (pdf)

Tenenbaum JB: Bayesian modeling of human concept learning. In Advances in Neural Information Processing Systems. Edited by Kearns MSS, Solla A, Cohn DA: Cambridge, MA: MIT Press: 1999.(pdf)

Upload Assignment 6 to Moodle

Problem_Set_6 .nb

Dec 4
26. Object recognition III feedback architectures

26_BidirectionalFeedback.key.pdf (pdf)

Torralba, A., Oliva, A., Castelhano, M. S., & Henderson, J. M. (2006). Contextual guidance of eye movements and attention in real-world scenes: the role of global features in object search. Psychol Rev, 113(4), 766-786. (pdf)

Chikkerur, S., Serre, T., Tan, C., & Poggio, T. (2010). What and where: A Bayesian inference theory of attention. Vision Research, 50(22), 2233–2247.

Dec 6


27. Empirical evidence for bidirectional computations



Longuet-Higgins, H. C., & Prazdny, K. (1980). The Interpretation of a Moving Retinal Image. Proceedings of the Royal Society of London B, 208, 385-397. (pdf)

Horn BKP (1986) Robot Vision. Cambridge MA: MIT Press., chapter 17 (pdf)

Schrater PR, Kersten D (2000) How optimal depth cue integration depends on the task. International Journal of Computer Vision 40:73-91. (pdf)

Upload a complete DRAFT of FINAL PROJECT to Moodle by Wednesday December 6th,
5 PM.
Dec 11
28. Vision for action, spatial layout, heading. Homegeneous coordinates.


Kalman filter notes (pdf)

  Upload your peer comments to Moodle by Monday Dec 11th
Dec 13
(Last day of class)
  In Class Project Presentations  

Drafts returned to you with Instructor comments

Dec 21
      Upload Final Revised Draft of Project to Moodle



Final Project Assignment.

Goal: This course integrates the behavioral, neural and computational principles of perception. Students often find the interdisciplinary integration to be the most challenging aspect of the course. Through writing, you will learn to synthesize results from diverse and typically isolated disciplines. By writing about your project work, you will learn to think through the broader implications of your project, and to effectively communicate the rationale and results of your contribution in words. You will do a final page research report in which you will describe, in the form of a scientific paper, the results of an original computer program on a topic in computational vision.

Your final project will involve: 1) a computer program and; 2) a 2000-3000 word final paper describing your project. For your computer project, you will do one of the following: 1) Write a program to simulate a model from the computer vision literature ; 2) Design and program a method for solving some problem in perception. 3) Design and program a psychophysical experiment to study an aspect of human visual perception. The results of your final project should be written up in the form of a short scientific paper or Mathematica Notebook, describing the motivation, methods, results, and interpretation.

If you choose to write your program in Mathematica, your paper and program can be combined can be formated as a Mathematica notebook. See: Books and Tutorials on Notebooks. If you do your final project using Python, you can turn your paper in as a Jupyter notebook.

Your paper will be critiqued and returned for you to revise and resubmit in final form. You should write for an audience consisting of your class peers.

Completing the final paper involves 4 steps. Each step requires that you email a document to the teaching assistant.

    1. Outline (2% of grade). You will submit a working title and paragraph outline by the deadline noted in the syllabus. These outlines will be critiqued in order to help you find an appropriate focus for your papers. (Consult with the instructor or TA for ideas well ahead of time).

    2. Complete draft (5% of grade). A double-spaced, complete draft of the paper must be turned in by the deadline noted in the syllabus. Papers should be between 2000 and 3000 words. In addition to the title, author and date lines, papers must include the following sections: Abstract, Introduction, Methods, Results, Discussion, and Bibliography. Use citations to motivate your problem and to justify your claims. Cite authors by name and date, e.g. (Marr & Poggio, 1979). Citations should be original sources, not wikipedia. Use a standard citation format, such as APA. (The UM library has information on style guides, and in particular APA style.) Papers must be typed, with a page number on each page. Figures should be numbered and have figure captions. This draft will be reviewed by your instructor and one of you class peers. The point break down for the total 5% is: 2 pts for completing Introduction, 2 pts for completing Methods, 1 pt for completing Discussion)

    3. Peer commentary (5% of grade). You will submit a written commentary (200 to 500 words) on a complete draft of one of your class peers. The project drafts and commentaries will be anonymous. The commentary should provide feedback to improve the quality and clarity of the writing.

    4. Final draft (20% of grade) and "Cover letter" (8% of grade). The final draft must be turned in by the date noted on the syllabus. The "Cover letter" should describe how your revision addressed comments from your peer evaluator and from your instructor. It should itemize key criticisms together with a brief description of the changes you made to your draft manuscript.

    5. Some Resources:

    6. Student Writing Support: Center for Writing, 306b Lind Hall and satellite locations (612.625.1893)

      NOTE: Plagiarism, a form of scholastic dishonesty and a disciplinary offense, is described by the Regents as follows: Scholastic dishonesty means plagiarizing; cheating on assignments or examinations; engaging in unauthorized collaboration on academic work; taking, acquiring, or using test materials without faculty permission; submitting false or incomplete records of academic achievement; acting alone or in cooperation with another to falsify records or to obtain dishonestly grades, honors, awards, or professional endorsement; altering, forging, or misusing a University academic record; or fabricating or falsifying data, research procedures, or data analysis. See too: and

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