class: center, middle, inverse, title-slide # 2018-01-22 Methods & Theories ## PSY 525.001 • Vision Science • 2018 Spring ### Rick Gilmore ### 2018-01-22 17:54:04 --- # Today's topics ## Theoretical approaches to vision ## Methods in vision research --- ## Goals - Why vision science matters to other areas of cognition - How vision (or perceptual methods) affect other areas of behavioral science --- ## Palmer's claims 1. Perception is knowledge acquisition 2. Knowledge is about objects and events 3. Knowledge is extracted by information processing 4. Information comes from reflected, refracted, or emitted light. --- class: center, middle ## Things to worry about ### Or general problems that vision science keeps front and center --- class: center, middle # Homunculus problem <div class="centered"> <a href="https://en.wikipedia.org/wiki/Homunculus_argument"> <img src="https://upload.wikimedia.org/wikipedia/commons/a/a1/Infinite_regress_of_homunculus.png" width=800px> </a> </div> --- class: center, middle # [Marr's three levels](http://www.albany.edu/~ron/papers/marrlevl.html) ## Computations ## Algorithms ## Implementations --- class: center, middle <a href="http://www.nature.com/nrn/journal/v15/n8/box/nrn3747_BX2.html"> <img src="http://www.nature.com/nrn/journal/v15/n8/images/nrn3747-i2.jpg" width=900px> </a> ([Grill-Spector et al., 2014](http://doi.org/10.1038/nrn3747)) --- class: center, middle # What is information processing, anyway? <div class="centered"> <img src="https://upload.wikimedia.org/wikipedia/commons/d/d1/Information_processing_system_%28english%29.PNG"> </div> --- class: center, middle <div class="centered"> <img src="img/palmer-1999-hierarchical-decomp.jpg" height=500px> </div> --- class: center, middle # What is a representation of property X? <div class="centered"> <img src="img/palmer-1999-representation-types.jpg" height=500px> </div> --- class: center, middle # Modeling the unseen environment <div class="centered"> <img src="http://1.bp.blogspot.com/-zbl8jqkg9hI/UPke9-U6WfI/AAAAAAAAAas/fmY43tNF6Is/s1600/200px-Kanizsa_triangle.svg.png" height=400px> </div> ### [Kanisza](https://en.wikipedia.org/wiki/Gaetano_Kanizsa) triangle --- class: center, middle # [Necker cube](https://en.wikipedia.org/wiki/Necker_cube) with illusory contours <div class="centered"> <img src="http://www.socsci.uci.edu/~ddhoff/subjnecker.gif" height=450px> </div> --- class: center, middle # Impossible figure <div class="centered"> <img src="http://vrf.wpengine.netdna-cdn.com/wp-content/uploads/2014/03/impossible-objects-02.jpg" height=450px> </div> --- class: center, middle # Inspired by M.C. Escher. <a href="https://en.wikipedia.org/wiki/M._C._Escher"> <img src="https://upload.wikimedia.org/wikipedia/en/e/e8/Escher_Waterfall.jpg" height=500px> </a> --- class: center, middle # Bottom-up vs. top-down <img src="http://www.psywww.com/gst/zz%20thecat.png"/> --- class: center # What must (sighted) animals do? -- ## Find food -- ## Find mates -- ## Avoid predators --- class: center # How does vision help them do these things? -- ## What is it? -- ## Where is it located or moving? -- ## How should I respond? --- class: center # How does vision arise? -- ## Empiricism vs. nativism -- ## Are 'maturational' accounts nativist? --- class: center, middle <img src="https://cdn-images-1.medium.com/max/800/1*q7-pmQwWmateR7jGjmIeCQ.jpeg"/> --- class: center, middle # Are parsimonious accounts necessarily better? <img src="https://i0.wp.com/theethicalskeptic.com/wp-content/uploads/2013/06/c9fhzhxuwaa_dco-large.jpg?resize=552%2C290&ssl=1"/> --- class: center # Classical theories of vision ## "Why do things look as they do?" (Koffka, 1935) -- ### A: [*Structuralism*](https://en.wikipedia.org/wiki/Structuralism_(psychology): "The (world/visual nervous system) is that way." -- ### A: *Empiricism vs. nativism*: "We (learn to/were born to) see them that way." -- ### A: *Atomism vs. holism*: "Because of the way (each small piece/the whole visual field) appears." -- ### A: *Introspection vs. behavior*: "How things *look* matters (more/less) than what we *do* with the information." --- # Theoretical approaches and their champions ## Gestaltism, [Max Wertheimer](https://en.wikipedia.org/wiki/Max_Wertheimer) <img src="https://yusylvia.files.wordpress.com/2010/03/gestalt_illustration-01.jpg" width=900px> Holism, emergent properties, psychophysiological isomorphism, physical Gestalt --- # Theoretical approaches and their champions ## Ecological optics, [James J. Gibson](https://en.wikipedia.org/wiki/James_J._Gibson) <div class="center"> <img src="http://www.csus.edu/indiv/w/wickelgren/psyc103/opticarray.jpg" height=350px> </div> Ambient optic array, information pickup, direct perception --- class: center, middle # What is first-person visual experience actually like? Gilmore, R.O., Raudies, F., Franchak, J. & Adolph, K. (2015). Understanding the development of motion processing by characterizing optic flow experienced by infants and their mothers. Databrary. Retrieved January 19, 2018 from http://doi.org/10.17910/B7.116 --- class: center, middle <video controls> <source height=450px src="https://nyu.databrary.org/slot/7739/0,26634/asset/16747/download?inline=true" type="video/mp4"> Your browser does not support the video tag. </video> --- # Theoretical approaches and their champions ## Constructivism, [Herman von Helmholtz](https://en.wikipedia.org/wiki/Hermann_von_Helmholtz) <img src="https://www.edge.org/images/gig.jpg" width=900px> Unconscious inference, likelihood principle (~ Gestalt Pragnanz), heuristics e.g., concavity vs. convexity a function of luminance + direction of illumination --- class: center # A 'Helmholtzian' demonstration of 'unconscious inference' ## Saccade ## Move eye with finger ## Why 'visual stability' in one case, not the other? --- class: center # Four stages of visual perception ## (Spatio-temporal structure of events, objects, entities in the world...) ## Image-based ## Surface-based ## Object-based ## Category-based --- class: center, middle <img src="img/palmer-1999-visual-info-processing.jpg" height=500px> --- class: center # Hierarchical + parallel processing <div class="center"> <img src="https://mechanism.ucsd.edu/gall/wh-wh-cs.jpg" height=450px> </div> --- class: inverse, center, middle # Break time --- class: inverse, center, middle # Methods in vision research --- class: center, middle # Psychophysical methods ## Measuring thresholds ## Signal detection theory ## Absolute vs. Difference thresholds ## Psychophysical scaling --- class: center, middle <img src="http://www.centerforworklife.com/cfwl-content/uploads/2013/02/canyouhmn.jpg"/> --- class: center # Measuring ([absolute/detection](https://en.wikipedia.org/wiki/Absolute_threshold)) thresholds <img src="https://betanews.com/wp-content/uploads/2013/12/Future-threshold.jpg" height=500px> --- class: center # Gustav Fechner's (1860) methods <img src="https://upload.wikimedia.org/wikipedia/commons/a/ae/Gustav_Fechner.jpg" height=200px/> ## Method of adjustment ## Method of limits ## Method of constant stimuli (constants) --- class: center # Method of adjustment <img src="http://petergowesky.com/wp-content/uploads/2014/07/volume-knob-wallpapers_17585_1600x1200.jpg" height=500px> --- class: center # Method of limits ## Psychophysical staircases a kind of method of limits <p><a href="https://en.wikipedia.org/wiki/File:Method_of_limits.png#/media/File:Method_of_limits.png"><img src="https://upload.wikimedia.org/wikipedia/en/d/d3/Method_of_limits.png" alt="Method of limits.png"></a><br><a href="https://creativecommons.org/licenses/by-sa/2.5/" title="Creative Commons Attribution-ShareAlike 2.5">CC BY-SA 2.5</a>, <a href="https://en.wikipedia.org/w/index.php?curid=9878731">Link</a></p> --- class: center # Method of constants <img src="https://github.com/gilmore-lab/child-motion-psychophysics/blob/master/group-analysis-child_files/figure-markdown_github/coh-by-pattern-and-age-plot-1.png?raw=true" height=450px> Gilmore, R.O., Seisler, A., Shade, M., O’Neill, M. (2017, April). School-age children perceive fast radial optic flow in noise more accurately than slow linear flow. Poster presentation at the Society for Research in Child Development, Austin, TX. [PDF](https://github.com/gilmore-lab/child-motion-psychophysics/blob/master/pubs/srcd-17-poster/gilmore-seisler-shade-oneill-srcd-2017.pdf). [Databrary](http://nyu.databrary.org/volume/218). [GitHub](https://github.com/gilmore-lab/moco-3-pattern-psychophysics/tree/master/child-motion-psychophysics). --- class: center, inverse # Your turn ## Pros and cons of method of adjustment? ## Pros and cons of method of limits? ## Pros and cons of method of constants? --- class: center # Psychometric functions ## Fitting psychometric functions is goal of psychophysical methods. ## Relates percent (proportion) detections vs. magnitude of some perceptual variable (brightness, contrast, motion speed, direction, etc...) --- class: center # Psychometric functions Usually on `\([0,100]\)` or `\([0,1]\)` scale. -- Often curvlinear, monotonic (increasing) functions of stimulus intensity -- `\(P(respond) = f(stimulus, observer, situation,...)\)` -- Analysis often focuses on *threshold* responses: detect (yes/no) or discriminate (same/different) --- class: center ## Hecht et al. experiment Hecht, S., Shlaer, S., & Pirenne, M. H. (1942). Energy, Quanta, and vision. *The Journal of General Physiology*, *25*(6), 819–840. jgp.rupress.org. Retrieved from https://www.ncbi.nlm.nih.gov/pubmed/19873316 What is the minimum quantity of light that can be reliably detected by human observers? --- class: center, middle ![](2018-01-22-methods-theories_files/figure-html/km_fig_1.2-1.png)<!-- --> Knoblauch, K., & Maloney, L. T. (2012). *Modeling Psychophysical Data in R*. Springer Science & Business Media. Chapter 1. --- class: center, middle ![](2018-01-22-methods-theories_files/figure-html/km_fig-1.png)<!-- --> Knoblauch, K., & Maloney, L. T. (2012). *Modeling Psychophysical Data in R*. Springer Science & Business Media. Chapter 1. --- # How to model these data? ```r str(HSP) ``` ``` ## 'data.frame': 30 obs. of 5 variables: ## $ Q : num 46.9 73.1 113.8 177.4 276.1 ... ## $ p : num 0 9.4 33.3 73.5 100 100 0 7.5 40 80 ... ## $ N : int 35 35 35 35 35 35 40 40 40 40 ... ## $ Obs: Factor w/ 3 levels "SH","SS","MHP": 1 1 1 1 1 1 1 1 1 1 ... ## $ Run: Factor w/ 2 levels "R1","R2": 1 1 1 1 1 1 2 2 2 2 ... ``` - Predictors (independent variables, IVs) - Quanta (Q), Number replications (N), Run, Observer (Obs) - Responses (dependent variables, DVs) - % seen (p) - *Notice*: Quanta are log-distributed --- class: center # One approach `$$P[yes]=\Phi(\frac{Q-Q_{0.5}}{\sigma})$$` where `\(Q_{0.5}\)` is the # of quanta that yields 50% responding, and `\(\sigma\)` determines the 'slope' of the function. The cumulative normal (Gaussian) distribution is one type of function `\(\Phi\)` that has the 'S' shape we want. There are others. With a bit of algebra, we can "linearize" this into a familiar form `$$\Phi^{-1}(E[R])=\frac{Q-Q_{0.5}}{\sigma}=\beta_0+\beta_1Q$$` where the `\(E[R]\)` are (0,1) responses, `\(B_0=-Q_{0.5}/\sigma\)` and `\(B_1=\sigma^{-1}\)`. Knoblauch, K., & Maloney, L. T. (2012). *Modeling Psychophysical Data in R*. Springer Science & Business Media. Chapter 1. --- class: center, middle ## Another approach Example adapted from <https://tomwallis.info/2014/05/06/simulating-data/> ![](2018-01-22-methods-theories_files/figure-html/wallis_sim-1.png)<!-- --> --- class: center, middle $$ p(respond)=\beta_0 + \beta_1log(contrast) + spatialfreq $$ --- class: center, middle ![](2018-01-22-methods-theories_files/figure-html/plot_b0-1.png)<!-- --> --- class: center, middle ![](2018-01-22-methods-theories_files/figure-html/plot_b1-1.png)<!-- --> --- class: center, middle <img src="http://www.stonesc.com/pubs/Contrast%20Metrics_files/image006.jpg"> Sensitivity increases with increasing contrast, and there are different "baseline" levels that vary by spatial frequency (peak in middle). --- class: center # Psychophysical functions ## What is the best *statistical* model of the decision process? ## [Logit](https://en.wikipedia.org/wiki/Logit), [probit](https://en.wikipedia.org/wiki/Probit), [Weibull](https://en.wikipedia.org/wiki/Exponentiated_Weibull_distribution) distributions commonly used ## Same issues apply here as with GLMs in other contexts (fixed vs. random effects; variables nominal/ordinal/interval/continuous; goodness-of-fit; etc.) --- class: inverse # Your turn ## Pros and cons of estimating psychophysical functions? ## Prerequisites for estimating psychophysical functions? ## Utility of fitting behavioral functions? --- class: center # [Signal detection theory](https://en.wikipedia.org/wiki/Detection_theory) | | Signal present | Signal absent | |-------------|----------------|-------------------| | Respond Yes | Hit | False Alarm | | Respond No | Miss | Correct rejection | `\(p(Hit) + p(Miss)=1\)`, `\(p(False Alarm) + p(Correct Rejection)=1\)` --- class: center, middle <img src="https://4.bp.blogspot.com/-wmZzvsY_Tec/Vws0f4MJn9I/AAAAAAAAORs/gipKxA7aDboP0gx2vSmyQS_ZoVBPzqaWA/s1600/Type%2BI%2Band%2BII%2Berror.jpg"> ## Goal: Minimize both (== maximize Hits & Correct Rejections)! --- class: center # Similar logic applies in medicine <img src="http://i.imgur.com/xjCetVL.png"> High *sensitivity* and *specificity* desired. --- class: center, middle ![](2018-01-22-methods-theories_files/figure-html/SDT_plot-1.png)<!-- --> Knoblauch, K., & Maloney, L. T. (2012). *Modeling Psychophysical Data in R*. Springer Science & Business Media. Chapter 3, p. 65. --- # Gaussian SDT - "Noise" distribution, "Signal" distribution offset by `\(d'\)`; variances of signal and noise distribution equal (or not) - Q: Given internal signal strength `\(d'\)` and signal `\(X_i\)`, what decision rule maximizes `\(p(corr)\)`? - A: Observer sets a criterion ($\beta$) & responds "yes" when $X_i>= \beta$ - A: Observer may have a 'bias' that shifts the criterion --- class: center, middle <a href="https://doi.org/10.3389/fpsyg.2015.00762"> <img src="https://www.frontiersin.org/files/Articles/147101/fpsyg-06-00762-HTML/image_m/fpsyg-06-00762-g001.jpg"> </a> Anderson, N. D. (2015). Teaching signal detection theory with pseudoscience. *Frontiers in Psychology*, *6*, 762. Retrieved from http://dx.doi.org/10.3389/fpsyg.2015.00762 --- (A) Response matrix of all signal-response combinations that can be made in a binary decision task. Green indicates correct decision, red indicates incorrect decision. (B) Proportions of hits and misses represented under the signal distribution. β reflects the subject criterion, `\(c\)` reflects bias, and `\(d'\)` reflects sensitivity which represents the difference in position between the two distributions. (C) Proportions of false alarms and correct rejections represented under the noise distributions. (D) A condition which hypothetically reflects low subject sensitivity. When the distributions are closer together (i.e., `\(d'\)` is smaller), the difference between the proportion of hits and false alarms is lower. (E) A condition which reflects high subject sensitivity. When the distributions are farther apart (i.e., `\(d'\)` is larger), the difference between the proportion of hits and false alarms is higher. Anderson, N. D. (2015). Teaching signal detection theory with pseudoscience. *Frontiers in Psychology*, *6*, 762. Retrieved from http://dx.doi.org/10.3389/fpsyg.2015.00762 --- # SDT in your (frequentist, traditional, null hypothesis significance testing) psychological life | | Effect ≠ 0 | Effect ~= 0 | |--------------|----------------|-------------------| | Reject `\(H_0\)` | Hit | False Alarm | | Don't reject `\(H_0\)` | Miss | Correct rejection | Maximizing correct decisions means minimizing *False Alarms* (small `\(\alpha\)`; aka Type I errors) AND minimizing *Misses* (small `\(\beta\)`, aka Type II errors) or maximizing 'power' (1- `\(\beta\)`) or *Hits*. --- # Mentioning in passing... ## Receiver Operating Characteristic (ROC) curves <img src="http://notmatthancock.github.io/images/roc-2.png"> --- class: inverse # Your turn ### Why might an observer choose a liberal decision criterion? A conservative one? ### How realistic is the assumption that the 'noise' and 'signal' distributions have the same `\(\sigma\)`? What can experimenters realistically manipulate or measure? ### Does the link between SDT, perceptual research, medical diagnosis, and NHST reasoning make sense? --- class: center # Absolute thresholds ![](2018-01-22-methods-theories_files/figure-html/unnamed-chunk-2-1.png)<!-- --> --- class: center # vs. Difference thresholds ```r parrots <- load.image(system.file('extdata/parrots.png',package='imager')) plot(parrots) ``` ![](2018-01-22-methods-theories_files/figure-html/unnamed-chunk-3-1.png)<!-- --> --- class: center, middle # Standard ![](2018-01-22-methods-theories_files/figure-html/unnamed-chunk-4-1.png)<!-- --> --- class: center, middle # Test ![](2018-01-22-methods-theories_files/figure-html/parrots_00625-1.png)<!-- --> --- class: center, middle # Standard ![](2018-01-22-methods-theories_files/figure-html/unnamed-chunk-5-1.png)<!-- --> --- class: center, middle # Test ![](2018-01-22-methods-theories_files/figure-html/parrots_0125-1.png)<!-- --> --- class: center, middle # Standard ![](2018-01-22-methods-theories_files/figure-html/unnamed-chunk-6-1.png)<!-- --> --- class: center, middle # Test ![](2018-01-22-methods-theories_files/figure-html/parrots_025-1.png)<!-- --> --- class: center, middle # Standard ![](2018-01-22-methods-theories_files/figure-html/unnamed-chunk-7-1.png)<!-- --> --- class: center, middle # Test ![](2018-01-22-methods-theories_files/figure-html/parrots_05-1.png)<!-- --> --- class: center, middle # Standard ![](2018-01-22-methods-theories_files/figure-html/unnamed-chunk-8-1.png)<!-- --> --- class: center, middle # Test ![](2018-01-22-methods-theories_files/figure-html/parrots_10-1.png)<!-- --> --- class: center, middle # Standard ![](2018-01-22-methods-theories_files/figure-html/unnamed-chunk-9-1.png)<!-- --> --- class: center, middle # Test ![](2018-01-22-methods-theories_files/figure-html/parrots_20-1.png)<!-- --> --- # Just-noticeable Difference (JND) ### Smallest reliably detected change in stimulus property ### (Max) Weber's Fraction `\(k\)` -> (Gustav) Fechner's Law $$ \frac{\Delta I}{I}=k $$ or $$log(\Delta I)-log(I)=log(k) $$ --- class: center # Psychophysical scaling ## Given 'anchor' or comparison stimulus... ## Assign *numeric* ratings to perceived qualities (Stevens) --- class: center, middle <img src="http://www.intropsych.com/ch04_senses/04stevenscurves.jpg" height=500px> $$ \Psi(I)=kI^\alpha $$ Not all scaling relations are logarithmic, but most are curvlinear! --- class: center, middle ## *Local* psychophysics ([Luce & Krumhansl, 1988](http://www.socsci.uci.edu/~rdluce/bio/pre1990/1988/Luce-Krumhansl_Book%20Chapter_1988.pdf)) Stimulus changes *"small enough to cause confusions among stimuli..."* ## vs. *Global* psychophysics *"...differences so large that there is no chance whatever of confusions between the extreme signals of the range..."* --- class: center, middle # Core issues: How to measure psychological states, `\(\Psi\)`? How to measure physiological states, `\(\Phi\)`? How to measure world/environment states, `\(W\)`? How to relate `\({\Psi, \Phi, W}\)` to one another? --- # Summing up ## Perceptual theories at the core of psychology ## Perceptual methods at the core of psychology --- # Next time... ## The retinal image --- class: center, middle Slides created via the R package [**xaringan**](https://github.com/yihui/xaringan). Rendered HTML and supporting files are pushed to GitHub where GitHub's 'pages' feature is used to host and serve the course website.