Eye Movements • Fixation : A period of time when the eye is focused on a Vision and Perception single point. • Saccade : An eye motion from one fixation point to another. • Normal vision alternates between saccades and fixations, with each lasting just 100ths of a second. Eye Movement Studies Early eye-tracking study • Alfred Yarbus • An image is presented to a subject. • “Eye movements and vision” Plenum Press 1967 • The subject may (or may not) be given a specific task to • Seven people studied the same picture and their eye carry out. movements were monitored. • A record is made of where the subjects’ eyes are directed • They were all educated and knew the picture. as they study the image. • One person was asked to look at the picture a number of times with different instructions as to what information to look for each time. Examine the picture. CABINET // Ways of Seeing 04/07/2010 12:20 pm Examine the picture An unexpected visitor (Ilya Repin, 1884) 1 CABINET // Ways of Seeing 04/07/2010 12:20 pm Decide how wealthy the family is. Seven different 2 people’s eye 1 movements on examining the picture How wealthy is the family? http://www.cabinetmagazine.org/issues/30/archibald.php Page 3 of 5 2 http://www.cabinetmagazine.org/issues/30/archibald.php Page 3 of 5 CABINET // Ways of Seeing 04/07/2010 12:20 pm Decide what the family were doing before the visitor arrived. Estimate the ages of the people in the room. CABINET // Ways of Seeing 04/07/2010 12:20 pm 3 What were the family doing How old are the people in the room? before the visitor arrived? 3 4 CABINET // Ways of Seeing 04/07/2010 12:20 pm Estimate how long the visitor has been away. Remember the position of the objects and people in the room. 4 http://www.cabinetmagazine.org/issues/30/archibald.php Page 4 of 5 5 How long has the Remember the positions of visitor been away? objects and people in the room http://www.cabinetmagazine.org/issues/30/archibald.php Page 4 of 5 6 1 Alfred L. Yarbus, Eye Movements and Vision, trans. Basil Haigh (New York: Plenum Press, 1967). 2 Yarbus, op. cit., p. 190. Sasha Archibald is an independent curator and writer based in Brooklyn. Cabinet is a non-profit organization. Please consider supporting us by subscribing to the magazine, buying a limited edition artwork, or making a tax-deductible donation. © 2008 Cabinet Magazine http://www.cabinetmagazine.org/issues/30/archibald.php Page 5 of 5 Graphical illusions TheThe Cafe WallCafé Illusion Wall Illusion • Help us understand how the human visual system works • Context affects judgement – sizes of surrounding objects – colours of adjacent objects – depth cues (perspective can be misinterpreted) • Angles are difficult for us – we overestimate acute angles – we underestimate obtuse angles The lines are all horizontal or vertical A Perspective Illusion The Ponzo Illusion The Müller-Lyer Illusion The Ames roomThe Ames Room Explanation The Ames Room Ponzo illusion Müller-Lyer illusion Poggendorf Illusion Zöllner Illusion The Zöllner Illusion 1 The Zöllner Illusion 2 The Poggendorf Illusion The Poggendorf Illusion Which of the two lower lines Which of the two lower lines is the extension of the upper line? is the extension of the upper line? The EhrensteinEhrenstein Illusion Illusion A Linelength Illusion A Line Length Illusion Tichener Illusion Jastrow Illusion Tichener Illusion The Jastrow Illusion An IrradiationIrradiation Illusion Illusion Mach BandingMach Banding The HermannHerman Grid Grid Colour Contrasts Simultaneous Contrast I The appearance of colours depends on their surroundings. Perception and Cognition Laws of Perception (1) • Weber’s Law • Graphical perception (Preattentive vision) – applies to a variety of perceptual encodings. – Some visual processing takes place without any – Consider two lines with lengths x and x + w. Weber’s conscious effort on our part. law says that the chance of detecting a difference depends on the value of w/x. • Graphical cognition – Let the difference between x and x + w be detected by a – Some visual processing requires that we consciously given individual with probability px(w). For a fixed p, let inspect the things that we are looking at. the value of w which is detected with this probability be wp(x). Then Weber’s law says wp(x)=kpx – We detect relative differences in values. this paper we focus on testing. For graphics, we want to address the question “Is what we see really there?” More precisely, is what we see in a plot of the sample an accurate reflection of the entire population? The rest of this section shows how to answer this question by providing a short refresher of statistical hypothesis testing, and describes how 700 testing can be adapted to work visually instead of numerically. 600 Hypothesis testing is perhaps best understood with an analogy to 500 400 the criminal justice system. The accused (data set) will be judged 300 guilty or innocent based on the results of a trial (statistical test). Each count 200 trial has a defense (advocating for the null hypothesis) and a prosecu- 100 tion (advocating for the alternative hypothesis). On the basis of how 0 evidence (the test statistic) compares to a standard (the p-value), the Laws of Perceptionjudge (2) makes a decision to convict (reject the null) or acquit (fail to Laws− 4of Perception−2 0 2 (3)4 reject the null hypothesis). x Unlike the criminal justice system, in the statistical justice system (SJS) evidence is based on the similarity between the accused and known innocents, using a specific metric defined by the test statistic. 1400 • Stevens’ Law The population of innocents, called the null distribution, is generated• Stevens’ 1200Law examples (area with ! = 0.7) by the combination of null hypothesis and test statistic. To determine 1000 – let p(x) be the perceived value of x the guilt of the accused we compute the proportion of innocents who 800 look more guilty than the accused. This is the p-value, the probability• Compare600 areas of size 2 and 1 ! count – Stevens’ Law says p(x)=Cx that the accused would look this guilty if they actually were innocent. 400 There are two types of mistakes we can make in our decision: we - p(2)/p(1)200 = 20.7/10.7 = 1.62 – C and ! depend on the encoding methodcan acquitused a and guilty on dataset (a type II error, or false negative), or falsely 0 the observer convict an innocent dataset (a type I error, or false positive). Just as 0 1 2 3 4 5 in the criminal justice system, the costs of these two mistakes are not - the bigger area is seen abs(x)as less than twice the size – Typically observed ranges for ! equal and vary based on the severity of the consequences (the risk of letting a guilty shoplifter go free is not equal to the risk of letting• Compare a areas of size 1/2 and 1 - length 0.9 - 1.1 guilty axe-murderer go free). Typically, as the consequences of our Fig. 2. (Top) Distribution of group means under the null hypothesis (dis- decisions become bigger, we want to become more cautious, and re- tribution of innocents). Vertical line indicates value of observed test 0.7 0.7 - area 0.6 - 0.9 quire more evidence to convict: an early-stage exploratory analysis– is p(1/2)/p(1)statistic. (Bottom) = Distribution0.5 /1 of absolute= 0.62 value of group means. This is free to make a few wrong decisions, but it is very important not to ap- a more appropriate comparison for the two-sided test, where the mag- - volume 0.5 - 0.8 prove a possibly dangerous drug after a late-stage clinical trial. It is– upthenitude smaller of difference area is is more seen important as more than the than direction. half the size to the analyst to calculate and calibrate these costs. To demonstrate these principles we use a small simulated example, an imaginary experiment designed to compare the accuracy of con- dition one vs. condition two in a usability study. Here, the defense argues that there is no difference between the two groups, and the prosecution argues that they are different. Statistical theory tells us to use the difference of the group means divided by the pooled stan- 1 2 3 dard deviation as the measure of guilt (the test statistic), and that under this measure the population of innocents will have (approximately) a y GGG G GGG GG G G GG GGGGG G G GG GGGGGG G G G t-distribution. Figure 2 shows this distribution for a sample of 10,000 innocents. The value of the observed test statistic is represented as Graphical inferencea vertical line on the histogram. Since we have no a-priori notion of x G GGGGGGG G G GGGG G G GGG GGGGG G whether the difference between groups will be positive or negative, it is better to compare the accused to the absolute value of the innocents, 4 5 6 as shown in the bottom plot. As you can see, there are few innocents • Buja, Cook, Hofmann, Wickham (about 3%) who appear as guilty as (or more guilty than) the accused y GGGGG GGG G GGGGGGG GG G GGGGGGG G G and so the decision would be to convict. These principles remain the same with visual testing, except for two • Generate random plots based on the null hypothesis and Group x GGGGGGG GG G GG G GGGG G G GG G GG G G Graphical inference for infovisaspects: the test statistic, and the mechanism of computing similarity.