Color perception Stimuli Fechnerian Scaling Analysis Outline Achromatic color perception Dimensionality of the Perceptual Space of Stimulus configurations Achromatic Colors Fechnerian Scaling Nora Umbach Research Methods and Mathematical Psychology Analysis of data February 2011 2 | Nora Umbach Color perception Stimuli Fechnerian Scaling Analysis Color perception Stimuli Fechnerian Scaling Analysis Color perception • We have a tendency to treat color as a property of objects Achromatic color perception • Experienced color is neither a property of objects, nor a property of light Stimulus configurations • The physical or physiological quantifications of color do not fully explain the psychophysical perception of color appearance Fechnerian Scaling Analysis of data 3 | Nora Umbach 4 | Nora Umbach
Color perception Stimuli Fechnerian Scaling Analysis Color perception Stimuli Fechnerian Scaling Analysis Color perception Dimensionality of the perceptual space of achromatic colors • Traditional view assumes that achromatic color perception • We have a tendency to treat color as a property of objects may be represented by a unidimensional achromatic color • Experienced color is neither a property of objects, nor a space (ranging from white to black) property of light • Logvinenko & Maloney (2006) and Nieder´ ee (2010) present recent evidence that this representation is at least • The physical or physiological quantifications of color do not two-dimensional fully explain the psychophysical perception of color appearance • Up to now there is no systematic investigation of the structure • In this talk we will only focus on achromatic colors of the perceptual space of achromatic colors • Our experiments aim at a characterization of the perceptual space of achromatic colors for individual observers 4 | Nora Umbach 5 | Nora Umbach Color perception Stimuli Fechnerian Scaling Analysis Color perception Stimuli Fechnerian Scaling Analysis Demonstration Demonstration 6 | Nora Umbach 6 | Nora Umbach
Color perception Stimuli Fechnerian Scaling Analysis Color perception Stimuli Fechnerian Scaling Analysis Ratio principle ratio principle: Lightness is determined merely by the luminance ratio between a given surface and its surround, without reference Achromatic color perception to the level of illumination. (Gilchrist, 2006, p. 82) • Prominent explanation of experimental results where subjects Stimulus configurations had to match two centers presented in different surrounds (postulated by Wallach, 1948) Fechnerian Scaling • Ratio principle postulates that centers will be adjusted until ratio between center and surround is (nearly) identical for Analysis of data both configurations • Infields will then be perceived as metameric (being of the same color) 7 | Nora Umbach 8 | Nora Umbach Color perception Stimuli Fechnerian Scaling Analysis Color perception Stimuli Fechnerian Scaling Analysis Stimulus presentation Stimulus configurations Surround ( cd m 2 ) 28.88 x 25.70 22.48 19.76 (a,s) (b,t) 17.22 36.57 41.02 45.92 51.29 57.07 Infield ( cd m 2 ) 9 | Nora Umbach 10 | Nora Umbach
Color perception Stimuli Fechnerian Scaling Analysis Color perception Stimuli Fechnerian Scaling Analysis Stimuli Stimuli gray1a gray2a gray3a gray4a gray5a gray1a gray2a gray3a gray4a gray5a gray1b gray2b gray3b gray4b gray5b gray1b gray2b gray3b gray4b gray5b 11 | Nora Umbach 11 | Nora Umbach Color perception Stimuli Fechnerian Scaling Analysis Color perception Stimuli Fechnerian Scaling Analysis Probability Distance Hypothesis Achromatic color perception The probability-distance hypothesis states that the probability with which one stimulus is discriminated from another is a function Stimulus configurations of some subjective distance between these stimuli. (Dzhafarov, 2002, p. 352) Fechnerian Scaling ψ ( x , y ) = f [ D ( x , y )] Analysis of data 12 | Nora Umbach 13 | Nora Umbach
Color perception Stimuli Fechnerian Scaling Analysis Color perception Stimuli Fechnerian Scaling Analysis Discrimination Probabilities Subjective Distances • Most basic cognitive ability: to tell two stimuli apart from • Subjective distances between stimuli are defined here, each other measuring the degree of similarity (or dissimilarity) between • Fechnerian Scaling computes ‘subjective’ distances among the underlying representations stimuli from their pairwise discrimination probabilities • Fechnerian distances satisfy all properties of a metric: • Subjects are required to give one of two answers: ‘x and y are D ( x , y ) ≥ 0 non-negativity (1) the same’ or ‘x and y are different’ D ( x , y ) = 0 iff x = y identity of indiscernibles (2) ψ ( x , y ) = P ( x and y are different ) D ( x , y ) = D ( y , x ) symmetry (3) • FS is suitable to describe spaces of arbitrary dimensionality D ( x , z ) ≤ D ( x , y ) + D ( y , z ) triangle inequality (4) 14 | Nora Umbach 15 | Nora Umbach Color perception Stimuli Fechnerian Scaling Analysis Color perception Stimuli Fechnerian Scaling Analysis Regular Minimality Achromatic color perception • Most fundamental property of discrimination probabilities • Only requirement for computation of Fechnerian distances Stimulus configurations • For any x � = y Fechnerian Scaling ψ ( x , x ) < min { ψ ( x , y ) , ψ ( y , x ) } . Analysis of data 16 | Nora Umbach 17 | Nora Umbach
Color perception Stimuli Fechnerian Scaling Analysis Color perception Stimuli Fechnerian Scaling Analysis Discrimination probabilities Discrimination probabilities gray1a gray2a gray3a gray4a gray5a gray1b gray2b gray4b gray5b gray1a gray2a gray3a gray4a gray5a gray1b gray2b gray4b gray5b gray1a 0.00 0.07 0.40 0.76 1.00 0.93 0.33 1.00 1.00 gray1a 0.00 0.07 0.40 0.76 1.00 0.93 0.33 1.00 1.00 gray2a 0.07 0.01 0.11 0.36 0.91 1.00 0.73 1.00 1.00 gray2a 0.07 0.01 0.11 0.36 0.91 1.00 0.73 1.00 1.00 gray3a 0.67 0.13 0.01 0.12 0.71 0.98 0.73 0.76 1.00 gray3a 0.67 0.13 0.01 0.12 0.71 0.98 0.73 0.76 1.00 gray4a 0.91 0.82 0.25 0.01 0.11 1.00 1.00 0.47 0.93 gray4a 0.91 0.82 0.25 0.01 0.11 1.00 1.00 0.47 0.93 gray5a 1.00 0.97 0.80 0.16 0.01 1.00 1.00 0.47 0.93 gray5a 1.00 0.97 0.80 0.16 0.01 1.00 1.00 0.47 0.93 gray1b 0.93 1.00 1.00 1.00 1.00 0.00 0.23 1.00 1.00 gray1b 0.93 1.00 1.00 1.00 1.00 0.00 0.23 1.00 1.00 gray2b 0.33 0.60 0.51 1.00 1.00 0.73 0.00 1.00 0.97 gray2b 0.33 0.60 0.51 1.00 1.00 0.73 0.00 1.00 0.97 gray4b 1.00 1.00 0.71 0.73 0.53 1.00 1.00 0.01 0.63 gray4b 1.00 1.00 0.71 0.73 0.53 1.00 1.00 0.01 0.63 gray5b 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.73 0.00 gray5b 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.73 0.00 18 | Nora Umbach 18 | Nora Umbach Color perception Stimuli Fechnerian Scaling Analysis Color perception Stimuli Fechnerian Scaling Analysis Psychometric function Psychometric function ‘Middle’ of cross ‘Middle’ of cross compared to rest compared to rest ψ ( gray3 , y ) ψ ( gray3 , y ) Surround gray11 gray10 gray9 gray8 gray7 gray1 gray2 gray3 gray4 gray5 Infield 19 | Nora Umbach 19 | Nora Umbach
Color perception Stimuli Fechnerian Scaling Analysis Color perception Stimuli Fechnerian Scaling Analysis Fechnerian Distances fechner • Check for regular minimality R> library(fechner) gray1a gray2a gray3a gray4a gray5a gray1b gray2b gray4b gray5b R> check.regular(psi) gray1a 0.00 0.12 0.34 0.69 0.94 1.50 0.67 1.61 2.00 $check gray2a 0.00 0.22 0.57 0.82 1.62 0.79 1.48 1.99 [1] "regular minimality" gray3a 0.00 0.35 0.60 1.70 1.01 1.26 1.99 $in.canonical.form gray4a 0.00 0.25 1.83 1.36 1.12 1.92 [1] TRUE gray5a 0.00 1.93 1.61 0.98 1.92 gray1b 0.00 0.97 1.99 2.00 • Calculate Fechnerian Distances gray2b 0.00 1.99 1.97 R> fs <- fechner(psi, comp=T, check=T) gray4b 0.00 1.35 R> fdis <- fs[[6]] gray5b 0.00 • MDS R> library(smacof) R> mds2 <- smacofSym(fdis, ndim=2) 20 | Nora Umbach 21 | Nora Umbach Color perception Stimuli Fechnerian Scaling Analysis Color perception Stimuli Fechnerian Scaling Analysis Fechnerian Distances Fechnerian Distances gray1a gray2a gray3a gray4a gray5a gray1b gray2b gray4b gray5b gray1a gray2a gray3a gray4a gray5a gray1b gray2b gray4b gray5b gray1a 0.00 0.12 0.34 0.69 0.94 1.50 0.67 1.61 2.00 gray1a 0.00 0.12 0.34 0.69 0.94 1.50 0.67 1.61 2.00 gray2a 0.00 0.22 0.57 0.82 1.62 0.79 1.48 1.99 gray2a 0.00 0.22 0.57 0.82 1.62 0.79 1.48 1.99 gray3a 0.00 0.35 0.60 1.70 1.01 1.26 1.99 gray3a 0.00 0.35 0.60 1.70 1.01 1.26 1.99 gray4a 0.00 0.25 1.83 1.36 1.12 1.92 gray4a 0.00 0.25 1.83 1.36 1.12 1.92 gray5a 0.00 1.93 1.61 0.98 1.92 gray5a 0.00 1.93 1.61 0.98 1.92 gray1b 0.00 0.97 1.99 2.00 gray1b 0.00 0.97 1.99 2.00 gray2b 0.00 1.99 1.97 gray2b 0.00 1.99 1.97 gray4b 0.00 1.35 gray4b 0.00 1.35 gray5b 0.00 gray5b 0.00 21 | Nora Umbach 21 | Nora Umbach
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