Understanding the mesopic vision

Zoltán Vas

Department of Image Processing and NeurocomputingUniversity of Pannonia

Hungary

Aims

Give a model to describe the mesopic luminance range

Achieve a safe detection threshold prediction

Based on this model, optimizing traffic lighting, car headlights

Give better experimental methods to model the mesopic range

Experimental method I.

Large achromatic background, illuminated by white phosphor LEDs (CCT=6000K, x=0.32,y=0.34), L=0.5cd/m2

Visual targets generated by two projectors of the same kind (HP V6210 DLP)

Experimental method II.

Two mayor methods: Fixed-step staircase (with increments, one up /one down rule) Quasi-stationer

Primary visual target: 2° filled disk at 20° eccentricity

Secondary (control) visual target: 2° red number, on-axis

Quasi-monochromatic: 440nm, 490nm, 540nm , 570nm, 600nm, 615nm (Half Band Width: 10nm)

Additive mixture of 615nm and 540nm, 615nm and 440nm, 490nm and 600 (two-peaks)

Trials I. Series 1-2.

In the first and second series the 490nm, 540nm, 615nm central wavelength HBW color filters were used, for quasi-monochromatic target

The additive mixture of these (490nm+615nm, and 540nm+615nm) was the two-peak target

Trials II. Series 3.

In these series the 490nm and 600nm central wavelength HBW color filters were used, to test the achromatic response

The T=aL-bM, D=cL+dM-eS, A=fL+gM, were used

Trials III. Series 4.

In the 4th series the same filters were used, as in the 3rd

The FSS staircase method was used, without control target (possible adaptation conflict)

Trials IV. Series 5.

The data of the additive mixture of 540nm+615nm central wavelength HBW color filters were compared with a quasi-monochromatic color filter

This quasi-monochromatic filter was assessed by an Excel script(570nm)

Trials – in the future

The 6th series start in October, a new method will be used, which is not the FSS staircase, with color filters used in Darmstadt too

A new experiment will start, modeling the dynamic background, psychological influence by using a realistic driving simulator

Models until today

By using the V(λ) and V’(λ) as the base, the model will have uncertainty (because of the additivity error, caused by the spectral integration)

Mayor models: Move model „X” model Intermediate model

CHC model

Based on the: L,M,S cone fundamentals V’(λ) function V*(λ) function (the Sharp et al photopic v.f.) Cone opponent channels included

For visual targets : quasi-stationer (over 2 s) 2°(or similar) visual targets on a large, uniform

background

CHC model and results

The photopic-type models predict higher, than the real threshold. This is caused by the spectral integration

CHC predicts better => safer detection Another advantage is, that we can plot the

Vmes,CHC(λ), which is the spectral sensitivity curve for observer-to-observer (it has more local maxima)

BUT!

The FSS staircase method can only be used with care for mesopic range detection tasks

The observers are influenced by nearly everything, e.g. temperature, mood, time…And that’s why we need a quicker but also precise method to understand better this visual range

Comparison of Staircase and Multi-step case method (MSC)

Miguel A. García-Pérez dealt with the FSS staircase method (Forced-choice staircase with fixed step sizes: asymptotic and small-sample properties, Vision Research 38. 1998)

It’s a good method, but for the mesopic scenario it can be used with care

Staircase I. - basics

D: set of events that trigger a step down U: set of events that trigger a step up : is a monotonic increasing psychometric

function Prob(D|x), Prob(U|x) are the probabilities of a step

down and up, at a stimulus level x, and there is a value x0 such that Prob(D| x0)=Prob(U| x0)

: is the step size

Up/down step variations

Dixon and Mood’s u/d method At every correct answer down, every wrong answer up.

Wetherill and Levitt’s transformed u/d method There are several sequences of responses over various

numbers of consecutive trials, but the up/down continue to be identical size

Karenbach’s weighted up/down method This is like the Dixon and Mood’s method, but the step size

down differs from the step size up Transformed and weighted up/down method

Combining the non-unitary sets D,U (like transformed), with equal sizes for the steps up, down (like weighted).

Psychometric functions I.

Where pl is the lapsing level, pg is the guessing level, F(x) is the probability of a psychometrical outcome at stimuli level x (in the following the x is replaced with m(Michelson-contrast), so the photometric function is restricted to 0≤m ≤ 1)

This function expresses the probability of a correct response, as a sum of the probabilities of detecting the patter and not lapsing (first summand), and not detecting, but guessing correctly (second summand).

( ) (1 ) ( ) 1 ( )l gx p F x p F x

Psychometric functions II.

For F, every function can be used, which qualifies as a cumulative distribution function.

García-Pérez used for F the Weibull function, so:

where α is the spread, and β is the location

( ) 1 (1 )exp , 0,1l l g

mm p p p m

Psychometric functions III.

From the presumed

convergence probability can be calculated

A convergence contrast was computed as the arithmetic mean of the distribution, and its standard deviation was used, to compute a convergence contrast interval with boundaries defined ± standard deviation away from the convergence contrast.

10( )x f

Psychometric functions IV.

Convergence percent-correct was determined by entering the convergence contrast into the psychometric function used in that run, and expressing the probability associated with it as a percentage, and a convergence percent-contrast interval was analogously obtained from the boundaries of the convergence contrast interval.

FSS staircase rules I.

They’ve tried out more step sizes, and methods: one-, two-, three-, four down/ one up and they got following rules: If > , the asymptotic convergence

approaches the guessing level if the step size increases

If = , the asymptotic convergence dependes on the starting value, but it begins a big fluctuation if the relative step size increases

If < the asymptotic convergence is largly invarinat, if the step size increases

Multi-step case method (MSC)

Based on experience in mesopic-trials The FSS staircase method converged not

fast enough That’s why I had to develop a new method, to

increase the performance of the convergence, and to decrease the time needed

MSC basic rules & step sizes

Preliminary phase (to assess the staring value) Multiple step sizes Adaptive choice between the step sizes based

on the performance of the observer Groups presented Steps:

Percentage % 100 75 50 25 0

Step size -3 -1 Repeat 1 3

MSC – percent-correct point

Near the threshold the number of 50% responses get more often

After 50% response was given twice after the other, the last ten groups will be shown

From this 40 responses the percent-correct point can be calculated by using the given responses

MSC vs. FSS staircase method I.

FSS staircase + Is more described by mathematical equations, Can calculate p.-c. p. Lot of people use this method

FSS staircase – Difficult to use Complicated equations Takes sometimes a long time to converge

MSC vs. FSS staircase method II.

MSC + Quick converge Simple equations Simple method to calculate p.-c. p. Using preliminary phase the convergence begins

from near the threshold value Based on experience

MSC – Not described by mathematic equations yet Not tested in other tasks

Thank you for your attention!

Plans for the future

Reproduction of the experiments in TUD

Comparing data, observers, understanding spatial influence

Experiments in „real-life” scenarios