Maximum Likelihood Difference Scaling Research Articles

Increasing magnitude of color differences amplifies category effects

Previous studies have identified differences in sensitivity characteristics between color discrimination and perception of suprathreshold color differences. However, it remains highly unclear how color difference sensitivity changes with increasing magnitudes of color difference along various color hues. This study aimed to quantify the sensitivity transition across various magnitudes of color differences and uncover the underlying mechanisms. Color discrimination sensitivities were measured using an adaptive staircase method for 32 isoluminant pedestal colors in the u'v' chromaticity diagram. For suprathreshold color differences, we employed the Maximum Likelihood Difference Scaling (MLDS) method to measure sensitivity to various color difference levels for the same 32 colors. Our findings confirmed the differences in sensitivity characteristics between discrimination and suprathreshold color difference perception. Furthermore, we observed increased sensitivities at many color category boundaries in suprathreshold color difference perception. By investigating the relation between the category effects and the color difference size levels through a model simulation, our findings suggest that the influence of color categories on the perception of color differences may become more pronounced as the magnitude of color differences increases.

Asymmetries between achromatic increments and decrements: Perceptual scales and discrimination thresholds.

The perceptual response to achromatic incremental (A+) and decremental (A-) visual stimuli is known to be asymmetrical, due most likely to differences between ON and OFF channels. In the current study, we further investigated this asymmetry psychophysically. In Experiment 1, maximum likelihood difference scaling (MLDS) was used to estimate separately observers' perceptual scales for A+ and A-. In Experiment 2, observers performed two spatial alternative forced choice (2SAFC) pedestal discrimination on multiple pedestal contrast levels, using all combinations of A+ and A- pedestals and tests. Both experiments showed the well-known asymmetry. The perceptual scale curves of A+ follow a modified Naka-Rushton equation, whereas those of A- follow a cubic function. Correspondingly, the discrimination thresholds for the A+ pedestal increased monotonically with pedestal contrast, whereas the thresholds of the A- pedestal first increased as the pedestal contrast increased, then decreased as the contrast became higher. We propose a model that links the results of the two experiments, in which the pedestal discrimination threshold is inversely related to the derivative of the perceptual scale curve. Our findings generally agree with Whittle's previous findings (Whittle, 1986, 1992), which also included strong asymmetry between A+ and A-. We suggest that the perception of achromatic balanced incremental and decremental (bipolar) stimuli, such as gratings or flicker, might be dominated by one polarity due to this asymmetry under some conditions.

Poster Session I: Criterion effects in maximum likelihood difference scaling: Similar is not always the opposite of different.

Maximum Likelihood Difference Scaling (MLDS) is an efficient method of estimating perceptual representations of suprathreshold physical quantities (Maloney & Yang, 2003), such as luminance contrast. In MLDS, observers can be instructed to judge which of two stimulus pairs are more similar to one another, or which of the two pairs are more different from one another. If the same physical attributes are used for both the similar and dissimilar tasks, the two criteria should produce the same perceptual scales. We estimated perceptual scales for suprathreshold achromatic square patches. Increments and decrements on the mid-gray background were estimated separately. Observers judged which pair of stimuli were more similar in half of the sessions, and more different in the other half sessions. For most observers, the two tasks produced the same perceptual scales: a decelerating curve for increment contrasts and a cubic curve for decremental contrasts (cf. Whittle, 1992). These scales predicted forced-choice contrast discrimination thresholds for both increments and decrements. However, for a subset of observers, the 'more different' judgments produced scales that accelerated with contrast for both increments and decrements; these scale shapes do not predict their discrimination thresholds. Our results suggest that, even with these simple stimuli, observers in an MLDS experiment may attend to different aspects of the stimulus depending on the assigned task.

Poster Session: Achromatic increments and decrements are different: the relationship between scaling and discrimination.

A basic problem in psychophysics is to relate the internal representation of a stimulus to its physical intensity. In this study, we measured perceptual scales for achromatic contrast with Maximum Likelihood Difference Scaling (MLDS), using squares against a mid-grey background. Observers compared two stimulus pairs and chose the more different pair. All four squares were either achromatic increments (A+), or achromatic decrements (A-). The MLDS result was then compared with 2AFC achromatic pedestal discrimination, with pedestals and tests that were all combinations of A+ and A-. The main result is not novel: A+ and A- obey different rules. A Naka-Rushton saturating function describes the A+ MLDS result well, and the derivative of that function is proportional to the A+ pedestal discrimination for some (but not all) observers. A- MLDS and discrimination results are more complicated and are reminiscent of the classic findings of Whittle (1986, 1992). The sensitivity of A- is a cubic polynomial function of pedestal contrast. These findings will be compared with a similar study of S-cone contrast (reported at VSS 2022), which found a different type of asymmetry between S+ and S-. Presumably these increment/decrement asymmetries are due to underlying differences between ON and OFF neural pathways. One implication is that using stimuli that include both contrast signs, such as gratings and flicker, may obscure important asymmetries in the processing of contrast.

Poster Session: Perceptual scaling and natural image statistics.

Visual coding is thought to be matched to many of the properties of the natural visual environment, such as the characteristic amplitude spectra or fractal geometry of natural scenes. This match has been probed in a wide variety of ways. Here we used the paradigm of "maximum likelihood difference scaling" (MLDS, Maloney and Knoblauch Ann Rev Vis Sci 2020) to explore the perceptual representation of the spatial structure of images. The MLDS task involves presenting pairs of images drawn from different levels along a dimension and judging which pair has greater difference. In our case the stimulus dimension corresponded to the slope of the image amplitude spectrum. Grayscale noise images were filtered to form a range of slopes from 0 to -2 in steps of 0.2. Further image arrays were generated by first binarizing the image intensities and then extracting only the edges to isolate the fractal structure (corresponding to fractal dimension range from 1 to 2 in steps of 0.1). For each array the MLDS task was used to estimate the perceived differences. Scaling for fractal dimension did not differentially favor natural fractal values. However for the amplitude spectra, the derived perceptual scales tended to be steeper for intermediate levels of the array and shallower for both strongly blurred or sharpened levels, consistent with greater perceptual salience for image differences that have more naturalistic spectra.

Perceptual scaling of suprathreshold chromatic increments and decrements using Maximum Likelihood Difference Scaling

Color contrast provides rich information about the world. In the present study, we produce perceptual scales for suprathreshold color contrasts of different major directions in cone contrast space. In particular, we compared cone isolating increments and decrements (L±, M±, S±), as well as achromatic increments and decrements (A±), equiluminant R and G, and increments and decrements along the color direction that modulates L and M cones equally with S cones unmodulated (L=M±). The method we used is Maximum Likelihood Difference Scaling (MLDS; Knoblauch & Maloney, 2008), a fast way of producing interval perceptual scales. For each color direction, seven contrast values were linearly sampled between the observer’s threshold and maximum contrast of the monitor. In each trial, four practiced observers compared two pairs of 1.5°x1.5° squares. The squares were flashed for 0.33 seconds. All four squares were of the same color direction but with four different contrasts. Observers chose the pair in which the two squares looked more different, or in other words, the pair that had a larger perceptual interval. To traverse all interval pairs generated by 7 contrast values, 35 trials were measured for each color direction in a given session, and repeated three times over sessions. The MLDS results are nicely fit with a Michaelis-Menten function, producing a decelerating curve shape for each tested color direction; this function is an estimate of the contrast transducer that may underlie contrast discrimination (Foley & Legge, 1981). The general pattern was slightly more curvature for increments than decrements in most color directions. Achromatic increment scales are the most nonlinear of all directions we examined, consistent with processing by a mechanism summing cone signals that are processed less linearly for increments than decrements. Our results indicate that MLDS is a good method for perceptual scaling of suprathreshold chromatic increments and decrements.

Linking perceived to physical contrast: Comparing results from discrimination and difference-scaling experiments.

Psychophysical approaches that allow us to estimate how perceived stimulus intensity is linked to physical intensity are import tools for studying nonlinear transformations of visual signals within different visual pathways. Here, we investigated how stimulus contrast is encoded in achromatic and chromatic pathways using simple grating stimuli. We compared two experimental approaches to this question: contrast discrimination (increment detection thresholds measured on contrast pedestals) and the maximum likelihood difference scaling (MLDS) approach introduced by Maloney and Yang (2003). The results of both experiments are expressed using simple models that include a transducer function mapping physical contrast to an internal signal the observer uses in making judgments, and an estimate of the variability of this representation (internal “noise”). We found that the transducers derived from both experiments have a similar form, but occupy different ranges of physical contrast in different stimulus conditions, reflecting difference in contrast sensitivity. This is consistent with past discrimination results, and in the difference-scaling case provides new evidence supporting the idea that suprathreshold chromatic and achromatic contrast are processed similarly, once differences in contrast sensitivity are taken into account. Model estimates of internal noise were higher in the difference-scaling experiment than the discrimination experiment, a finding we attribute to a difference in task complexity. Finally, we fit an alternative version of the MLDS model in which internal noise increased with response level. This alternative was no better at predicting holdout data in a cross-validation analysis than the original constant-variance model.

User Study Comparing Linearity and Orthogonalization for Polarimetric Visualizations

Traditionally, polarimetric imaging data is visualized by mapping angle of polarization, degree of polarization, and intensity to hue, saturation, and value coordinates of HSV color space. Due to possible perceptual uniformity issues in HSV, a method based on CAM02-UCS color space has been recently proposed. In this user study, the perceptual uniformity and nonlinear bias of the encoding of the degree of polarization parameter into the chromatic magnitude color channel is modeled by a power-law relationship between stimulus scale level and is estimated from responses to paired 2-alternative forced choice questions using Maximum Likelihood Difference Scaling. Estimated exponent and noise parameters for these methods are compared for same-hue and different-hue conditions to determine whether the chromatic magnitude channel can be used to orthogonality encode data parameters independently from the hue channel. Overall, the HSV condition displayed more nonuniformity, more nonlinear bias, and more non-orthogonality than the UCS condition. The results here indicate a lower bound for differences between methods since the intensity was chosen for the “best case” of HSV. These results further support the claim that the chromatic magnitude color channel of a uniform color space can be used to encode a data parameter independently of the hue channel in a multivariate colormapping visualization.

Estimation of perceptual scales using ordinal embedding.

In this article, we address the problem of measuring and analyzing sensation, the subjective magnitude of one's experience. We do this in the context of the method of triads: The sensation of the stimulus is evaluated via relative judgments of the following form: “Is stimulus more similar to stimulus or to stimulus ?” We propose to use ordinal embedding methods from machine learning to estimate the scaling function from the relative judgments. We review two relevant and well-known methods in psychophysics that are partially applicable in our setting: nonmetric multidimensional scaling (NMDS) and the method of maximum likelihood difference scaling (MLDS). Considering various scaling functions, we perform an extensive set of simulations to demonstrate the performance of the ordinal embedding methods. We show that in contrast to existing approaches, our ordinal embedding approach allows, first, to obtain reasonable scaling functions from comparatively few relative judgments and, second, to estimate multidimensional perceptual scales. In addition to the simulations, we analyze data from two real psychophysics experiments using ordinal embedding methods. Our results show that in the one-dimensional perceptual scale, our ordinal embedding approach works as well as MLDS, while in higher dimensions, only our ordinal embedding methods can produce a desirable scaling function. To make our methods widely accessible, we provide an R-implementation and general rules of thumb on how to use ordinal embedding in the context of psychophysics.

Measuring and Modeling Visual Appearance.

In studying visual perception, we seek to develop models of processing that accurately predict perceptual judgments. Much of this work is focused on judgments of discrimination, and there is a large literature concerning models of visual discrimination. There are, however, non-threshold visual judgments, such as judgments of the magnitude of differences between visual stimuli, that provide a means to bridge the gap between threshold and appearance. We describe two such models of suprathreshold judgments, maximum likelihood difference scaling and maximum likelihood conjoint measurement, and review recent literature that has exploited them.

Toward reliable measurements of perceptual scales in multiple contexts

A central question in psychophysical research is how perceptual differences between stimuli translate into physical differences and vice versa. Characterizing such a psychophysical scale would reveal how a stimulus is converted into a perceptual event, particularly under changes in viewing conditions (e.g., illumination). Various methods exist to derive perceptual scales, but in practice, scale estimation is often bypassed by assessing appearance matches. Matches, however, only reflect the underlying perceptual scales but do not reveal them directly. Two recently developed methods, MLDS (Maximum Likelihood Difference Scaling) and MLCM (Maximum Likelihood Conjoint Measurement), promise to reliably estimate perceptual scales. Here we compared both methods in their ability to estimate perceptual scales across context changes in the domain of lightness perception. In simulations, we adopted a lightness constant, a contrast, and a luminance-based observer model to generate differential patterns of perceptual scales. MLCM correctly recovered all models. MLDS correctly recovered only the lightness constant observer model. We also empirically probed both methods with two types of stimuli: (a) variegated checkerboards that support lightness constancy and (b) center-surround stimuli that do not support lightness constancy. Consistent with the simulations, MLDS and MLCM provided similar scale estimates in the first case and divergent estimates in the second. In addition, scales from MLCM–and not from MLDS–accurately predicted asymmetric matches for both types of stimuli. Taking experimental and simulation results together, MLCM seems more apt to provide a valid estimate of the perceptual scales underlying judgments of lightness across viewing conditions.

Suprathreshold contrast response in normal and anomalous trichromats.

Maximum likelihood difference scaling was used to measure suprathreshold contrast response difference scales for low-frequency Gabor patterns, modulated along luminance and L-M color directions in normal, protanomalous, and deuteranomalous observers. Based on a signal-detection model, perceptual scale values, parameterized as $ d^\prime $d', were estimated by maximum likelihood. The difference scales were well fit by a Michaelis-Menten model, permitting estimates of response and contrast gain parameters for each subject. Anomalous observers showed no significant differences in response or contrast gain from normal observers for luminance contrast. For chromatic modulation, however, anomalous observers displayed higher contrast and lower response gain compared to normal observers. These effects cannot be explained by simple pigment shift models, and they support a compensation mechanism to optimize the mapping of the input contrast range to the neural response range. A linear relation between response and contrast gain suggests a neural trade-off between them.

The influence of observer lapses on maximum-likelihood difference scaling

The influence of observer lapses on maximum-likelihood difference scaling

Maximum likelihood difference scales represent perceptual magnitudes and predict appearance matches.

One central problem in perception research is to understand how internal experiences are linked to physical variables. Most commonly, this relationship is measured using the method of adjustment, but this has two shortcomings: The perceptual scales that relate physical and perceptual variables are not measured directly, and the method often requires perceptual comparisons between viewing conditions. To overcome these problems, we measured perceptual scales of surface lightness using maximum likelihood difference scaling, asking observers only to compare the lightness of surfaces presented in the same context. Observers were lightness constant, and the perceptual scales qualitatively and quantitatively predicted perceptual matches obtained in a conventional adjustment experiment. Additionally, we show that a contrast-based model of lightness perception predicted 98% of the variance in the scaling and 88% in the matching data. We suggest that the predictive power was higher for scales because they are closer to the true variables of interest.

Dissociation of equilibrium points for color-discrimination and color-appearance mechanisms in incomplete chromatic adaptation.

We compared the color-discrimination thresholds and supra-threshold color differences (STCDs) obtained in complete chromatic adaptation (gray) and incomplete chromatic adaptation (red). The color-difference profiles were examined by evaluating the perceptual distances between various color pairs using maximum likelihood difference scaling. In the gray condition, the chromaticities corresponding with the smallest threshold and the largest color difference were almost identical. In contrast, in the red condition, they were dissociated. The peaks of the sensitivity functions derived from the color-discrimination thresholds and STCDs along the L-M axis were systematically different between the adaptation conditions. These results suggest that the color signals involved in color discrimination and STCD tasks are controlled by separate mechanisms with different characteristic properties.

Color constancy supports cross-illumination color selection.

We rely on color to select objects as the targets of our actions (e.g., the freshest fish, the ripest fruit). To be useful for selection, color must provide accurate guidance about object identity across changes in illumination. Although the visual system partially stabilizes object color appearance across illumination changes, how such color constancy supports object selection is not understood. To study how constancy operates in real-life tasks, we developed a novel paradigm in which subjects selected which of two test objects presented under a test illumination appeared closer in color to a target object presented under a standard illumination. From subjects' choices, we inferred a selection-based match for the target via a variant of maximum likelihood difference scaling, and used it to quantify constancy. Selection-based constancy was good when measured using naturalistic stimuli, but was dramatically reduced when the stimuli were simplified, indicating that a naturalistic stimulus context is critical for good constancy. Overall, our results suggest that color supports accurate object selection across illumination changes when both stimuli and task match how color is used in real life. We compared our selection-based constancy results with data obtained using a classic asymmetric matching task and found that the adjustment-based matches predicted selection well for our stimuli and instructions, indicating that the appearance literature provides useful guidance for the emerging study of constancy in natural tasks.

Seeing liquids from static snapshots

Perceiving material properties can be crucial for many tasks—such as determining food edibility, or avoiding getting splashed—yet the visual perception of materials remains poorly understood. Most previous research has focussed on optical characteristics (e.g., gloss, translucency). Here, however, we show that shape also provides powerful visual cues to material properties. When liquids pour, splash or ooze, they organize themselves into characteristic shapes, which are highly diagnostic of the material’s properties. Subjects viewed snapshots of simulated liquids of different viscosities, and rated their similarity. Using maximum likelihood difference scaling (Maloney & Yang, 2003), we reconstructed perceptual scales for perceived viscosity as a function of the physical viscosity of the simulated fluids. The resulting psychometric function revealed a distinct sigmoidal shape, distinguishing runny liquids that flow easily from viscous gels that clump up into piles. A parameter-free model based on 20 simple shape statistics predicted the subjects’ data surprisingly well. This suggests that when subjects are asked to compare the viscosity of static snapshots of liquids that differ only in terms of viscosity, they rely primarily on relatively simple measures of shape similarity.

Maximum Likelihood Difference Scaling versus Ordinal Difference Scaling of emotion intensity: a comparison

We compare the utility of Maximum Likelihood Difference Scaling (MLDS) and Ordinal Difference Scaling (ODS) for the measurement of emotion intensity. MLDS and ODS are both nonmetric probabilistic scaling methods based on difference measurement; however, MLDS uses quadruple comparisons (comparison of pairs of stimulus pairs) as input data, whereas ODS uses graded pair comparison judgments, where participants indicate the size of the difference between two stimuli on an ordinal response scale. In two studies using different kinds of emotional stimuli (disgust-inducing pictures, and descriptions of situations eliciting relief), quadruple comparisons and graded pair comparisons of the stimuli were collected and submitted to MLDS and ODS respectively. The scaling solutions were compared in terms of the reliability of the estimated scale values and their correlations to direct ratings of emotion intensity. The findings of both studies suggest that ODS performs at least as well as MLDS on these criteria. In addition, in most cases, good to high agreement between the scale values estimated by the two methods was found. Hence, ODS may be used as an economical alternative to MLDS for the difference scaling of emotional stimuli.

Using maximum likelihood difference scaling to measure visual discomfort

Using maximum likelihood difference scaling to measure visual discomfort

Indirect scaling methods for testing quantitative emotion theories

Two studies investigated the utility of indirect scaling methods, based on graded pair comparisons, for the testing of quantitative emotion theories. In Study 1, we measured the intensity of relief and disappointment caused by lottery outcomes, and in Study 2, the intensity of disgust evoked by pictures, using both direct intensity ratings and graded pair comparisons. The stimuli were systematically constructed to reflect variables expected to influence the intensity of the emotions according to theoretical models of relief/disappointment and disgust, respectively. Two probabilistic scaling methods were used to estimate scale values from the pair comparison judgements: Additive functional measurement (AFM) and maximum likelihood difference scaling (MLDS). The emotion models were fitted to the direct and indirect intensity measurements using nonlinear regression (Study 1) and analysis of variance (Study 2). Both studies found substantially improved fits of the emotion models for the indirectly determined emotion intensities, with their advantage being evident particularly at the level of individual participants. The results suggest that indirect scaling methods yield more precise measurements of emotion intensity than rating scales and thereby provide stronger tests of emotion theories in general and quantitative emotion theories in particular.