Which of the following refers to the just-noticeable difference between two stimuli?

21.2.2.2 Sarnoff JND Vision Model

The Sarnoff JND vision model received a technical Emmy award in 2000 and is one of the best known QA systems based on human vision models. This model was developed by Lubin and coworkers, and details of this algorithm can be found in [38].

Preprocessing steps in this model include calibration for distance of the observer from the images. In addition, this model also accounts for fixation depth and eccentricity of the observer's visual field. The human eye does not sample an image uniformly since the density of retinal cells drops off with eccentricity, resulting in a decreased spatial resolution as we move away from the point of fixation of the observer. To account for this effect, the Lubin model resamples the image to generate a modeled retinal image. The Laplacian pyramid of Burt and Adelson [77] is used to decompose the image into seven radial frequency bands. At this stage, the pyramid responses are converted to units of local contrast by dividing each point in each level of the Laplacian pyramid by the corresponding point obtained from the Gaussian pyramid two levels down in resolution. Each pyramid level is then convolved with eight spatially oriented filters of Freeman and Adelson [78], which constitute Hilbert transform pairs for four different orientations. The frequency decomposition so obtained is illustrated in Fig. 21.3(c). The two Hilbert transform pair outputs are squared and summed to obtain a local energy measure at each pixel location, pyramid level, and orientation. To account for the contrast sensitivity of human vision, these local energy measures are normalized by the base sensitivities for that position and pyramid level, where the base sensitivities are obtained from the CSF.

The Sarnoff model does not use the threshold elevation approach to model masking used by the VDP, instead adopting a transducer or a contrast gain control model. Gain control models a mechanism that allows a neuron in the HVS to adjust its response to the ambient contrast of the stimulus. Such a model generalizes better to the case of supra-threshold distortions since it models an underlying mechanism in the visual system, as opposed to measuring visibility thresholds. The transducer model used in [38] takes the form of a sigmoid nonlinearity. A sigmoid function starts out flat, its slope increases to a maximum, and then decreases back to zero, i.e., it changes curvature like the letter S.

Finally, a distance measure is calculated using a Minkowski error between the responses of the test and distorted images at the output of the vision model. A psychometric function is used to convert the distance measure to a probability value, and the Sarnoff JND vision model outputs a spatial map that represents the probability that an observer will be able to discriminate between the two input images (reference and distorted) based on the information in that spatial location.

Just Noticeable Difference

One of the classic psychoacoustic experiments is the measurement of a just noticeable difference (jnd), which is also called a difference limen. In these tests a subject is asked to compare two sounds and to indicate which is higher in level, or in frequency. What is found is that the jnd in level depends on both the intensity and frequency. Table 3.3 shows jnd level values at various sound pressure levels and frequencies. For sound levels exceeding 40 dB and at frequencies above 100 Hz, the jnd is less than 1 dB. At the most sensitive levels (greater than 60 dB) and frequencies (1000–4000 Hz), the jnd is about a quarter of a dB. When the jnd is 0.25 dB it means that we can notice a sound, with the same spectrum that is 13 dB below the level of the background. This has important implications for both privacy and intelligibility in the design of speech reinforcement systems.

Table 3.3. Minimum Detectable Changes (jnd) in Level for Sine Waves, dB (Pierce, 1983)

The jnd values in frequency for sine waves are shown in Table 3.4. Like the jnd in level, it is also dependent on both intensity and frequency. At 2000 Hz, where we are most sensitive, the jnd is about 3 cents (0.3% of an octave) or about 0.5% of the pure tone frequency for levels above 30 dB. This is about 10 Hz. Some trained musicians can tell the difference between a perfect fifth (702 cents) and an equal tempered fifth (700 cents), so that greater sensitivity is not uncommon. Note that these comparisons are done by sounding successive tones or by varying the tone, not by comparing simultaneous tones where greater precision is obtainable by listening for beats. Piano tuners who tune by ear use this latter method to achieve precise tuning.

Table 3.4. Minimum Detectable Changes (jnd) in Frequency for Sine Waves, Cents (Pierce, 1983)

6.6.2 Difference threshold

The difference threshold is the minimum amount of stimulus change required to produce a sensation difference, referred to as the just noticeable difference on the psychological continuum. E. H. Weber, a 19th century physiologist, determined that physical stimulus intensity must be increased by a constant fraction of its starting value in order to be just noticeably different. Weber’s law is written as

(6.17)ΔΦ/Φ=c

where ∆Ф is the change in stimulus intensity required to be just noticeably different; c is a constant fraction of the starting stimulus intensity. Weber’s prediction has been confirmed for a wide range of stimulus intensities and sensory modalities and is shown to be an extremely useful calculation providing an index of sensory discrimination that can be compared across different conditions and modalities. Because of the fact that the Weber’s fraction is a unit-less measure, it serves as an index of sensory discrimination that can be compared across different conditions. For evaluating the moisture sensitivity using different fabric stimuli, one should compare the values of the Weber fractions to examine the effect of fabric stimulus on moisture sensitivity. Weber’s fraction should only be considered as an approximation of differential sensitivity; however, since it increases dramatically at levels of stimulus intensities near the absolute threshold.

It may be noted that the moisture sensation is only one of the many sensations contributing to clothing comfort. Future investigations of moisture sensation or other sensorial comfort variables could examine the effects of various levels of these factors on subject sensitivity [84]

3.1 Introduction

The problem with colour as normal observers experience it is that it is a fundamentally unexplained kind of output of our sensory system. As such it is not subject to direct measurement. The fundamental assumption of technological colour measurement is that there is a definable relationship between tristimulus values and perceived colour. Empirical experience shows that this is generally the case only in very limited conditions. It is generally assumed that there is a direct relationship between colour-matching functions and vision properties. Most individuals vary in their colour-matching functions to a greater or lesser degree from the average, and so presumably does their colour vision (Kuehni, 2003a).

Human eyes can distinguish between some 10 million colours. Measurement of difference in colour between two objects is one of the most complicated aspects of colour vision. The colour discrimination may be general/overall or of specific psychophysical attributes such as hue, chroma or lightness. For such colourant users as textile, leather, paper and paint industries, the difference in colour of two specimens, namely a standard and a sample, or of different portions of a coloured specimen may be more important than the measurement of absolute colour (Luo, 1986). The prime difficulty is that the perception of colour difference by an individual is not a precise phenomenon and may vary on successive assessments (Zeller and Hemmendinger, 1978). Individuals show remarkable variation in judging the magnitude of perceptual differences between two coloured samples, one representing a standard and the other a batch, or when judging if the batch is an acceptable match to the standard. In other words, their judgements are largely subjective. To have a generally accepted objective, technology for evaluation and decision making can be of significant help in the interactions between manufacturer and purchaser.

The colour of a product may be judged generally to be ‘acceptable’ or ‘unsatisfactory’, or it may be judged in more detail to be ‘too light’, ‘too red’ or ‘too blue’. Such a judgement can be made visually or instrumentally based on a perceived difference between an ideal product standard and a sample. When this difference is quantified, tolerances are established. Tolerances are limits within which a product is considered acceptable, while falling outside is unacceptable. The tolerances allow us to make quick and easy pass/fail or ship/don’t ship decisions. Instrumental tolerances are expressed in any of the colour scales or indices. In order to set tolerances, an ideal product standard as well as a number of products determined acceptable or unacceptable beforehand, is required.

Two levels of visual colour differences between standard and sample are used to establish colour tolerances:

Minimum perceptible difference, i.e. a just noticeable difference.

Maximum acceptable difference, which is the largest acceptable difference.

Manufacturers are generally concerned about the maximum acceptable difference rather than a minimum perceptible difference, and the colour tolerances are usually based on the former. The colour-difference evaluation is necessary for day to day colour control and for colour matching in colouration industries such as textile, paint, etc. Colour-difference formulae have accelerated the instrumental pass/fail device a success, but still much is to be done for complete satisfaction. The goal of colour-difference formulae is to accurately and objectively define a colour difference so that it agrees with average visual assessments.

However, many problems of colour-difference evaluations are still unsolved. This is apparent from the fact that at least 40 different colour-difference formulae have been developed globally. Each colour-difference formula has been formulated for a specific field of application in which it is claimed to be most appropriate. The fact that the CIELAB formulae recommended by the CIE in 1976 is very similar to the ANLAB formula derived in 1944 suggests that little progress has been made during that period. In recent years, efforts have been made to develop a single such formula which is universally applicable.

3.1.1.1 Gaze-dwell

Gaze-dwell is a variant of selecting objects that does not involve the use of gestures or voice commands. This action consists of a user gazing at an object and remaining fixated on the object. A fixation is a period of time (from less than 100 ms up to several seconds Holmqvist et al. 2011) that the gaze location is static within a specific region.

Gaze-dwell is utilized to allow the system to register that the object is intended to be selected/activated and has not been actuated inadvertently. Sticking with the same example of zooming in on an object, the user would gaze at the zoom button and continue to gaze at the button until the zoom tool became active.

The period of time that the user will need to ‘dwell’ is programmable and should be determined based upon the user's physical capabilities to remain fixated on a target, just-noticeable differences between deactivated, selected and activated states and slowing down the workflow unnecessarily causing user annoyance.

Gaze: tips

The following items should be considered when designing an interface that utilizes gaze selection.

Be mindful of target sizing

Highlight object when targeted by gaze cursor

Be conscious of field of view (FOV) and target placement

Differentiate hover from selection cues (visual and audible)

Be mindful of time to confirm selection using gaze-dwell

Weber's law of JND

It is known from psychophysics that the human haptic perception system is limited, and it is often modeled by Weber's law [377,378]. Specifically, this law states that the JND, the size of the difference threshold, is proportional to the amplitude (or intensity) of the initial stimulus itself. Weber's law of JND is represented by the following equation:

(5.1)DI=k⋅I,

where k is a constant and I and DI denote the initial stimulus and the JND, respectively. The constant k, also called the Weber fraction, depends on the investigated stimulus property, e.g., force, stiffness or velocity and the body part, i.e., the limb or joint where it is applied. A brief summary of the Weber fraction k of human perceptual discrimination for selected haptic stimuli is shown in Table 5.1.

Table 5.1. Weber fraction k of human perceptual discrimination for haptic stimuli [379].

Force perception has been intensively studied. Of note is that the relative perception thresholds of force feedback are not completely independent of the intensity of the forces being applied. Specifically, smaller Weber fractions (in the range of 7% to 10%) were observed for larger forces from 0.5 N to 200 N; whereas for forces with lower intensity (below 0.5 N), the Weber fraction was found to be within the range of 15% to 27% [373]. The JND of Weber's law has been used as a packet rate reduction technique in haptic codec development, the so-called perceptual deadband-based kinesthetic data reduction approach [380,381]. The main idea being that the current stimuli need to be only transmitted when they are above the JND, meaning the change with respect to the previously applied stimulus is consciously perceivable by humans.

The Method of Limits

To avoid the problem that different observers tend to make their adjustments at different rates and engage in “backtracking” to varying extents, a second procedure is often preferred, namely, the method of limits (or “just noticeable differences”). In this method, the starting point and the size of the increments or decrements in the variable are controlled by the experimenter. At each step in either an ascending or a descending series, the observer reports whether the variable appears “less than”, “equal to”, or “greater than” the standard, and the experimenter notes the value of the variable at which the observer's response changes from “lesser” (or “greater”) to “equal” (or to the converse).

As with the method of adjustment, it is clear that, unless the observer can discriminate perfectly, there will be a range of values of the variable, close to that of the standard, within which he will find some difficulty in reaching a judgment of “lesser” or “greater” and will be likely to say “equal”. Such a region of indecision makes it likely (though not necessary) that the mean for ascending trials will differ from that for descending ones. However, even when the observer is forbidden to make “equal” judgments, but must opt for “lesser” or “greater”, the means for ascending and descending trials may still turn out to be different. This has generally been “explained” as arising from two kinds of error on the part of the observer. The first of these, the error of habituation, is the tendency to persist in saying “lesser” in an ascending (or “greater” in a descending) series of trials. The second, the error of anticipation, is the converse tendency to change response too soon.

Because the amounts of error on ascending and descending trials may not be equal, the PSE is often found to be different from the value of the standard. If it lies above the standard, there is said to be a positive constant error, and, if below, a negative one.

Dynamic range

3.2.2 Baseline Contrast Sensitivity (Base Sensitivity)

The baseline contrast sensitivity determines the amount of energy in each subband that is required in order to detect the target in an (arbitrary or) flat mid-gray image. As we discussed earlier, this is sometimes referred to as the just noticeable difference or JND. We will use tb(k) to denote the baseline sensitivity of the k-th band or DCT coefficient. Note that the base sensitivity is independent of the location n.

The base sensitivities can be obtained from the contrast sensitivity function (CSF), as in [3], or can be derived empirically and listed in a table, as in [5]. The base sensitivities are then adjusted to account for variations in luminance and texture masking to obtain the overall sensitivity t(k, n). An alternative approach, implemented in Daly's model [2], is to filter the image by the contrast sensitivity function before the frequency decomposition.

The key parameters for the contrast sensitivity are the viewing distance (in inches) and the resolution of the display device (in pixels per inch). Alternatively, one can specify the viewing distance in image heights and the image height in pixels (assuming the same horizontal and vertical display resolution). In either case, one must derive the “display visual resolution” in pixels per degree [14].

Since the contrast sensitivity function has a band-pass characteristic (e.g., see [2]), if we assume a single fixed viewing distance, the metric may show a degradation in image quality as we move away from the image. To avoid this, one can assume a range of viewing distances [2], or a minimum viewing distance. This will result in a flattening of the CSF. This flattening is commonly assumed in image halftoning applications [16, 20] because it is the low-pass characteristic of the eye that is critical for halftoning.

Local Contrast Adaptation

In Figure 6.2–6 we see a pair of small squares, one on a light background and the other on a dark background. While the small squares appear to have different gray levels, in fact the gray levels are the same. This effect occurs because the HVS adapts to surrounding brightness levels when it interprets the brightness of an object.

There is also a local contrast adaptation wherein the JND moves upward as the background brightness moves away from the average contrast of the object. Such a test can be performed via the approach sketched in Figure 6.2–7, where we note that the small central square is split and slightly darker on the left. For most people, this effect is more evident from the display on the left, where the contrast with the local background is only slight. However, on the right the large local contrast with the local background makes this effect harder to perceive. Effectively, this means that the JND varies somewhat with local contrast, or said another way, there is some kind of local masking effect.