Probability Summation Model Research Articles

Interrupted mosaic speech revisited: Gain and loss in intelligibility by stretchinga).

Our previous investigation on the effect of stretching spectrotemporally degraded and temporally interrupted speech stimuli showed remarkable intelligibility gains [Udea, Takeichi, and Wakamiya (2022). J. Acoust. Soc. Am. 152(2), 970-980]. In this previous study, however, gap durations and temporal resolution were confounded. In the current investigation, we therefore observed the intelligibility of so-called mosaic speech while dissociating the effects of interruption and temporal resolution. The intelligibility of mosaic speech (20 frequency bands and 20 ms segment duration) declined from 95% to 78% and 33% by interrupting it with 20 and 80 ms gaps. Intelligibility improved, however, to 92% and 54% (14% and 21% gains for 20 and 80 ms gaps, respectively) by stretching mosaic segments to fill silent gaps (n = 21). By contrast, the intelligibility was impoverished to a minimum of 9% (7% loss) when stretching stimuli interrupted with 160 ms gaps. Explanations based on auditory grouping, modulation unmasking, or phonemic restoration may account for the intelligibility improvement by stretching, but not for the loss. The probability summation model accounted for "U"-shaped intelligibility curves and the gain and loss of intelligibility, suggesting that perceptual unit length and speech rate may affect the intelligibility of spectrotemporally degraded speech stimuli.

Interrupted mosaic speech revisited: Gain and loss of stretching on intelligibility

Periodicity and temporal fine structure provide a perceptual cue to connect speech fragments when the speech is interrupted. In mosaic speech stimuli, which are noise-vocoded with stepwise amplitude and spectral envelopes, interruption drastically reduces intelligibility because of lacking the perceptual cue. Here we report that the intelligibility of mosaic speech stimuli, consisting of 20 frequency bands and 20-ms segment duration, decreased from 95% to 78% and 33% when they were interrupted by 20- and 80-ms gaps. However, when the mosaic segments were stretched to fill the silent gaps, the intelligibility improved again to 92% and 54%, resulting in gains of 14% and 21% respectively. By contrast, intelligibility dropped by 7% with stretching and filling 160-ms gaps. The intelligibility minimums (9%–16%) were observed at the 160-ms original gap duration irrespective of stretching ratios. It is possible that stretching with short gaps effectively restored the original amplitude envelopes, whereas, with long gaps, the effect was detrimental. Furthermore, a probability summation model with a short and a long integration window, by which the intelligibility minimums were predicted for lowpass-filtered interrupted speech stimuli, seems to be highly relevant to the current results.

Checkerboard and interrupted speech: Intelligibility contrasts related to factor-analysis-based frequency bandsa).

It has been shown that the intelligibility of checkerboard speech stimuli, in which speech signals were periodically interrupted in time and frequency, drastically varied according to the combination of the number of frequency bands (2-20) and segment duration (20-320 ms). However, the effects of the number of frequency bands between 4 and 20 and the frequency division parameters on intelligibility have been largely unknown. Here, we show that speech intelligibility was lowest in four-band checkerboard speech stimuli, except for the 320-ms segment duration. Then, temporally interrupted speech stimuli and eight-band checkerboard speech stimuli came in this order (N = 19 and 20). At the same time, U-shaped intelligibility curves were observed for four-band and possibly eight-band checkerboard speech stimuli. Furthermore, different parameters of frequency division resulted in small but significant intelligibility differences at the 160- and 320-ms segment duration in four-band checkerboard speech stimuli. These results suggest that factor-analysis-based four frequency bands, representing groups of critical bands correlating with each other in speech power fluctuations, work as speech cue channels essential for speech perception. Moreover, a probability summation model for perceptual units, consisting of a sub-unit process and a supra-unit process that receives outputs of the speech cue channels, may account for the U-shaped intelligibility curves.

Checkerboard and interrupted speech: Critical intelligibility differences observed in factor-analysis-based checkerboard speech stimuli

It has been shown that the intelligibility of checkerboard speech stimuli, in which speech signals were periodically interrupted in time and frequency, drastically varied according to the combination of the number of frequency bands (2–20) and segment duration (20–320 ms). However, the effects of the number of frequency bands between 4 and 20 and the ways of frequency divisions on intelligibility have been basically unknown. Here we show that 8-band checkerboard speech stimuli were more intelligible than temporally interrupted speech stimuli and 4-band checkerboard speech stimuli, irrespective of segment duration (n = 19 and 20). At the same time, U-shaped intelligibility curves were observed for 4-band and possibly 8-band checkerboard speech stimuli. Furthermore, when the frequency divisions were determined according to regular intervals on a critical bandwidth scale rather than factor analysis results of speech power fluctuations, intelligibility improved at the 160- and 320-ms segment duration. These results suggest that the factor-analysis-based frequency bands perform as speech cue channels that are essential for speech perception and that a probability summation model based on a perceptual unit of speech perception may account for the U-shaped intelligibility curves if the model is modified to include the speech cue channels.

Binocular Summation Is Intact in Intermittent Exotropia After Surgery.

Purpose: To determine binocular summation of surgically treated intermittent exotropia (IXT) patients by measuring the contrast threshold.Methods: We recruited 38 surgically treated IXT patients aged 8–24 years and 20 age-matched healthy controls. All participants had normal or corrected-to-normal visual acuity (Snellen ≥ 20/20) in both eyes. The IXT patients had undergone the surgery at least a year prior to the study. Twenty-one of them obtained good alignment and 17 experienced a recurrence of exotropia. We measured the observers' monocular and binocular contrast sensitivities (CS) at six spatial frequencies (1.5, 3, 6, 12, 18, 24 cycles/degree) as an index of visual information processing at the threshold level. Binocular summation was evaluated against a baseline model of simple probability summation based on the CS at each spatial frequency and the area under the log contrast sensitivity function (AULCSF).Results: The exo-deviation of IXTs with good alignment was −6.38 ± 3.61 prism diopters (pd) at 33 cm and −5.14 ± 4.07 pd at 5 m. For the patients with recurrence, it was −23.47 ± 5.53 pd and −21.12 ± 4.28 pd, respectively. There was no significant difference in the binocular summation ratio (BSR) between the surgically treated IXT patients, including those with good alignment and recurrence, and normal controls at each spatial frequency [F(2,55) = 0.416, P = 0.662] and AULCSF [F(2,55) = 0.469, P = 0.628]. In addition, the BSR was not associated with stereopsis (r = −0.151, P = 0.365).Conclusion: Our findings of normal contrast sensitivity binocular summation ratio in IXT after surgical treatment suggest that the ability of the visual cortex in processing binocular information is intact at the contrast threshold level.

The processing of compound radial frequency patterns

Radial frequency (RF) patterns can be combined to construct complex shapes. Previous studies have suggested that such complex shapes may be encoded by multiple, narrowly-tuned RF shape channels. To test this hypothesis, thresholds were measured for detection and discrimination of various combinations of two RF components. Results show evidence of summation: sensitivity for the compounds was better than that for the components, with little effect of the components’ relative phase. If both RF components are processed separately at the point of detection, they would combine by probability summation (PS), resulting in only a small increase in sensitivity for the compound compared to the components. Summation exceeding the prediction of PS suggests a form of additive summation (AS) by a common mechanism. Data were compared to predictions of winner-take-all, where only the strongest component contributes to detection, a single channel AS model, and multi-channel PS and AS models. The multi-channel PS and AS models were modelled under both Fixed and Matched Attention Window scenarios, the former assuming a single internal noise source for both components and compounds or different internal noise sources for components and compounds respectively. The winner-take-all and single channel models could be rejected. Of the remaining models, the best performing one was an AS model with a Fixed Attention Window, consistent with detection being mediated by channels that are efficiently combined and limited by a single source of noise for both components and compounds.

Full Reference Objective Quality Assessment for Reconstructed Background Images

With an increased interest in applications that require a clean background image, such as video surveillance, object tracking, street view imaging and location-based services on web-based maps, multiple algorithms have been developed to reconstruct a background image from cluttered scenes. Traditionally, statistical measures and existing image quality techniques have been applied for evaluating the quality of the reconstructed background images. Though these quality assessment methods have been widely used in the past, their performance in evaluating the perceived quality of the reconstructed background image has not been verified. In this work, we discuss the shortcomings in existing metrics and propose a full reference Reconstructed Background image Quality Index (RBQI) that combines color and structural information at multiple scales using a probability summation model to predict the perceived quality in the reconstructed background image given a reference image. To compare the performance of the proposed quality index with existing image quality assessment measures, we construct two different datasets consisting of reconstructed background images and corresponding subjective scores. The quality assessment measures are evaluated by correlating their objective scores with human subjective ratings. The correlation results show that the proposed RBQI outperforms all the existing approaches. Additionally, the constructed datasets and the corresponding subjective scores provide a benchmark to evaluate the performance of future metrics that are developed to evaluate the perceived quality of reconstructed background images.

Rejecting probability summation for radial frequency patterns, not so Quick!

Radial frequency (RF) patterns are used to assess how the visual system processes shape. They are thought to be detected globally. This is supported by studies that have found summation for RF patterns to be greater than what is possible if the parts were being independently detected and performance only then improved with an increasing number of cycles by probability summation between them. However, the model of probability summation employed in these previous studies was based on High Threshold Theory (HTT), rather than Signal Detection Theory (SDT). We conducted rating scale experiments to investigate the receiver operating characteristics. We find these are of the curved form predicted by SDT, rather than the straight lines predicted by HTT. This means that to test probability summation we must use a model based on SDT. We conducted a set of summation experiments finding that thresholds decrease as the number of modulated cycles increases at approximately the same rate as previously found. As this could be consistent with either additive or probability summation, we performed maximum-likelihood fitting of a set of summation models (Matlab code provided in our Supplementary material) and assessed the fits using cross validation. We find we are not able to distinguish whether the responses to the parts of an RF pattern are combined by additive or probability summation, because the predictions are too similar. We present similar results for summation between separate RF patterns, suggesting that the summation process there may be the same as that within a single RF.

On the probability summation model for laser-damage thresholds.

This paper explores the probability summation model in an attempt to provide insight to the model's utility and ultimately its validity. The model is a statistical description of multiple-pulse (MP) damage trends. It computes the probability of n pulses causing damage from knowledge of the single-pulse dose-response curve. Recently, the model has been used to make a connection between the observed n −1∕4 trends in MP damage thresholds for short pulses (<10 μs) and experimental uncertainties, suggesting that the observed trend is an artifact of experimental methods. We will consider the correct application of the model in this case. We also apply this model to the spot-size dependence of short pulse damage thresholds, which has not been done previously. Our results predict that the damage threshold trends with respect to the irradiated area should be similar to the MP damage threshold trends, and that observed spot-size dependence for short pulses seems to display this In this paper, we develop the application of the PSM to laser- damage thresholds in greater detail than in previous works and consider the consequences of assuming its validity. We do not attempt to prove or disprove the model, rather we develop a set of predictions that must all be considered when using or assess- ing the model against experimental data. The model has been used to make a connection between the n −1∕4 trend and exper- imental uncertainties, 2,3 which we wish to address. We will also show that the model can account for the dependence of the MP ED50 trends on spot size and that it may also provide an explan- ation for the single, short-pulse ED50 dependence on spot size. Important note: The PSM relates the dose-response curve for a single pulse (SP) to the dose-response curve for MPs, and this paper contains a great deal of discussion about dose-response curves and their shape. One very important property of a dose- response curve is its sharpness, i.e., the difference between a dose for which damage is virtually impossible and a dose for which damage is virtually guaranteed. Unfortunately, there are two quantities that are in common use to characterize this property, and both are often called slope. The first definition, which is used in this paper and denoted as SL, refers to the slope of the best fit line obtained with probit analysis. The second

Fourth-root summation of contrast over area: No end in sight when spatially inhomogeneous sensitivity is compensated by a witch's hat.

Measurements of area summation for luminance-modulated stimuli are typically confounded by variations in sensitivity across the retina. Recently we conducted a detailed analysis of sensitivity across the visual field (Baldwin, Meese, & Baker, 2012) and found it to be well described by a bilinear "witch's hat" function: Sensitivity declines rapidly over the first eight cycles or so, but more gently thereafter. Here we multiplied luminance-modulated stimuli (4 cycles/degree gratings and "Swiss cheeses") by the inverse of the witch's hat function to compensate for the inhomogeneity. This revealed summation functions that were straight lines (on double log axes) with a slope of -1/4 extending to ≥33 cycles, demonstrating fourth-root summation of contrast over a wider area than has previously been reported for the central retina. Fourth-root summation is typically attributed to probability summation, but recent studies have rejected that interpretation in favor of a noisy energy model that performs local square-law transduction of the signal, adds noise at each location of the target, and then sums over signal area. Modeling shows our results to be consistent with a wide field application of such a contrast integrator. We reject a probability summation model, a quadratic model, and a matched template model of our results under the assumptions of signal detection theory. We also reject the high threshold theory of contrast detection under the assumption of probability summation over area.

Response Times to Gustatory-Olfactory Flavor Mixtures: Role of Congruence.

A mixture of perceptually congruent gustatory and olfactory flavorants (sucrose and citral) was previously shown to be detected faster than predicted by a model of probability summation that assumes stochastically independent processing of the individual gustatory and olfactory signals. This outcome suggests substantial integration of the signals. Does substantial integration also characterize responses to mixtures of incongruent flavorants? Here, we report simple response times (RTs) to detect brief pulses of 3 possible flavorants: monosodium glutamate, MSG (gustatory: "umami" quality), citral (olfactory: citrus quality), and a mixture of MSG and citral (gustatory-olfactory). Each stimulus (and, on a fraction of trials, water) was presented orally through a computer-operated, automated flow system, and subjects were instructed to press a button as soon as they detected any of the 3 non-water stimuli. Unlike responses previously found to the congruent mixture of sucrose and citral, responses here to the incongruent mixture of MSG and citral took significantly longer (RTs were greater) and showed lower detection rates than the values predicted by probability summation. This outcome suggests that the integration of gustatory and olfactory flavor signals is less extensive when the component flavors are perceptually incongruent rather than congruent, perhaps because incongruent flavors are less familiar.

Laser-induced retinal damage threshold for repetitive-pulse exposure to 100-μs pulses.

The laser-induced retinal injury thresholds for repetitive-pulse exposures to 100-μs-duration pulses at a wavelength of 532 nm have been determined for exposures of up to 1000 pulses in an in vivo model. The ED50 was measured for pulse repetition frequencies of 50 and 1000 Hz. Exposures to collimated beams producing a minimal retinal beam spot and to divergent beams producing a 100-μm-diameter retinal beam spot were considered. The ED50 for a 100-μs exposure was measured to be 12.8 μJ total intraocular energy for a minimal retinal beam spot exposure and 18.1 μJ total intraocular energy for a 100-μm-diameter retinal beam spot. The threshold for exposures to N > 1 pulse was found to be the same for both pulse repetition frequencies. The variation of the ED50 with the number of pulses is described well by the probability summation model, in which each pulse is considered an independent event. This is consistent with a threshold-level damage mechanism of microcavitation for single-pulse 100-μs-duration exposures. The data support the maximum permissible exposure levels for repetitive-pulse exposure promulgated in the most recent laser safety guidelines.

Damage threshold from large retinal spot size repetitive-pulse laser exposures.

The retinal damage thresholds for large spot size, multiple-pulse exposures to a Q-switched, frequency doubled Nd:YAG laser (532 nm wavelength, 7 ns pulses) have been measured for 100 μm and 500 μm retinal irradiance diameters. The ED50, expressed as energy per pulse, varies only weakly with the number of pulses, n, for these extended spot sizes. The previously reported threshold for a multiple-pulse exposure for a 900 μm retinal spot size also shows the same weak dependence on the number of pulses. The multiple-pulse ED50 for an extended spot-size exposure does not follow the n dependence exhibited by small spot size exposures produced by a collimated beam. Curves derived by using probability-summation models provide a better fit to the data.

Recalibration of the Multisensory Temporal Window of Integration

Recalibration of the Multisensory Temporal Window of Integration

A no-reference objective image quality metric based on perceptually weighted local noise

This work proposes a perceptual based no-reference objective image quality metric by integrating perceptually weighted local noise into a probability summation model. Unlike existing objective metrics, the proposed no-reference metric is able to predict the relative amount of noise perceived in images with different content, without a reference. Results are reported on both the LIVE and TID2008 databases. The proposed no-reference metric achieves consistently a good performance across noise types and across databases as compared to many of the best very recent no-reference quality metrics. The proposed metric is able to predict with high accuracy the relative amount of perceived noise in images of different content.

Contrast integration over area is extensive: A three-stage model of spatial summation

Classical studies of area summation measure contrast detection thresholds as a function of grating diameter. Unfortunately, (i) this approach is compromised by retinal inhomogeneity and (ii) it potentially confounds summation of signal with summation of internal noise. The Swiss cheese stimulus of T. S. Meese and R. J. Summers (2007) and the closely related Battenberg stimulus of T. S. Meese (2010) were designed to avoid these problems by keeping target diameter constant and modulating interdigitated checks of first-order carrier contrast within the stimulus region. This approach has revealed a contrast integration process with greater potency than the classical model of spatial probability summation. Here, we used Swiss cheese stimuli to investigate the spatial limits of contrast integration over a range of carrier frequencies (1-16 c/deg) and raised plaid modulator frequencies (0.25-32 cycles/check). Subthreshold summation for interdigitated carrier pairs remained strong (∼4 to 6 dB) up to 4 to 8 cycles/check. Our computational analysis of these results implied linear signal combination (following square-law transduction) over either (i) 12 carrier cycles or more or (ii) 1.27 deg or more. Our model has three stages of summation: short-range summation within linear receptive fields, medium-range integration to compute contrast energy for multiple patches of the image, and long-range pooling of the contrast integrators by probability summation. Our analysis legitimizes the inclusion of widespread integration of signal (and noise) within hierarchical image processing models. It also confirms the individual differences in the spatial extent of integration that emerge from our approach.

A model-based analysis of the “combined-stimulation advantage”

Improvements in speech-recognition performance resulting from the addition of low-frequency information to electric (or vocoded) signals have attracted considerable interest in recent years. An important question is whether these improvements reflect a form of constructive perceptual interaction-whereby acoustic cues enhance the perception of electric or vocoded signals-or whether they can be explained without assuming any interaction. To address this question, speech-recognition performance was measured in 24 normal-hearing listeners using lowpass-filtered, vocoded, and "combined" (lowpass+vocoded) words presented either in quiet or in a realistic background (cafeteria noise), for different signal-to-noise ratios, different lowpass-filter cutoff frequencies, and different numbers of vocoder bands. The results of these measures were then compared to the predictions of three models of cue combination, including a "probability-summation" model and two Gaussian signal detection theory (SDT) models-one (the "independent-noises" model) involving pre-combination noises, and the other (the "late-noise" model) involving post-combination noise. Consistent with previous findings, speech-recognition performance with combined stimulation was significantly higher than performance with vocoded or lowpass stimuli alone, and it was also higher than predicted by the probability-summation model. The two Gaussian-SDT models could account quantitatively for the data. Moreover, a Bayesian model-comparison procedure demonstrated that, given the data, these two models were far more likely than the probability-summation model. Since these models do not involve any constructive-interaction mechanism, this demonstrates that constructive interactions are not needed to explain the combined-stimulation benefits measured in this study. It will be important for future studies to investigate whether this conclusion generalizes to other test conditions, including real EAS, and to further test the assumptions of these different models of the combined-stimulation advantage.

Flexible Resource Allocation for the Detection of Changing Visual Features

Failure to detect change under circumstances where visual input is interrupted or attention is distracted is indicative of the capacity limits of visual short-term memory. The current study attempts to probe the nature of these limits. In experiment 1, the appearance of single Gabor patches was altered across colour, size, or speed, and set size was manipulated by means of a visual cue. In experiment 2, performance for detecting single and multiple changes to Gabor patches was compared under the constraint that the inherent detectability of each individual change was the same. Experiment 1 yielded a particular set size (4) and a particular level of change magnitude at which performance was equivalent across change type. On the basis of these parameter values, experiment 2 revealed that the detectability of two features changing within one object was the same as the detectability of a single feature changing across two objects, and that this level of detectability could be predicted by a simple model of probability summation. Together, these results suggest that performance is determined by the magnitude of featural changes independently of the way they are distributed across objects. We suggest they are adequately explained by a flexible-resource-allocation model rather than a slot-allocation model.

Time course of the integration of spatial frequency-based information in natural scenes

It is known that visual information is processed separately and based on multiple spatial frequencies. Therefore, integration of information is important for categorization of natural scenes. To clarify the time course of visual integration, we examined categorization accuracies for spatially filtered images as a function of image exposure duration. Results indicated that, with image durations of 100-ms, accuracy was superior with spatially integrable images when compared with accuracy levels based upon the probability summation model estimated from accuracies of separately presented low- and high-frequency images. This finding suggests that spatial frequency integration begins earlier than 100-ms after the image onset.

Bar-like S-cone stimuli reveal the importance of an intermediate temporal filter

The relative involvement of different temporal frequency-selective filters underlying detection of chromatic stimuli was studied. Diverse spectral stimuli were used, namely flashed blue and yellow light spots, wide bars, and narrow bars. The stimuli were temporally modulated in luminance having constant wavelength. Although the bar-like stimuli apparently reduced the sensitivity at short and long wavelengths, the cone-opponent mechanism still remained responsible for the actual stimulus detection at different temporal frequencies. The bar-like stimuli increased sensitivity for temporal frequencies around 3-6 Hz, revealing involvement of an intermediate temporal frequency-selective filter in detection, the so-called transient-1 filter. A probability summation model for the method of adjustment was developed that assumes that detection depends on the properties of the temporal filters underlying the temporal frequency-sensitivity curve. The model supports the notion that at least two temporal frequency-selective filters are necessary to account for the shape of the sensitivity curves obtained for blue bar-like stimuli.