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Adaptation to sine-wave gratings selectively reduces the sensory gain of the adapted stimuli
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Adaptation to sine-wave gratings selectively reduces the sensory gain of the adapted stimuli

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Content ADAPTATION TO SINE-WAVE GRATINGS SELECTIVELY REDUCES THE SENSORY GAIN OF THE ADAPTED STIMULI by Debbie Yen Dao A Thesis Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree MASTER OF ARTS (PSYCHOLOGY) May 2004 Copyright 2004 Debbie Yen Dao R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. UMI Number: 1421767 INFORMATION TO USERS The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleed-through, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. UMI UMI Microform 1421767 Copyright 2004 by ProQuest Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. UNIVERSITY OF SOUTHERN CALIFORNIA THE GRADUATE SCHOOL UNIVERSITY PARK LOS ANGELES, CALIFORNIA 90089-1695 This thesis, written by nphhip YeiLJlaQ - under the direction of h S T thesis committee, and approved by all its members, has been presented to and accepted by the Director of Graduate and Professional Programs, in partial fulfillment of the requirements for the degree of Master of Arts Director Date Thesis Committee ■ ' Chair R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 1 1 Table of Contents List of Tables iv List of Figures v Abstract vi INTRODUCTION 1 Review of adaptation effects at the observer level 1 Review of adaptation effeets at the neural level 4 Rationale for current study 8 METHOD 10 Apparatus 10 Stimulus and Display 11 Experiment I (Pilot study); Staircase Proeedure 12 Experiment 2; Measuring Psychometrie Functions 15 Control Experiments 16 Observer 16 RESULTS 17 Experiment 1 (Pilot Study): Staircase Procedure 17 Experiment 2: Psychometric Functions 21 Relationship between the adapted and the control conditions 22 Threshold-versus-contrast (TVC) curves derived from the psychometric 27 Functions MODEL 33 The egePTM 33 The cgcPTM and Threshold Predictions 38 The cgcPTM and the PTM 39 Data Modeling 40 Modeling Implications 47 The cgcPTM and post-adaptation effects 52 The PTM and post-adaptation effects 54 DISCUSSION 54 Summary 54 Contrast gain control 56 Relation to neural literature 57 Conclusion 58 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. m REFERENCES 59 APPENDIX: The cgcPTM and the PTM 63 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. IV List of Tables Table 1: Staircase threshold contrast values for all observers (Pilot Study) 18 Table 2: Contrast threshold values from pilot study averaged across 19 observers Table 3: Models used to fit to psychometric functions 28 Table 4: Comparison of 2aipim ax model to other models for observer J.S. 29 Table 5: Comparison of 2alplm ax model to other models for observer D.D. 30 Table 6; Comparison of 2aipim ax model to other models for observer A.B. 31 Table 7: PTM models used to fit TVC functions to the threshold contrasts 43 Table 8: F statistics and / values for TVC functions fit to contrast 45 thresholds obtained from pilot study Table 9; F statistics and values for TVC functions fit to thresholds 46 obtained from Experiment 2 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. V List of Figures Figure 1; Hypothetieal ehanges in eell response funetions following 7 adaptation Figure 2: Sample trial 14 Figure 3: Threshold vs. contrast funetions from pilot study (averaged across 20 observers) Figure 4: Weibull fits to psychometric functions of observer J.S. 24 Figure 5: Weibull fits to psychometrie funetions of observer D.D. 25 Figure 6; Weibull fits to psychometric funetions of observer A.B. 26 Figure 7: Threshold vs. contrast functions averaged across observers 32 Figure 8: CgcPTM 34 Figure 9: PTM 41 Figure 10: egcPTM fits to psychometric functions of observer J.S. 48 Figure 11: egePTM fits to psychometrie funetions of observer A.B. 49 Figure 12: cgcPTM fits to psychometric functions of observer A.B. 50 Figure 13: Schematic cartoon of adaptation effects 51 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. VI Abstract Prolonged exposure to sine-wave gratings selectively decreases sensitivity to the adapted stimulus at both the perceptual and neural levels. At the observer level, contrast sensitivity is reduced for stimuli of the same orientation and spatial frequency as the adapted stimulus after adaptation. Similarly, at the neural level, VI simple and complex cells show decreased cell activity in response to stimuli of the same orientation and spatial frequency as the adapted stimulus. In order to compare changes at the observer and neural levels, we measured adaptation effects across full psychometric functions at the behavioral level. We developed the contrast gain control Perceptual Template Model (cgcPTM), which describes adaptation effects at both levels. The cgcPTM is mathematically equivalent to the existing Perceptual Template Model (PTM). In either framework, adaptation selectively reduces the gain of the perceptual template at the adapted spatial frequency and orientation without altering internal noise, or changing transducer non-linearity. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Adaptation to Sine-wave Gratings Selectively Reduces the Sensory Gain of the Adapted Stimuli 1. Introduction At the observer level, Blakemore and Campbell established in their 1969 study that prolonged exposure to sine-wave gratings results in decreased contrast sensitivity specifically for stimuli of the same orientation and spatial frequency as the adapted stimulus (C Blakemore & Campbell, 1969b). Since their early findings, they and others have suggested that the specificity of adaptation effects is evidence for the existence of neural channels tuned to specific spatial frequencies and orientations in visual cortex. Adaptation procedures have been useful in probing these channels to understand their characteristics. There has been progress in characterizing adaptation effects including their spatial frequency and orientation bandwidths, time course, and selectivity. In addition to studies describing adaptation effects at the observer level, there have been significant developments in studies that illuminate adaptation effects at the cellular level. While observer and neural adaptation effects appear to be in agreement, a clear relationship between these two levels of analysis has not yet emerged. 2. Review of adaptation effects at the observer level What follows is a brief review of what is known about grating adaptation. Adaptation effects of reduced contrast sensitivity are observed in both central and peripheral vision (Greenlee, Georgeson, Magnussen, & Harris, 1991; Sharpe & Tolhurst, R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 1973; Williams, Wilson, & Cowan, 1982). Reduced contrast sensitivity is observed following adaptation to low (Tolhurst & Barfield, 1978) and high (C Blakemore & Campbell, 1969a) contrast adaptation gratings. Maximum contrast sensitivity reduction is found when observers adapt to a high contrast grating (Foley & Boynton, 1993; Georgeson & Harris, 1984) after which contrast thresholds may be elevated by up to five times the contrast threshold obtained without adaptation (C Blakemore & Campbell, 1969a, 1969b). While adaptation effects are specific to the adapting stimulus in orientation and in spatial frequency, they are independent of grating phase (Foley & Boynton, 1993; Jones & Tulunay-Keesey, 1980). Desensitization due to adaptation occurs quickly, requiring only a short exposure to the adapting stimulus to elicit an increase in contrast threshold (C Blakemore & Campbell, 1969a; Foley & Boynton, 1993); Foley and Boynton have reported that contrast threshold as a function of the adaptation time period increases most rapidly within 67 msec and that subsequent increases in adaptation stimulus duration does not produce much larger contrast threshold increases. Despite the quick rise in contrast threshold in the first few milliseconds of adaptation, Magnussen and Greenlee (Magnussen & Greenlee, 1985) have reported that thresholds continue to rise for up to 30-60 min of adaptation before saturating. Following exposure to the adaptation simulus, contrast threshold elevations are apparent within 50 msec (Foley & Boynton, 1993) to 300 msec (Greenlee et al, 1991). Since Blakemore and Campbell’s report, many studies have confirmed that adaptation effects are indeed stimulus-specific with respect to orientation and spatial R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. frequency (Colin Blakemore, Muncey, & Ridley, 1973; Greenlee & Thomas, 1992; Menees, 1998; C. F. Stromeyer, Klein, Dawson, & Spillmann, 1982). The orientation and spatial frequency specificity of adaptation after-effects may be characterized by describing orientation and spatial frequency bandwidths. Bandwidth refers to the size of the range of spatial frequencies or orientations over which contrast sensitivity is reduced by at least half of maximum contrast sensitivity without any adaptation. Orientation bandwidths of adaptation contrast threshold elevation has been reported to be between 13.5 degrees (C. Blakemore & Nachmias, 1971) and 45 degrees (Greenlee & Magnussen, 1988). This large discrepancy between reports may be due to different methods of measuring contrast thresholds; the former report comes from a study that used the method of adjustment whereas the latter report comes from a study that used a detection paradigm. Contrast threshold elevation is observed for spatial frequencies within one octave of the adapting stimulus (C Blakemore & Campbell, 1969b; Stecher, Sigel, & Lange, 1973a, 1973b). Swift and Smith have reported spatial frequency bandwidth to be between 1/3 and 2/3 octave of the adapting stimulus (Swift & Smith, 1982); Georgeson and Harris have estimated the bandwidth to be approximately 1.4 octaves (Georgeson & Harris, 1984). Beyond a certain octave, however, facilitation (a decrease contrast threshold) is observed (de Valois, 1977; Tolhurst & Barfield, 1978). Tolhurst and Barfield found that beyond 1-2 octaves, contrast sensitivity enhancement occurred; De Valois found that contrast sensitivity enhancement occurred beyond 2.75-3 octaves of the R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. adapting spatial frequency. That there is facilitation between channels suggests that channels are not independent of one another and has been interpreted as evidence for an inhibitory relationship between channels differing in sensitivity to different spatial frequencies (de Valois, 1977). 3. Review of adaptation effects at the neural level At the neural level, following adaptation to a visual pattern or adaptation to prolonged micro stimulation, neurons in visual cortex exhibit hyperpolarization (Carandini & Ferster, 1997; Ohzawa, Sclar, & Freem an,; Sanchez-Vives, Nowak, & McCormick, 2000a, 2000b) and therefore produce fewer action potentials in response to the same visual or stimulation pattern. Multiple studies confirm that contrast adaptation effects are not due to GABAergic inhibition among neurons (DeBruyn & Bonds, 1986; McLean & Palmer, 1996; Vidyasagar, 1990). Instead, Filyason and Cynader have proposed that changes in pre-synaptic mechanisms of transmitter release are the reason for decreased activity or hyperpolarization in post-synaptic neurons in visual cortex (Finlayson & Cynader, 1995). However, more evidence has been provided that suggest otherwise; post-synaptic rather than pre-synaptic changes in VI appear to be the primary cause of decreased neural activity following adaptation (Carandini, 2000; Carandini & Ferster, 1997; Sanches-Vives, Nowak, & McCormick, 2000a, 2000b). This has been most elegantly established by Sanchez-Vives and her colleagues in a pair of studies, one studying cat simple and complex cells in vivo and the other studying simple and complex R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. cells in vitro. Both studies point to activated potassium current as the primary cause of hyperpolarization. A mechanism that involves post-synaptic changes predicts that following contrast adaptation, a higher contrast stimulus would be required to elicit the same level of activity in an adapted cell. In other words an adapted cell requires higher stimulus energy in order to produce the same level of activity that it did prior to adaptation. If this is correct, then in a response function that measures cell activity versus increasing stimulus contrast, the function should shift rightward following adaptation. On the other hand, a mechanism that involves pre-synaptic changes predicts that following contrast adaptation, a neuron whose activity is limited by its inputs would not be able to achieve the same level of activity despite higher stimulus contrasts. The response function would shift downwards and saturate at a lower activity level. Please see Figure 1 for an illustration of these points. Ohzawa and colleagues have demonstrated that following adaptation, there is a rightward lateral shift in the response function measuring cell activity at increasing stimulus contrast (Ohzawa et al.) in cells from cat striate cortex. A similar study of monkey simple and complex cells by Sclar and colleagues (Sclar, Lennie, & DePriest, 1989) also demonstrates a rightward lateral shift in response functions following adaptation. The works of Sanchez-Vives and colleagues and Carandini and Ferster further confirm this phenomenon (Sanchez-Vives et al., 2000a, 2000b). This lateral shift in response functions following adaptation suggests that post-synaptic changes such as R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. those described by the Sanchez-Vives group are responsible for adaptation effects observed at the neural levels; at present, it appears that post-synaptic changes best describe adaptation effects at the neural level. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Figure 1. A. < D u Stimulus Contrast B. < u 0 0 C 0 O h W O O 01 (0 U Stimulus Contrast Figure 1. Predicted change in neural firing rate in response to the adapted stimulus following adaptation. The solid curves represent cell activity as a function of stimulus contrast prior to adaptation; the dashed curves represent cell activity after adaptation. (A.) If adaptation effects were due to pre-synaptic changes, then the response curve would shift downwards. (B.) If adaptation were due to changes in post-synaptic mechanisms, then the cell response function would shift rightwards. R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. 4. Rationale for current study As was mentioned earlier, a clear relationship between neural and observer changes following contrast adaptation is yet to be described. Both pre- and post-synaptic changes (a shift down or a shift rightward in the response function, respectively) predict that at a given test contrast within a range of the response function, there will be a decrease in cellular response after adaptation. They both predict what was first reported by Blakemore and Campbell (C Blakemore & Campbell, 1969b) about changes at the observer level: that at a given contrast value, contrast sensitivity is decreased following adaptation. In order to determine whether pre- or postsynaptic changes might also describe changes at the observer level, it is therefore necessary to measure changes in contrast sensitivity not just at one contrast value but at a full range of test contrasts by measuring full psychometric functions at the observer level. With full psychometric functions measured at both levels, changes in neural and in behavioral response can be compared by observing the changes that occur in cellular response functions and the changes that occur in psychometric functions following adaptation. Stromeyer and colleagues have measured adaptation effects on grating detection using four test contrast values, including a zero-contrast blank condition (C. F. Stromeyer, 3rd, Klein, & Stemheim, 1977). From their data, it appears that after adaptation, there is a lateral shift in the psychometric functions plotting stimulus detectability versus stimulus contrast. However, with only four contrast values, their data R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. do not provide enough information with which to measure full psychometric functions; it is difficult to decipher from their data the contrast at which performance saturates. Therefore, their data do not illustrate exactly how the psychometric function changes after adaptation; direct comparisons between behavioral changes and neural changes cannot be made with certainty. In 1996, Snowden and Hammett measured threshold contrasts for a contrast matching task following adaptation (Snowden & Hammett, 1996). They used a range of standard contrasts but used only one criterion value at which to define threshold contrast of the test stimulus; it is difficult to infer the characteristics of the full psychometric function using their data and to compare responses at the cellular and the observer levels. The present study measures full psychometric functions for detection of a sine- wave grating oriented -1-45 degrees prior to and after adaptation to a sine-wave grating oriented +45 degrees. To distinguish possible mechanisms behind adaptation effects, full psychometric functions were measured in each of six external noise levels. Lu and Dosher (Lu & Dosher, 1999) have demonstrated that by gauging performance at multiple external noise levels, mechanisms including stimulus gain changes and changes in internal noise may be distinguished. Our data were modeled using the Perceptual Template Model (PTM) (Lu & Dosher, 1999), which has already been used to successfully account for phenomena in attention (Dosher & Lu, 2000a, 2000b; Lu & Dosher, 1998, 2000; Lu, Lesmes, & Dosher, 2002), motion perception (Lu, Liu, & Dosher, 2000), and perceptual learning (Dosher & Lu, 1998, 1999). R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 10 We observed a lateral rightward shift in the psychometric functions in all external noise levels following adaptation. We developed a new model, the contrast gain control Perceptual Template Model (cgcPTM), which is mathematically equivalent to the existing PTM, to account for the data and conclude that following adaptation, there is a decrease in the sensory gain of the adapted stimulus. Our findings at the observer level nicely reflect what has already been reported of changes at the neural level; following contrast adaptation, a lateral shift in the response function describes changes at both the neural and the observer levels. This parallelism suggests that a mechanism involving post-synaptic changes at the neural level may be generalized to illustrate changes at the observer level as well. Method 1. Apparatus All stimuli (adapting, signal, and noise frames) were generated and displayed using MATLAB and Psychtoolbox on a Macintosh G-4 computer. The stimuli were presented on a Nanao Technology FlexScan 6600 monitor with a P4 phosphor and a refresh rate of 120 frames/s, driven by the Macintosh videocard. A linear lookup table evenly dividing the monitor’s entire dynamic range into 256 levels was generated using a psychophysical procedure. All displays were viewed binocularly with the natural pupil at a viewing distance of 137.5 cm in a dark room with the computer monitor being the only light source. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 11 2. Stimulus and Display The adapting stimulus was a sinusoidal grating with spatial frequency equal to 4 cpd and tilted positive 45 degrees to the right. It was rendered on a 192 X 192 pixel grid subtending 4.43 X 4.43 deg. The grating was presented in a circular window with a diameter subtending 4.43 degrees of visual angle and was counter-phase flickered at 2 Hz. Counter-phase flickering the adapting stimulus ensured that the visual system was thoroughly adapted independent of phase; furthermore, it eliminated the possibility that afterimages may be responsible for adaptation effects. To achieve a 2 Hz counter-phase flicker, 30 frames were used for each second that the adapting stimulus was presented. Each frame remained on the screen for 4 refreshes. For each frame, n, the luminance l(x, y) at location (x, y) was defined as follows: l(x,y) - lAl.O + c , *sin [2 ;^(-x co s6-ysixi6 + 2t^ / / ) ] * sin (1) 30 Where/ = 4 cycles per degree, 0 = 45 deg, Iq = 27 cd/m , and C p e ak = 0.80. The local contrast, c(x,y) = [l(x,y) - k] / k, was defined as : c(x,y) = c^^^,sm 27f {xco&B- ysinO)*sin (2 * 2 ;r(n -l))' 30 (2) R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 12 The test signals were circularly-windowed sinusoidal gratings tilted +45 degrees (to the right) or -45 degrees (to the left) with luminance l(x,y) at location (x,y) defined by the following equation: l{x, y) = /(,{l .0 + sin[2;^(- xcos - y sin //)]} (3) Where/ = 4 cycles per degree, 0 = +45 deg or -45 deg, k = 27 cd/m^, and C p eak was either determined by a staircase procedure or specified by the experimenter. The local stimulus contrast was defined as: l(x,y) = (o{l.O + Cp^^ sin[iftf( - xcos6>- y sin0)]\ (4) Each test pattern was rendered on a 64 X 64 pixel grid, subtending 1.48 X 1.48 deg. External noise frames were of identical size to signal frames and were made of 2 X 2 pixel patches, each subtending 0.065 deg X 0.065 deg. The gray level of each pixel patch was sampled from a Gaussian distribution of 0 and specified variance contingent upon the desired amount of external noise. The maximum standard deviation of the noise was 33% or less to guarantee that the external noise conformed to the Gaussian distribution. 3. Experiment 1 (Pilot study): Staircase Procedure In a pilot study, we used two staircases to measure adaptation effects. A double­ staircase procedure was used to estimate the contrasts required to achieve two thresholds R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 13 for each of six external noise levels (noise rms contrasts equal to 0, 0.0206, 0.0413, 0.0825, 0.1650, or 0.33). A 3/1 staircase (three correct responses resulted in a 10% decrease in signal contrast; one incorrect response resulted in a 10% increase) and a 2/1 staircase (2 correct responses decreased signal contrast by 10%; 1 incorrect response increased it by 10%) were used to determine the contrasts corresponding to 79.3% accuracy (d’ = 1.634) and 70.7% accuracy id’ = 1.089), respectively. The threshold contrasts values were estimated after one session consisting of two blocks, each with 40 trials per noise level for the 3/1 staircase, and 32 trials per noise level for the 2/1 staircase. A two-interval-forced-choice procedure was used. Each block began with a 2 minute presentation of the adapting stimulus. The initial adaptation period and the first trial were separated by 1 s. Each trial began with 6 s of re-adaptation to the adapting stimulus, followed by 50 ms, then two intervals separated by 500 ms. Each interval began with a brief beep followed by a 50 ms pause, and consisted of three frames, each lasting 33.3 ms. The signal interval was composed of (1) a noise frame; (2) a test stimulus tilted either -f-45 deg or -45 deg; and (3) a noise frame. The interval without the signal was composed of (1) a noise frame; (2) a blank field; and (3) a noise frame. The observer identified the interval containing the signal test patch with a key press. A correct response was immediately followed by two brief beeps. An incorrect response was followed by no beep. The program paused for 1 s before proceeding to the next trial. A typical trial is visualized in Figure 2. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 14 Figure 2. Ills *low beep* 33.3 ins .Vv3 ms 33.3 ms Interval 1 Inter-interval Pause Interval 2 500 ms 50.0 ms *low beep* 33.3 ms 133.3 ms |{33.3 ms Figure 2. A typical trial with a +45 degree target in the first interval. Each trial began with six seconds of re-adaptation to the adapting stimulus (not pictured). R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 15 Each session consisted of randomly interleaved trials in which the target could be oriented either positive or negative 45 degrees; there were an equal number of test gratings of each orientation. The trials were also randomly interleaved with respect to external noise level. Observers knew whether to look for a positive or a negative 45 degree target based on the beep presented with each interval: a low beep signified a positive 45 degree target; a high beep signified a negative 45 degree target. 4. Experiment 2: Measuring Psychometric Functions 4.1 Contrast placement for psychometric functions From the threshold contrasts determined by the staircase procedure, we estimated five contrasts (ci, ca, C 3, C 4, C 5) that would span the full psychometric function for each external noise level. These contrasts were determined in the following way: C 2 was set to equal the threshold contrast determined from the 2/1 (70.7% accurate) staircase; C 4 was set to equal the threshold contrast determined from the 3/1 (79.3% accurate) staircase; ci = 0 .5 * ( c2); C3 = 0 .5 * ( c2 + C4); and C5 = 2 *(C4). 4.2 Measuring Psychometric Functions To measure psychometric functions in each of the six external noise levels, an experimental procedure identical to that of the first experiment was used; however, instead of using staircases, we used the method of constant stimuli to present the test R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 16 contrasts, which were determined in the procedure described above. For this experiment, ten sessions, each consisting of 240 trials were run for each observer. 5. Control Experiments In addition to using the -45 degrees oriented test following adaptation to a +45 degrees oriented grating as a control condition, a control experiment was run in which observers performed the same detection task (detection of a +/- 45 degree oriented grating) described above but without adaptation. Just as in Experiment 2, there were ten sessions, each consisting of 240 trials. The subject ran one session of the control experiment each time before running a session of Experiment 2. From this point on, the condition in which observers performed a detection task of a +45 degree oriented grating following adaptation to a +45 degree oriented grating will be referred to as the adapted condition; all other conditions will be referred to as the control conditions. 6. Observers Two University of Southern California students, naive to the study’s purposes (A.B. and J.S.), and the author (D.D.) served as observers in the experiment. All observers had corrected-to-normal vision. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 17 Results 1. Experiment 1 (Pilot Study): Staircase Procedure Threshold contrasts from the pilot study were averaged across observers and are shown in in Tables 1 & 2 and plotted in Figure 3. The threshold-versus-extemal noise contrast curves were fit using a model that is described later in this paper. It is clear from both staircases, that adaptation to a grating parallel in orientation (-1-45 degrees) to the test grating increases detection threshold contrast relative to the detection threshold contrast of an orthogonal grating (+45 degree adaptation stimulus and -45 degree test signal). At a criterion value of 79.3% correct {d’ = 1.634, 3-up-1-down staircase), in the three lowest noise contrast conditions (0, 0.0206, and 0.0413 rms contrast), the average threshold contrast for the parallel condition was 111.56% greater than the average threshold contrast for the orthogonal condition. At the same criterion value and in the three highest noise contrast conditions (0.0825, 0.1650, and 0.33 rms contrast), the average threshold contrast for the parallel condition was 77.87% greater than that in the orthogonal condition. At a criterion value of 70.7% correct {d’ = 1.089, 2-up-1-down staircase), the average threshold contrast in the low noise conditions was 117.81% greater in the parallel than in the orthogonal condition; the average threshold contrast in the high noise conditions was 60.00% greater. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 18 Table 1 Staircase threshold contrast values for all observers (Pilot Study) External Noise Level 0 0.0206 0.0413 0.0825 0.1650 0.33 AB 45 79.3% 0 .06143 0 . 05427 0.05774 0.05091 0.0 9 1 5 0 0 .25369 70.7% 0.03545 0.04050 0.05539 0.03983 0 .0 8 1 6 0 0.14675 135 79.3% 0.02052 0.03001 0.02575 0.03458 0 .0 7091 0.11630 70.7% 0.01452 0.02048 0.01721 0.0 3 1 5 6 0 .0 5009 0 .09719 DD 45 79.3% 0 .04575 0.03716 0.04331 0.03664 0.08802 0.19798 70.7% 0 .03273 0.03320 0.03879 0.03152 0.05920 0.13098 135 79.3% 0 .01832 0.01543 0 .02569 0.03384 0 .0 5534 0.12222 70.7% 0 .01627 0.01316 0.01445 0.02517 0 .0 3948 0.08979 JS 45 79.3% 0 .04017 0.03661 0.04138 0.05666 0 .1 2741 0 .26381 70.7% 0.02503 0.03359 0 .03088 0.03808 0 .0 9148 0.18731 135 79.3% 0.01982 0.01920 0.02537 0.02803 0 .0 4 9 4 5 0.10317 70.7% 0.02327 0.01199 0.01920 0.02526 0 .0 4426 0.07944 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 19 Table 2 Contrast threshold values from pilot study averaged across observers 0 0.0206 External Noise Contrast 0.0413 0.0825 0.1650 0.33 1.634 Adaptation 0.0491 0.0427 0.0475 0.0481 0.1023 0.2385 Control 0.0196 0.0215 0.0256 0.0321 0.0586 0.1139 % increase 151.2 98.1 85.4 49.5 74.7 109.4 = 1.089 Adaptation 0.0311 0.0358 0.0417 0.0365 0.0774 0.1550 Control 0.0180 0.0152 0.0170 0.0277 0.0446 0.0888 % increase 72.4 135.1 145.9 31.9 73.6 74.5 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 20 Figure 3. 3/1 Staircase (79.3% Criterion) 2/1 Staircase (70.7% Criterion) s 0.320 o ■s 0.100 C 3 a o u 3 .S 0.032 H 0.010 0,001 0.01 0.1 1.0 1.320 1.100 1.032 1.010 0.1 1.0 0,001 0.01 External Noise Contrast (% / 100) Figure 3. Threshold versus contrast functions for data collected from the pilot study and averaged across observers. The data on the left panel are from the 3/1 staircase; those on the right are from the 2/1 staircase. There is an increase in contrast threshold at all noise levels and at both criterion levels following adaptation. Control (no adaptation) conditions are represented by solid lines and diamonds (-♦-), the adapted condition is represented by dashed lines and circles (— o— ). R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. 21 2. Experiment 2: Psychometric Functions Psychometric functions for each of the three observers are presented in Figures 4- 6 . For each observer, six sets of psychometric functions are shown: one set for each of the six external noise levels. We determined that all control conditions yielded equivalent data (statistical procedure described in the following section); the control data are therefore averaged and treated as one. In these figures, the curve on the left represents the control conditions; the curve on the right represents the adapted condition. The curves were fit with Weibull functions, defined in the following way: P - 0.40 + (m ax- 0.50)(l - 2 ''" '“^"^) (5) where P equals the proportion correct, max equals the maximum proportion correct (in this case, 1), c equals the test contrast, a represents the horizontal shift of the function, and P is the slope of the function. A maximum likelihood procedure was used to fit the curves, where the likelihood was defined as a function of the total number of trials W, the number of correct responses, if,-, and the percent correct predicted by Equation 6 : Likelihood = TT -----^ ^ P ^ " " ' (l - P ^ (6) As can be seen in the figures, psychometric functions for the adapted condition shift laterally towards the right with respect to the psychometric functions for the control R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 2 2 conditions, reflecting a decrease in contrast sensitivity following adaptation. A more detailed description of the relationship between the adapted condition and the control conditions follows. 2.1. Relationship between the adapted and the control conditions We found that the three control conditions (detection of a +45 degree grating following adaptation to a +45 degree grating, detection of a +45 degree grating without adaptation, and detection of a -45 degree grating without adaptation) generated equivalent data. In addition, the difference between the control conditions and the adapted conditions was only a change in the horizontal shift of the psychometric functions; the slope remained unchanged. These conclusions were reached after running a chi-square test to compare nine separate models in which different combinations of the parameters a, /?, and max were left to vary among the conditions. In the fullest model (4a4p4max), all parameters (a, p, and max) in equation (5) are free to vary among all four conditions (the total parameters free to vary, k, is equal to 12). In the most reduced model (laip im ax ), no parameters were free to vary among the conditions. All nine models can be reviewed in Table 3, where the number 1 indicates that a parameter for a condition was varied and a 0 indicates that within a model, a parameter was held constant between all conditions that also show a 0 for that parameter. Chi-square (y^) statistics were used to judge whether the full and the reduced models were equivalent: R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Z \ d f ) = 2.0 log ^ max Likelihood ^ m a x L jfe /j/io o d ,„ y 23 (7) where # = For all observers, and in all noise levels, the 2alplm ax model provided the most parsimonious fit where data from the three control conditions are accounted for by one curve and data for the adapted condition are accounted for by another curve—both curves have the same slope, p, and same maximum performance value but different shifts, a. The quality of the fit from this reduced model is statistically equivalent with the fullest model, 4a4p4max (p > 0.10). The comparison between the 2aipim ax model and the other models can be seen in Tables 4-6, which show p-values from the chi-square tests. As can be seen, the reduced model provides a fit of the data that is equivalent to the fuller models. From the statistical analysis, there appears to be an adaptation effect between the control and adapted conditions—in all but two cases, the 2 alp lm ax model is significantly better (p < .005) than the la ip im a x model, which assumes no adaptation effect. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 24 Figure 4. u 0) o U o u C S V - Noise Level 1 /o 0.6 Noise Level 3 Noise Level 5 1 .8 0.6 0.4 1 0.8 0.6 0.4 _o 0.6 0.4 0.32 0.032 0.1 0 0.01 Noise Level 2 - o m 0.6 0.4 Noise Level 4 - o Noise Level 6 0.6 0.4 0.32 0 0.01 0.032 0.1 Signal Contrast Figure 4. Psychometric functions for observer J.S.; fit with WeibuH functions. Control (no adaptation) conditions are represented by solid lines and diamonds (-♦-), the adapted condition is represented by dashed lines and circles (— o— ). R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 25 Figure 5. Noise Level 1 Noise Level 2 0.6 0.4 Noise Level 3 0.8 0.6 0.4 Noise Level 4 tj ( U o U c o 0.6 to 0.4 Noise Level 5 1 0.8 0.6 0.4 Noise Level 6 0.6 0.4 0.32 0.032 0.1 0.6 0.032 0.1 0.32 0.01 Signal Contrast Figure 5. Psychometric functions for observer D.D.; fit with Weibull functions. Control (no adaptation) conditions are represented by solid lines and diamonds (-♦-), the adapted condition is represented by dashed lines and circles (— o— ). R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 26 Figure 6. O S i i- o o c o C S £ Noise Level 1 0.6 0,4 Noise Level 3 Noise Level 5 1 /O .8 0,6 0,4 0,8 0,6 0,4 0,6 0,4 0,01 0.032 0,1 0.32 Noise Level 2 1 .8 0,6 a " o 0,4 Noise Level 4 ,9 Noise Level 6 - O 0,6 0,4 0.32 0.032 0.1 0 0.01 Signal Contrast Figure 6 . Psychometric functions for observer A.B.; fit with Weibull functions. Control (no adaptation) conditions are represented by solid lines and diamonds (-♦-), the adapted condition is represented by dashed lines and circles ( - o — ). R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 27 2.2. Threshold-versus-contrast (TVC) curves derived from the psychometric functions Threshold contrasts at three threshold criterion levels (65%, 75%, and 85% correct) were derived from each of the Weibull-fitted psychometric functions. Threshold contrasts versus external noise contrasts were plotted for each of the three criterion levels and are shown in Figure 7. They were fit using the model which will be described in the next section of this paper. As can be seen, these TVC functions reflect the same trend observed in the pilot study, which employed a two-staircase procedure. There is an increase in threshold contrast in the adapted condition when compared to the control conditions. Again, there is a higher threshold increase at lower noise levels than at higher noise levels. At the three lowest noise levels, there were average increases of 98.02%, 98.47%, and 98.87% in threshold contrast in the 65%, 75%, and 85% criterion levels, respectively. At the three highest noise levels, there were average increases of 81.69%, 82.26%, and 82.64% in threshold contrast in the 65%, 75%, and 85% criterion levels, respectively. This consistency across criterion levels gave us the first hint that changes following adaptation are likely not non-linearity changes (Lu & Dosher, 1998). R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 28 Table 3 Models used to fit to psychometric functions Model Adapt + 45 Adapt +135 No Adapt + No Adapt + k deg target deg target 45 deg target 135 deg target Condition a P max a p Max A p max a p max 4a4p4max 1 1 1 1 1 1 1 1 1 1 1 1 12 4alp2m ax 1 0 1 1 0 0 1 0 0 1 0 0 7 2a4p2max 1 1 1 0 1 0 0 1 0 0 1 0 8 2 a 2 p2 max 1 1 1 0 0 0 0 0 0 0 0 0 6 2 aip im ax 1 0 0 0 0 0 0 0 0 0 0 0 4 2 a ip 2 max 1 0 1 0 0 0 0 0 0 0 0 0 5 3aipim axA 1 0 0 0 0 0 1 0 0 0 0 0 5 3aipim axB 1 0 0 0 0 0 0 0 0 1 0 0 5 laip im ax 0 0 0 0 0 0 0 0 0 0 0 0 3 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 29 Table 4 Comparison of 2aipim ax model to other models for observer J.S. Model Noise Level 4a4p4- max 4alp2- max 2a4p2- max 2 a 2 p2 - max 2 a lp 2 - max 3 a lp l- maxA 3 a ip i- maxB l a i p i ­ max 1 0.1207 0.0104* 0.1094 0.5852 0.4310 0.0017* 0.0154* 0 .0 0 0 2 * 2 0.9699 0.5247 0.8772 0.5603 0.3136 0.6469 0.5334 0 .0 0 2 0 * 3 1 .0 0 0 0 0 .0 0 1 2 * 1 .0 0 0 0 0.0876 0.0479* 0.0005* 0.1986 0 .0 0 0 0 * 4 0.9780 0.9338 0.9228 0.9331 0.7732 0.5683 0.6889 0 .0 0 0 0 * 5 1 .0 0 0 0 0.2660 0.1701 0.0465* 0.2643 0.2178 0.1197 0 .0 0 0 0 * 6 0.6217 0.8969 1 .0 0 0 0 0.6142 0.6193 0.5905 0.8102 0 .0 0 0 0 * p < .05 R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. 30 Table 5 Comparison of 2aipim ax model to other models for observer P .P . Model 4a4p4- 4alp2- 2a4p2- 2 a 2 p2 - 2 a lp 2 - 3 a lp l- 3 a lp l- laip im ax Noise max max max max max maxA maxB Level l.Oe-004 X 1 1 .0 0 0 0 0.7858 0.8735 0.7598 0.4587 0.6836 0.7548 0.0005* 2 0.3189 0.0195* 0.6687 0.8116 0.5835 0.5213 0.0610 0.1309* 3 0.9997 0.8392 0.7431 0.4738 0.4786 0.6073 0.6148 0 .0 0 0 0 * 4 0.3840 0.0804 0.1095 0.7905 0.8229 0.4445 0 .0 1 2 0 * 0 .0 0 0 0 * 5 1 .0 0 0 0 1 .0 0 0 0 1 .0 0 0 0 1 .0 0 0 0 1 .0 0 0 0 0.5068 0.0646 0 .0 0 0 1 * 6 1 .0 0 0 0 0.1278 0.0842 0.0206* 0.0673 0.1528 0.2463 0.0074* * p < .05 R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. 31 Table 6 Comparison of 2aipim ax model to other models for observer A.B. Model 4a4p4- 4aip2- 2a4p2- 2 a 2 p2 - 2 a ip 2 - 3 a ip i- 3 a lp l- laip im ax Noise max max max max max maxA maxB Level 1.0e-008x 1 0.0777 0.0054* 0.0578 0.0618 0.3162 0.0152* 1 .0 0 0 0 0.0031* 2 0.6416 0.2258 0.3952 0.8429 0.6559 0.7529 0.1510 0 .0 0 0 0 * 3 0.0985 0.0042* 0.0967 0 .1 0 2 2 0.0866 0.8473 0.0078* 0.2050* 4 0.8267 0.3248 0.2535 0.8426 1 .0 0 0 0 0.1368 0.0727 0 .0 0 0 0 * 5 1 .0 0 0 0 1 .0 0 0 0 1 .0 0 0 0 1 .0 0 0 0 1 .0 0 0 0 0.1991 0.1305 0 .0 0 0 0 * 6 0.2859 0.4215 0.8537 0.1535 0.1821 0.4965 0.8728 0 .0 0 0 0 * * p < .05 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 32 Figure 7. o -C J S 0.320 0.100 0.032 0.010 65% Criterion 0.320 0.100 o o O- © 0.032 0.010 c o 85% Criterion 75% Criterion a e Averaged across 0,001 0.01 0.1 1.0 criterion levels O . ------ ® 1.0 0,001 0.01 0.1 External Noise Contrast (% / 100) Figure 7. Threshold versus contrast functions at three threshold criterion levels, averaged across observers. The fourth panel represents the threshold contrasts averaged across criterion levels. Control (no adaptation) conditions are represented by solid lines and diamonds (-♦-), the adapted condition is represented by dashed lines and circles (— o— ). R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 33 Model 1. The cgcPTM We developed a model, the contrast gain control Perceptual Template Model (cgcPTM), which is mathematically equivalent to the existing Perceptual Template Model (Lu & Dosher, 1998), to model the data. The cgcPTM consists of six elements; (1) a perceptual template, (2) a non-linear transducer function, (3) pre gain control internal noise, (4) contrast gain control, (5) post gain control internal noise, and (6 ) a decision process. A schematic diagram of the model is provided in Figure 8 . 1.1. The Perceptual Template The perceptual template passes stimulus inputs of specific spatial frequency and orientation through a processor with different gains. Prior to adaptation, we assume that the total gain across feature space and time equals 1 .0 and that the gain for a signal­ valued stimulus is equal to p. For a signal stimulus of contrast c, the perceptual template output has an amplitude 5: 5 = /3c (8 ) R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. 34 Figure 8. OBSERVER post-cgc noise pre-cgc noise ( Signal ) decision non-linearity perceptual template ( Noise } dx dt contrast gain control Figure 8 . The cgcPTM (contrast gain control Perceptual Template Model). R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 35 In addition to the signal is external noise (white Gaussian noise added by the experimenter) with equal energy across all spatial frequencies. Because the total gain is equal to 1.0 , the perceptual template’s output for external noise has a standard deviation, (T e x t, equal to the standard deviation, Next, of the external noise: (9) 1.2. Non-linear Transducer Function Next in the model, is a non-linear transducer function, || • |P, through which the signal and external noise are processed such that S'= ( 10) and a '=N ^ (11) n v - » ^ * n vf ext ext 1.3. Pre Gain Control Internal Noise Pre gain control internal noise (which is equivalent to additive internal noise in the PTM) follows after the stimuli have been processed by the perceptual template and R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 36 the non-linear transducer function. Pre gain control internal noise is modeled with a Gaussian distribution of mean equal to 0 and standard deviation, c T a d d = A /a d d - At this point, the total noise in the system, a, is characterized by both the external noise and the additive internal noise such that the noise variance is equal to; (12) and the total energy of the signal and noise is equal to: 1.4. Contrast Gain Control A contrast gain control process modifies the stimulus gain such that signal strength is divided by the total stimulus energy (equation 13). ip’c’ ) (Wa) Similarly, the noise variance is divided by stimulus energy: R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 37 g l /2 1.5. Post Gain Control (Multiplicative) Internal Noise A second internal noise source follows after contrast gain control has been implemented and is modeled as post gain control internal noise (multiplicative internal noise in the PTM) whose variance is defined as: a ,^= N (15) m ul mul Now the noise variance is equal to the sum of the variances of all the noises: C T n o i.f' 1.6. Decision Process All of the elements mentioned above—/?, c, y, C ext, ^add, and < T m u i— characterize the signal representation in the system, which is in turn subject to a decision process. In the case of this experiment, the decision process is a detection process wherein the output R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 38 must be either positive or negative. The cgcPTM is not limited to detection tasks alone; therefore, the decision process will not be elaborated here. 2. The cgcPTM and Threshold Predictions The cgcPTM provides clear predictions of contrast thresholds given c, y, (T e x t, (T a d d , and fT m u i. Defining signal discriminability, d ’, as the ratio of the signal amplitude to the total noise standard deviation, d’ can be determined by equations (14) and (16): r^l}2 j ^ N + N ^ ext ^ add 1 7 1 /2 + iV 1/2 (17) SimpUfying equation (17) leaves the following: d'= fj 4-N ^ + N + N + N ^ ext ^ add ^ mul \ P ^ ^ ext ^ add )f” n J ' + N „ ‘' +N^, 1/2 (18) The threshold contrast, c^, is defined as the signal contrast needed to achieve a d ’ criterion level. By rearranging equation (15), C x is equal to: R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 39 1 n J ^ + n mul d _1 _ 2r (19) 3. The cgcPTM and the PTM The cgcPTM deviates from the original PTM in several respects. The PTM has five elements: (1) a perceptual template, (2) a non-linear transducer function, (3) multiplicative internal noise, (4) additive internal noise, and (5) a decision process. There is no contrast gain control; the multiplicative noise is dependent on the signal amplitude and the external noise variance; additive noise comes after the multiplicative noise and before the decision process. A schematic diagram of the PTM is provided in Figure 9. A full description of the PTM is provided by Lu and Dosher (Lu & Dosher, 1998). The PTM predicts d ’ to be d'-. 1/2 (20) and Crto be R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 1 ^ , 2 mul 40 i/2r (21) We prove that the cgcPTM is mathematically equivalent to the original PTM (see Appendix A). We used this format of the PTM to find the best fitting model for the data and to fit threshold versus contrast (TVC) functions to the data. 4. Data Modeling The TVC functions from the staircase experiment and from the experiment measuring psychometric functions were modeled using the PTM equation (26) from the previous section. To fit TVC curves to the data, a gradient-descent method was used to minimize the sum of the squared differences (sqdiff = [log(crtheory) - log(Cr)]^) between the actual threshold contrast measured and the threshold contrast predicted by the PTM. According to the PTM, a number of parameters may change as a result of adaptation. For example, adaptation may alter the non-linearity transducer function, alter internal noise, or alter the gain of the perceptual template. In order to determine which factors were altered following adaptation, we sought to find the most parsimonious model that accounted for the data. So we modeled the data with different combinations of parameters (Wxt, Wdd, -V m u i, P, y) left free to vary between the control and the adapted conditions. Seven models were tested. In the fullest model (Model 1), all parameters were free to vary between the two conditions; the total number of parameters varied R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 41 Figure 9. OBSERVER Nm Na ( Signal ) decision non-linearity perceptual template ( Noise 3 Figure 9. The PTM (Perceptual Template Model). R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 42 among the two groups is equal to ^ = 10. In Model 2, only the internal noises, N^ui and A ^ a d d were free to vary (k = 7). In Model 3, and 7/ext were free to vary between the two conditions (k = 7). In Model 4, only y was free to vary (k = 6). In Model 5, y S was free to vary (k = 6). In Model 6 ,7/ext was free to vary (k = 6). And in the most reduced model, Model 7, no parameters were free to vary between the two groups; therefore, the total number of parameters varied among the two groups was equal to k = 5. Table 7 gives a summary of each model. As in Table 3, in Table 7, the number 1 indicates that a parameter for a condition was varied and a 0 indicates that within a model, a parameter was held constant between all conditions that also show a 0 for that parameter. The goodness of fit for each model was determined by: r ' = 1 . 0 - Y , sqdiff X ) - mean[log{c^ ) F (22) An F statistic was used to compare the reduced models to the fullest model: j r f 1 2 V ('2 3 ') T n l \ 4/2 ^ rpHurpH '* ' 1 — fu ll where df\ = kfuii - ^reduced and df2 = N - km; N is the number of predicted data points. Tables 8-9 display the F-statistics comparing each model to the fullest model. Model 1. Goodness-of-fit (r^) values are also provided in this table. The two most R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 43 Table 7 PTM models used to fit TVC functions to the contrast thresholds Model m l m2 a l a2 g l ^2 bl b2 el e2 k 1 1 0 1 0 1 0 1 0 1 0 10 2 1 0 1 0 0 0 0 0 0 0 7 3 0 0 0 0 0 0 1 0 1 0 7 4 0 0 0 0 1 0 0 0 0 0 6 5 0 0 0 0 0 0 1 0 0 0 6 6 0 0 0 0 0 0 0 0 1 0 6 7 0 0 0 0 0 0 0 0 0 0 5 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 4 4 reduced models, Model 3 and Model 5 are both equivalent to the fullest model. We chose to fit the data with Model 3 and not Model 5 so as not to ignore possible gain effects in the noise around the stimulus. Model 3, in which A ^ e x t and P are modified in the adapted condition, suggests a decrease in gain after adaptation. 4.1. Model fits for the staircase data Figure 3 shows TVC functions representing threshold contrasts averaged across subjects for both staircases (3-up-l-down, d ’ ~ 1.063; and 2-up-1-down, <i’= 1.089). The bottom curve represents threshold contrasts in the control condition in which observers adapted to a +45 degree oriented grating and detected a -45 degree test. The top curve represents the threshold contrasts in the adapted condition. The data were fit with Model 3. V m ui is equal to 0.5105, Vaddis equal to 0.0003, P is equal to 4.6454, and y is equal to 3.0000 in both the adapted condition and the control condition. In the adapted condition, P is multiplied by a constant, m = 0.4679; and v V e x t is multiplied by H 2 = 0.8133 = 0.95), that is stimulus gain 0?) is reduced by about half and gain on noise is reduced by about twenty percent. 4.2. Model fits for data from psychometric functions For the data from experiment 2, similar parameter values were obtained when using the cgcPTM to fit TVC functions to threshold contrasts derived from the fitted Weibull functions at the 65%, 75%, and 85% criterion levels. In the reduced, cgcPTM, V m ui is equal to 0.3276, V add is equal to 0.0006, p is equal to 4.6411, and y is equal to R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 45 Table 8 study. Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Model 7 Model 1 -- F{3, 26)= F(3, 26) = F(4, 26) = F{4, 26) = F(4, 26) = F(5, 26) = 8.6027* -0.0968 8.0210* 0.2718 15.5435* 12.4343* Model 2 -- - - F(l,29) = F(l,29) = F(l,29) = F(2,29) = 2.6801 -10.5571 15.5299* 7.7645* Model 3 - - - F(l,29) = F(l,29) = F{1,29) = F(2,29) = 40.1443* 1.7080 77.4558* 38.7265* Model 4 - -- - - - - F(l,30) = 11.7519* Models - - - - - - F(l,30) = 72.8782* Model 6 -- - - ~ - - F(l,30) = -0.0006 Model 7 - - - - - - - r 0.9532 0.8668 0.9541 0.8458 0.9495 0.7451 0.7451 * p < 0.005 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 46 Table 9 2 F statistics and r values for TVC functions fit to thresholds obtained from Experiment 2. Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Model 7 Model 1 F(3, 26)= 28.58* F(3, 26) = 0.0346 F(4, 26) = 36.83* F(4, 26) = 0.026 F(4, 26) = 63.84* F(5, 26) = 51.07* Model 2 F(l,29) 15.98* F(l,29) = -22.23 F(l,29) = 44.02* F(2,29) = 22.01* Model 3 F(l,29) 163.56* F(1,29) = 0 F(l,29) = 283.56* F(2,29) = 141.68* Model 4 — — — — — F(l,30) = 18.69* Model 5 — — — — — — F(l,30) = 293.34* Model 6 — — — — — “ F(l,30) = 0 Model 7 -- -- - - - - - 0.9737 0.8869 0.9736 0.8246 0.9736 0.7153 0.7153 * p < 0.001 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 47 3.0000 in both the adapted condition and the control conditions. In the adapted condition, however, fi is multiplied by a constant, pn = 0.5185; and T V e x t is multiplied by pij - 0.9248. ( = 0.97). As with the staircase data, the stimulus gain is reduced by about fifty percent. The gain on external noise is reduced by about ten percent. 4.3. The cgcPTM used to fit psychometric functions The cgcPTM / PTM can also be used to fit full psychometric functions using equation 20 to predict d ’ values and from there, to predict percent correct using the relation for normal distributions: d '- z{percentcorrect) - z(l - percentcorrect) (24) Psychometric functions were fit directly with the reduced model using a gradient decent method. Psychometric functions fit with the cgcPTM are shown in Figures 10-12. 5. Modeling implications As was stated earlier, the best fitting model was Model 3 in which the parameters free to vary were the stimulus gain, fi, and essentially the gain on external noise, Aext. This suggests that following adaptation, gain is reduced at and around the adapted stimulus orientation and spatial frequency. This change can be visualized in the cartoon in Figure 13. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 48 Figure 10. Observer J.S. Noise Level 1 N oise Level 3 1 0.8 0.6 0.4 0 0.01 0.032 0.1 Noise Level 2 1 0.8 0.6 0.4 1 m 0.8 0.6 0.4 Noise Level 4 o O J o U c o 0.8 0.6 0.4 Noise Level 5 1 0.8 0.6 0.4 Noise Level 6 1 0.8 0.6 0.4 O 0.32 0 0.01 0.032 0.1 Signal Contrast 0.32 Figure 10. Psychometric functions for observer J.S.; fit with the cgcPTM. Control (no adaptation) conditions are represented by solid lines and diamonds (- ♦ -), the adapted condition is represented by dashed lines and circles (— o— ). R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. 4 9 Figure 11. Observer D.D. o u fc o U c o c < j s- tu T M oise Level 1 Noise Level 2 0.8 0.6 0.4 Noise Level 3 1 0.8 0.6 0.4 Noise Level 4 1 0.8 0.6 0.4 Noise Level 5 1 0.8 0.6 0.4 Noise Level 6 0.8 0.6 0.4 0.32 0 0.01 0.032 0.1 0.8 0.6 0.4 0.32 0.032 0.1 0 0.01 Signal Contrast Figure 11. Psychometric functions for observer D.D.; fit with the cgcPTM. Control (no adaptation) conditions are represented by solid lines and diamonds (-♦-), the adapted condition is represented by dashed lines and circles (— o— ). R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 50 Figure 12. Observer A.B. o < u fa o U a .2 o S i tin Noise Level 1 0.6 0.4 Noise Level 3 1 0.8 0.6 0.4 Noise Level 5 1 0.8 0.6 0.4 0.032 0.1 0.32 0 0.01 1 0.8 0.6 0.4 Noise Level 2 1 0.8 0.6 0.4 Noise Level 4 1 0.8 0.6 0.4 Noise Level 6 0 0.01 0.032 0.1 Signal Contrast 0.32 Figure 12. Psychometric functions for observer A.B.; fit with the cgcPTM. Control (no adaptation) conditions are represented by solid lines and diamonds (- ♦ -), the adapted condition is represented by dashed lines and circles (— o— ). R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 51 Figure 13. Pre-Adaptation — Signal J ■ Perceptual Template Noise Post A daptation I Figure 13. A cartoon of the cgcPTM. In this cartoon, the signal and template are in fourier space and the noise is in image space for ease of visualization. A full description of the cartoon is given in the text. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 52 Prior to adaptation, a signal at a particular orientation and spatial frequency that passes through a perceptual template tuned to that orientation and spatial frequency comes out unchanged. White noise going through the same template is effectively filtered for the tuned orientation and spatial frequency. After adaptation, the perceptual template changes such that its height is effectively reduced by 50% at the tuned orientation and the overall area is decreased by about 10%. Gain on stimulus and noise is effectively reduced around the adapted orientation and spatial frequency. 6. The cgcPTM and post-adaptation effects Characterizing adaptation effects using the cgcPTM shows that there are specific changes in model parameters following adaptation. After adaptation, gain on signal is modified such that the signal amplitude is equal to: S"={k,-PYd (25) where k\ is a constant. The gain on external noise is also modified by a constant, k2 so that the noise variance is equal to: R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 53 The stimulus energy following adaptation is equal to: (27) {k-i is a constant). These are the only modifications in model parameters following adaptation. Divisive contrast gain control follows with these new stimulus and noise values and post­ gain control internal noise is added as it was before. As a result, following adaptation, d ’ in terms of original signal and noise parameters is equal to: (K-ffYc’ pl/2 r.1 /2 172 + A d'= [K 'P Y c^ ik2-N„,f - k N j + N j ( E ' P d'= 1/2 (28) A gain change, not a change non-linearity or internal noise, follows from the physiology data. The physiology data, as discussed in the introduction to this paper. R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. 54 generally show a rightward shift with no change in non-linearity in activity versus stimulus contrast functions. An increase or decrease in internal noise should cause the activity versus contrast functions to shift either up or down at all stimulus contrasts; however, this is the case in neither our data nor the physiology data. Another possible change following adaptation is a change in the decision structure; our design of a two- interval-forced-choice task rules out the likelihood of a change in decision structure. 7. The PTM and post-adaptation effects In terms of the PTM, which has been stated to be mathematically equivalent to the cgcPTM, after adaptation, the PTM predicts the following: (1) is modified by a constant [i\, and (2) Aext is modified by a constant H2. Both and//a are constants less than 1.0. After adaptation, then, c^is equal to: c ’ A /? 2 _________________________ add 1 fs [ ^ ^,2 mul (29) Discussion 1. Summary Full psychometric functions were measured for a detection task in four conditions. In the adapted condition, observers adapted to and detected a grating oriented +45 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 55 degrees. In the first control condition, observers adapted to a grating oriented +45 degrees and detected a grating oriented -45 degrees. The remaining two control conditions involved detection of a grating oriented either positive or negative 45 degrees without adaptation. Data for each condition were collected in six external noise levels; five different test contrasts were used to measure each psychometric function. As expected, following adaptation to a grating of a specific orientation and spatial frequency, observers’ detection threshold contrasts were increased for stimuli of the same orientation and spatial frequency. An increase in threshold was not observed in any of the three control conditions; in fact, all of the control conditions generated equivalent data. In agreement with those who have measured adaptation effects at more than one test contrast (Snowden & Hammett, 1996; C. F. Stromeyer, 3rd et al., 1977), following adaptation in the adapted condition, there was a rightward shift in the psychometric functions. Our analysis of the data suggests adaptation effects do not reflect a change in non- linearity. This is substantiated by the fact that threshold increases were consistent across criterion levels and by the model (cgcPTM) that best fit the data. Meese and Holmes (Meese & Holmes, 2002) and Foley (Foley, 1994) have also presented models in which non-linearity is non-adaptable. Instead of non-linearity change, the cgcPTM demonstrates that adaptation effects are the result of diminished gain at the adapted stimulus. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 56 2. Contrast Gain Control Contrast gain control has been cited as the underlying mechanism for adaptation at both the neural and the psychophysical levels. Greenlee and colleagues have suggested that contrast gain control may be the visual system’s way to self-calibrate (Greenlee et al., 1991; Greenlee & Heitger, 1988): following prolonged exposure to a stimulus of specific characteristics, the gain on the adapted channel is reduced so that the average activity across channels across time is equal. Decreasing response to a constant and redundant stimulus may allow the system to remain sensitive to stimuli differing in orientation and spatial frequency; this may be a way to optimize information transfer (Wainwright, 1999). Several gain control models have been proposed to account for changes at the behavioral level (Foley, 1994; Georgeson & Harris, 1984; Meese & Holmes, 2002; Wilson & Humanski, 1993). Wilson and Humanski (Wilson & Humanski, 1993) developed a divisive gain control model in which a stimulus passes through (1) oriented receptive fields, (2) response non-linearity, and (3) gain control units. Each gain control unit receives a weighted sum of output responses from multiple channels, and then it provides an inhibitory signal that divides the stimulus to its output unit. Adapted channels are hypothesized to have strengthened connections between the summation process and the gain control unit, thereby receiving increased inhibitory feedback from their gain control units and displaying decreased activity. The cgcPTM is consistent with Wilson and Humanski’s model. Though our data do not allow us to judge conclusively whether contrast gain control is a feedback or a feed-forward process, we have presented R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. 57 the cgcPTM as having a feed-forward mechanism when it can be conceptualized as having either. At the neural level, there is evidence from rat (Finlayson & Cynader, 1995), cat (Carandini & Ferster, 1997; Ohzawa et a l.,; Sanches-Vives et al., 2000a; Sanchez-Vives et al., 2000a), and monkey (Sclar et al., 1989)visual cortex that cell response to the adapted stimulus decreases following adaptation. Ohzawa and colleagues (Ohzawa et al.) found that cell response depends on the test stimulus contrast and its relation to the adapted stimulus contrast; they observed that cortical neurons seem to code contrast changes based on relative contrast rather than absolute contrast. The lateral shift in cell response verses test contrast appears to be evidence for the type of contrast gain control described by Ohzawa and colleagues and has been observed in the cited neural literature. Our data at the behavioral level also exhibit this lateral shift and suggest contrast gain control; at the same time, our model provides insight as to how gain control is achieved. 3. Relation to neural literature The common lateral shift in psychometric functions at both the behavioral and the cellular levels suggests that adaptation phenomena at both levels can be described by a common model. Data at both levels implicate contrast gain control. At the neural level, the work of Sanchez-Vives and colleagues (Sanchez-Vives et al., 2000a, 2000b) strongly suggests that post-synaptic hyperpolarization is responsible for decreased cellular activity following adaptation—not changes in pre-synaptic processes. Because there are parallel R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 5 8 changes in activity at the neural and behavioral levels, it is possible that the effects of post-synaptic changes might be generalized to describe changes at the behavioral level. It is also possible that changes at the neural level can be characterized by the cgcPTM just as behavioral changes can be. 4. Conclusion We have developed a model, the contrast gain control Perceptual Template Model, that can account for adaptation effects at the behavioral level. Decreased contrast sensitivity appears to be the result of a decrease in gain to the adapted stimulus at and around the adapted orientation. Testing at a full range of contrast values, we find similar changes in response at the observer level as has been reported at the cellular level. The cgcPTM provides a framework with which to understand adaptation effects at both levels. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 59 References Blakemore, C., & Campbell, F. W. (1969a). Adaptation to spatial stimuli. The Journal of Physiology, 200, 11P-13P. Blakemore, C., & Campbell, F. W. (1969b). On the existence of neurones in the human visual system selectively sensitive to the orientation and size of retinal images. The Journal o f Physiology, 203, 237-260. Blakemore, C., Muncey, J. P., & Ridley, R. M. (1973). Stimulus specificity in the human visual system. Vision Research, 13, 1915-1931. Blakemore, C., & Nachmias, J. (1971). The orientation specificity of two visual after­ effects. Journal o f Physiology, 213, 157-174. Carandini, M. (2000). Visual cortex: Fatigue and adaptation. Current Biology, 10, R605- R607. Carandini, M., & Ferster, D. (1997). A tonic hyperpolarization underlying contrast adaptation in cat visual cortex. Science, 276, 949-952. de Valois, K. K. (1977). Spatial frequency adaptation can enhance contrast sensitivity. Vision Research, 17, 1057-1065. DeBruyn, E. G., & Bonds, A. B. (1986). Contrast adaptation in cat visual cortex is not mediated by GAB A. Brain Research, 383, 339-342. Dosher, B. A., & Lu, Z.-L. (1998). Perceptual learning reflects external noise filtering and internal noise reduction through channel re weighting. Proc. Natl. Acad. Sci. USA, 95, 13988-13993. Dosher, B. A., & Lu, Z.-L. (1999). Mechanisms of perceptual learning. Vision Research, 39, 3197-3221. Dosher, B. A., & Lu, Z.-L. (2000a). Mechanisms of perceptual attention in precuing of location. Vision Research, 40, 1269-1292. Dosher, B. A., & Lu, Z.-L. (2000b). Noise exclusion in spatial attention. Psychological Science, 11, 139-146. Finlayson, P. G., & Cynader, M. S. (1995). Synaptic depression in visual cortex tissue slices: an invitro model for cortical neuron adaptation. Experimental Brain Research, 106, 145-155. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 6 0 Foley, J. M. (1994). Human luminance pattern vision mechanisms: masking experiments require a new model. Journal o f the Optical Society o f America A, 11, 1710-1719. Foley, J. M., & Boynton, G. M. (1993). Forward pattern masking and adaptation: Effects of duration, interstimulus interval, contrast, and spatial and temporal frequency. Vision Research, 33, 959-980. Georgeson, M. A., & Harris, M. G. (1984). Spatial selectivity of contrast adaptation: Models and data. Vision Research, 24, 729-741. Greenlee, M. W., Georgeson, M. A., Magnussen, S., & Harris, J. P. (1991). The time course of adaptation to spatial contrast. Vision Research, 31, 223-236. Greenlee, M. W., & Heitger, F. (1988). The functional role of contrast adaptation. Vision Research, 28,191-191. Greenlee, M. W., & Magnussen, S. (1988). Interactions among spatial frequency and orientation channels adapted concurrently. Vision Research, 28, 1303-1310. Greenlee, M. W., & Thomas, J. P. (1992). Effect of pattern adaptation on spatial frequency discrimination. Journal o f the Optical Society o f America A: Optics & Image Science, 9, 857-862. Jones, R. M., & Tulunay-Keesey, U. (1980). Phase selectivity of spatial frequency channels. Journal o f the Optical Society o f America, 70, 66-70. Lu, Z.-L., & Dosher, B. A. (1998). External noise distinguishes attention mechanisms. Vision Research, 38, 1183-1198. Lu, Z.-L., & Dosher, B. A. (1999). Characterizing human perceptual inefficiencies with equivalent internal noise. Journal o f the Optical Society o f America A: Optics & Image Science Special Issue: Noise in imaging systems and human vision, 16, 764-778. Lu, Z.-L., & Dosher, B. A. (2000). Spatial attention: Different mechanisms for central and peripheral temporal precues? Journal o f Experimental Psychology: Human Perception & Performance, 26, 1534-1548. Lu, Z.-L., Lesmes, L. A., & Dosher, B. A. (2002). Spatial attention excludes external noise at the target location. Journal o f Vision, 2, 312-323. Lu, Z.-L,, Liu, C. Q., & Dosher, B. A. (2000). Attention mechanisms for multi-location first- and second-order motion perception. Vision Research, 40, 173-186. R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. 61 Magnussen, S., & Greenlee, M. W. (1985). Marathon adaptation to spatial contrast: Saturation in sight. Vision Research, 25, 1409-1411. McLean, J., & Palmer, L. A. (1996). Contrast adaptation and excitatory amino acid receptors in cat strate cortex. Visual Neuroscience, 13, 1069-1087. Meese, T. S., & Holmes, D. J. (2002). Adaptation and gain pool summation: alternative models and masking data. Vision Research, 42, 1113-1125. Menees, S. M. (1998). The effect of spatial frequency adaptation on the latency of spatial contrast detection. Vision Research, 38, 3933-3942. Ohzawa, I., Sclar, G., & Freeman, R. D. (1985). Contrast Gain Control in the Cat's Visual System. Journal o f Neurophysiology, 45, 651-667. Sanches-Vives, M. V., Nowak, L. G., & McCormick, D. A. (2000a). Cellular mechanisms of long-lasting adaptation in visual cortical neurons in vitro. Journal o f Neuroscience, 20, 4286-4299. Sanches-Vives, M. V., Nowak, L. G., & McCormick, D. A. (2000b). Membrane mechanisms underlying contrast adaptation in cat area 17 in vivo. Journal of Neuroscience, 20, 4267-4285. Sanchez-Vives, M. V., Nowak, L. G., & McCormick, D. A. (2000a). Cellular mechanisms of long-lasting adaptation in visual cortical neurons in vitro. Journal o f Neuroscience, 20, 4286-4299. Sanchez-Vives, M. V., Nowak, L. G., & McCormick, D. A. (2000b). Membrane mechanisms underlying contrast adaptation in cat area 17 in vivo. Journal of Neuroscience, 20, 4267-4285. Sclar, G., Lennie, P., & DePriest, D. D. (1989). Contrast adaptation in striate cortex of macaque. Vision Research, 29, 747-755. Sharpe, C. R., & Tolhurst, D. J. (1973). Orientation and spatial frequency channels in peripheral vision. Vision Research, 13, 2103-2112. Snowden, R. J., & Hammett, S. T. (1996). Spatial frequency adaptation: Threshold elevation and perceived contrast. Vision Research, 36, 1797-1809. Stecher, S., Sigel, C., & Lange, R. V. (1973a). Composite adaptation and spatial frequency interactions. Vision Research, 13, 2527-2531. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 6 2 Stecher, S., Sigel, C., & Lange, R. V. (1973b). Spatial frequency channels in human vision and the threshold for adaptation. Vision Research, 13, 1691-1700. Stromeyer, C. F., 3rd, Klein, S., & Stemheim, C. E. (1977). Is spatial adaptation caused by prolonged inhibition? Vision Research, 17, 603-606. Stromeyer, C. F., Klein, S., Dawson, B. M., & Spillmann, L. (1982). Low spatial- frequency channels in human vision: Adaptation and masking. Vision Research, 22, 225-233. Swift, D. J., & Smith, R. A. (1982). An action spectrum for spatial-frequency adaptation. Vision Research, 22, 235-246. Tolhurst, D. J., & Barfield, L. P. (1978). Interactions betwen spatial frequency channels. Vision Research, 18, 951-958. Vidyasagar, T. R. (1990). Pattern adaptationi in cat visual cortex is a cooperative phenomenon. Neuroscience, 36, 175-179. Wainwright, M. J. (1999). Visual adaptation as optimal information transmission. Vision Research, 39, 3960-3974. Williams, D. W., Wilson, H. R., & Cowan, J. D. (1982). Localized effects of spatial- frequency adaptation. Journal o f the Optical Society o f America, 72, 878-887. Wilson, H. R., & Humanski, R. (1993). Spatial frequency adaptation and contrast gain control. Vision Research, 33, 1133-1149. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 63 Appendix. The cgcPTM and the PTM This appendix provides evidence that the cgcPTM and the PTM are mathematically equivalent. Schematic diagrams of the cgcPTM and the PTM are provided in figures 2 and 3. From mere observation of the two models, there appear to be important differences. The cgcPTM has a contras gain control mechanism by which the signal and noise are modified, it has a division element in which the stimulus and noise are divided by their total energy, and multiplicative noise comes relatively later in the model than it does in the PTM. The PTM, on the other hand, has no such gain control mechanism, division process; and multiplicative noise occurs before additive noise. Despite these apparent differences, the two models are mathematically equivalent and provide equivalent predictions of contrast thresholds before and after adaptation. We modeled the data according to the PTM, as described in the Models section, such that following adaptation, the signal gain, fi, is modified by a Constant, //i, and the external noise standard deviation, iV ex t, is modified by a constant /12. The signal to noise ratio, d ’, is therefore: Recall from the Models section that the cgcPTM predicts that following adaptation, d ’ would be defined by equation (28), reproduced below for convenience: R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 64 By rearranging equation (15), < 5 ? 'c g c p ™ becomes: (k, - 0 f c ' CgcPTM \k ,-N j'+ N j[{k , ■(if’'c^’'+{k,-N„f’' ] + N j ( N j + \ ) + { N j - k J ^ (31) Functional equivalence requires the equation of coefficients of external variables, N ext and c. Equivalence of equations (22) and (30) provide the following mappings: P=I3 f =1 jji =ki fl2 = N m u l — N m u l A ^ a d d ’ = (A ^ a d d )^ ’ ( A ^ m u l^ +1) + (A ^ m u l^ ' h) R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 
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Creator Dao, Debbie Yen (author) 
Core Title Adaptation to sine-wave gratings selectively reduces the sensory gain of the adapted stimuli 
School Graduate School 
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Degree Program Psychology 
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