Commentaries on Stanley Klein's Research Articles
164. Levi DM & Klein SA (2003). Noise provides some new signals about the spatial vision of amblyopes. J Neurosci. 23, 2522-2526.
Levi & Klein (2003) is a follow-up to Levi & Klein (2002) where we measured classification images for detection and vernier acuity of a bandpass bar that consisted of a sum over a discrete number (1st to 11th harmonic) of Fourier components. The advantage of using a small number of components is that the classification image can be obtained by linear regression rather than by the standard "reverse correlation". The linear regression method is more accurate so that one can get a classification image in substantially fewer trials than the usual methods. The Levi & Klein (2002) paper found that for both the detection task and the vernier task observers deviated from the ideal template in that they used more high spatial frequencies than optimal. They attended to the very central bar near fixation more than the ideal observer would. Levi & Klein (2003) found a different story for amblyopes where there was a dramatic decline in the classification image tuning at high spatial frequencies, more than would have been expected from the observer's acuity loss.
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173. Levi DM, Klein SA & Chen I (2005). What is the signal in noise? Vision Res. 45 1835-1846.
Levi, Klein & Chen (2005) is the first classification image (CI) vision paper to use noise rather than a fixed pattern as the target. Previously, noise was only used as the noise background. We were interested in learning what aspect of the noise was being used as signal for detecting changes in the noise. The classification image was based on Fourier power (independent of phase) rather than Fourier amplitude. We expected to find either a relatively flat (in frequency space) classification image or one that followed the expected contrast sensitivity function. However, the classification images that we found were shifted to higher frequencies than expected. Straightforward multichannel models were unable to match the data. We had to come up with a fascinating ad hoc mechanism to account for this data. An important feature of this paper is that it is the first CI paper to discriminate between systematic and random noise, where systematic noise produces response errors that are the same every time an identical stimulus is presented. To measure systematic noise we used a multipass formalism where each sample of noise is presented more than once. Our results showed that systematic noise is negligible except at very low noise levels. Present multichannel models of pattern detection have nonlinear summation across neighboring frequencies producing systematic noise near detection threshold. We were slightly surprised that systematic noise was not found at higher noise strengths, implying that at suprathreshold levels the human visual system is a relatively unbiased power detector that doesn't pay special attention to local contrast features. Further discussion of systematic noise is provided in the commentary to Li, Levi & Klein (2006)
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165. Levi DM, Li RW & Klein, SA (2003). "Phase capture" in the perception of interpolated shape: cue combination and the influence function. Vision Res. 43, 2233-2243.
172. Levi DM, Li RW & Klein, SA (2005). "Phase capture" in amblyopia: the influence function for sampled shape. Vision Res. 45 1793-1805.
Levi, Li & Klein (2003 & 2005) involve cue combination in normals (LLK2003) and amblyopes (LLK2005). We measured the perceived location of a 0.8 octave Gabor patch (envelope SD=2/3 carrier wavelength) relative to four similar reference patches (an inner pair and an outer pair). The observer's task was to position the central test patch so that it was perceived to lie on a circle defined by the reference patches. In a single run the reference Gabors had the following characteristics randomly intermixed: a) Three possible envelope centers (on a circle curved upward, downward or aligned), b) Five possible carrier phases (all five Gabors at zero phase, inner reference pair shifted up or down by 90 deg, outer reference pair shifted up or down by 90 deg). Linear regression was used to determine the relative importance of the three cues: envelope centers, inner patch phase, outer patch phase. This "importance function" triplet can be considered to be a classification image. The relative importance of the envelope and carrier cues depended strongly on patch separation. For normal vision we examined the hypothesis that the envelope and carrier cue weightings are proportional to the inverse variance of each cue. The variance of the two cues was obtained from Whitaker's data on thresholds for detecting envelope shifts and carrier shifts as a function of spatial frequency and separation. Our hypothesis that cue combination is based on inverse variance worked very well. This result was quite gratifying since it was able to account for wide range of separations and a factor of three change in viewing distance. The inverse variance weighting is in agreement with results in other modalities such as haptic/visual interactions as explored by Banks and colleagues. We also found subject dependent biases of judged circularity, where typically an oblate positioning looked circular.
For amblyopic observers (Levi, Li & Klein, 2005) there was an expected loss of dependence on inner carrier phase as compared to normals (the outer carrier phase of normals was already degraded). The surprising finding was an increased effect of the outer reference Gabor. In normals an upward shift of the outer reference carrier produced a downward shift in the match for the central test Gabor, a property of being on a circle. However, in the amblyopic eye the central match was often in the same direction as the shift of the outer reference. It is as if there is a visual capture of the composite pattern by the outer reference. We argue that this could be a form of crowding where the outer and inner reference Gabors become mixed together. This novel measure of crowding, where one feature can "drag" or "merge with" another feature, is a more interesting attribute of crowding than the more usual threshold elevation effect..
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177. Li RW, Levi DM & Klein SA. (2006). The receptive field and internal noise for position acuity change with feature separation. Journal of Vision. 6, 311-321.
Li, Levi & Klein (2006) is of interest both for the question that it asks and also for the new methods that it introduced. The question we asked was what information is used for making vernier judgments. Each of the two vernier lines consisted of five Gabor patches with the gap between patches fixed within a run but varied across runs from very close (1.1 carrier wavelengths) to well separated (10 wavelengths). The classification image showed that for closely spaced lines (a small gap between lines) the weighting of the five patches was a slowly decreasing function of patch number with the inner patches (those closest to the midline) having the largest weightings, as would be expected. The surprising finding was that for the large separations more than 50% of the weighting was for the innermost patch with negligible or even negative weighting on the outermost patch. One of the four observers showed a more uniform weighting, but still with a sharply negative weighting of the outer patch. A decreased weighting of the outermost patch could be a consequence of uncertainty of overall orientation but the discontinuous nature of the weighting pattern suggests a baffling inefficiency in the vernier mechanism. The novel 10-pass nature of our methodology, discussed next, gives us high confidence in the replicability of our results.
In addition to determining the weighting of the cues used for making vernier judgments, this paper takes classification image (CI) research in three unique directions: 1) The noise used for generating the CI was additive position noise (rather than the standard luminance noise) whereby the centroids of each of the Gabor functions were jittered in the direction of the vernier offset. 2) The multipass methodology was increased to 10 passes rather than the typical 2-pass or 3-pass. The 10-pass method enabled us to obtain a relatively accurate estimate of the judged vernier offset and standard deviation for each noise condition. 3) The 10-pass methodology provided us with a unique method for estimating the systematic noise component as distinguished from the random noise component (see the Levi, Klein & Chen (2005) commentary for more details on systematic noise). Systematic noise can be explained with the following example. Consider the case in which the vernier offset is determined by just two Gabor patches rather than 10. Then a classification image formula could be written as: offset = a*x1 + b*x2 + c*x1*x2 + higher order terms, where x1 and x2 are the position values for the two Gabors. The ideal observer would have parameters values of c = 0 and a = b =0.5. The classification image methodology measures a and b giving the weightings of the two samples. Parameter c is an example of consistent noise that could degrade performance. Our 10-pass methodology allowed us to assess the strength of arbitrary nonlinear terms that would contribute to consistent noise. Our measurement showed that the contribution of consistent noise was negligible. Thus possible nonlinear interactions were unlikely to account for the unusual classification image pattern discussed in the preceding paragraph. .
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Detection and Discrimination
166. Yu C., Klein SA, Levi DM. (2003). Cross- and iso- oriented surrounds modulate the contrast response function: The effect of surround contrast. Journal of Vision 3, 527-540
Yu, Klein & Levi (2003) measured contrast discrimination of a central two cycle test pattern in the presence of a surrounding annulus of the same spatial frequency with aligned or orthogonal orientation. We measured the dependence of facilitation and inhibition on the full range of center and surround contrasts. For the orthogonal orientation strong facilitation was found when the surround contrast was low, and inhibition was never found. This result was surprising because most physiological studies showed strong surround inhibition, but those studies used high contrasts in the annulus. For the case of iso-oriented surrounds we found both inhibition and facilitation depending on the center/surround contrast ratio. We developed a simple model that could account for most of the data and a more complicated model that included contrast tuning was able to account for sharp discontinuities when the test contrast was close to the surround contrast. See further discussion of contrast tuning in our perceptual learning paper (Li, Levi & Klein 2004). This study made it clear to us that there is still much to learn about center-surround interactions in the simple domain of contrast judgments.
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170. Hanharan S, Levi DM & Klein SA (2005). "Crowding" in normal and amblyopic vision assessed with Gaussian and Gabor C's. Vision Res. 45, 617-633.
Hanharan S, Levi DM & Klein SA (2005) show aspects other than contrast that are involved in some types of surround masking or inhibition. This paper continues our search for aspects of strabismic amblyopic vision that resemble normal peripheral vision. We measured the detection threshold for identifying the orientation of a small letter C when surrounded by small flanker masks. The target letter was either narrow-band or low pass filtered to allow the scale (size) to be varied. We found that in both amblyopic and peripheral vision the extent of masking was substantially larger than in normal foveal vision. One of the interesting findings of this study was an apparent decoupling of peripheral masking from amblyopic masking in the feature specificity of masking. In the amblyopic eye the masking was relatively independent of contrast polarity (for low pass targets and maskers) and independent of orientation (for narrow-band targets and maskers). In normal peripheral vision masking would have been much reduced.
One of the special features of this paper are modeling calculations of a hypothesis for masking based on Fourier space considerations that had been suggested by Hess and by Thibos. Our fairly general modeling analyses show clearly (to us at least) that Fourier space approaches are not able to explain the data. One of the neat aspects of this modeling are the very pretty "peacock" figures (see Fig. 12) that we use to present our findings and make our point.
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171. Carney T, Klein SA (2005). Visual resolution: operational definitions with an eye towards historical precedence. Vision Res. 45, 949-954.
Carney & Klein (2005) was a different sort of paper and was fun. It was a response to a short letter that Westheimer wrote critiquing our "test-pedestal" article (Carney & Klein, 1997) titled "Resolution acuity is better than Vernier acuity". With that provocative title it wasn't surprising that Westheimer had to respond. His objection was that our two-line vs. one line task for resolution could be done with a blur cue rather than a two-ness cue. It turns out that the challenge to devise a robust discrimination task that eliminates the blur cue is really interesting. We examine a number of possible 3-line vs 2-line discrimination tasks in both the space and the frequency domain. We propose several good candidates for a "true resolution" task. Our experiments showed that for these stimuli, thresholds are close to one minute of arc, rather than 0.35 min for 2-line vs. 1-line tasks where blur can be used. It is gratifying that for these "true resolution" tasks the "test-pedestal" framework may still hold, with the one minute of arc thresholds corresponding to the detection of a 60 c/deg grating at 100% contrast (possibly in the dipper regime).
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176. Klein SA (2006a) Separating transducer nonlinearities and multiplicative noise in contrast discrimination. Vision Res. 46 4279-4293.
Klein (2006a) is on a topic that has been bothering me ever since my first vision paper: Stromeyer & Klein (Vision Research, 1974: how to explain the increase in contrast discrimination thresholds as the reference contrast is increased. The two standard explanations are: 1) a saturating contrast response function and 2) multiplicative noise. It has been notoriously difficult to devise experiments able to distinguish the two factors. Kontsevich, Chen & Tyler (2002) claim their 2AFC data provides evidence for multiplicative noise with an accelerating, not a saturating, contrast response function. Georgeson & Meese and Katkov, Sagi & Tsodyks offer rebuttals. In Klein (2006), I examine all these articles and end up claiming that there is indeed evidence for multiplicative noise, but of a type different from what Kontsevich imagined. I used this paper as a vehicle to explore several other topics having to do with statistics and experimental design that are rarely discussed. Topic 1 is the question of how to get error bars on parameter estimates. I found (in agreement with Kontsevich) that the multiplicative noise exponent and its standard errors (Table 4) to be q = 0.76±0.03, 0.83±0.08, 0.84±0.03, 0.85±0.04, for the four observers, where q=0 would be no multiplicative noise. These SEs are so small that the null hypothesis seems to be soundly rejected. However, those calculations of SE are based on the regression being linear regression, whereas this regression was nonlinear. Usually the linear approximation is fine for estimating SEs, but not this time. When done properly using a grid search one finds that the chi square surface deviates strikingly from the linear approximation and only two of the four values of q truly differ significantly from zero. Furthermore, one of those two has a chi square that is sufficiently large that Georgeson suggests that subject's data should be thrown out. Topic 2 that I raise is the question of under what circumstances does one throw out a subject or throw out data points. I argue that the subject that Georgeson wants to throw out is actually the most important subject for answering the question of the presence of multiplicative noise. I present a new type of analysis, inspired by Katkov et al., that reduces the chi square for that controversial subject to a statistically acceptable range, thereby removing Georgeson's objection and providing evidence for multiplicative noise. Topic 3 is the question of how to compare alternate fits to a data set from models that are not embedded in one another. The various models for the shape of the contrast response function and the multiplicative noise had different numbers of parameters and therefore provided a fine example to discuss questions of goodness of fit.
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168. Li RW, Levi DM, Klein SA. (2004). Perceptual learning improves efficiency by re-tuning the decision 'template' for position discrimination. Nat. Neurosci. 7, 178-183.
Li, Levi & Klein (2004) asked what aspect of the vernier stimulus is used to achieve the hyperacuity thresholds. It's surprising that this question, so ideally suited for classification image methods hadn't been done earlier. Two important features of this paper are: 1) With training the observer's efficiency goes up. 2) Classification images reveal that the source of the increased efficiency was an increase in the discrimination template size. Before training only the inner few samples were used, consistent with the observer's poor overall efficiency. After training the number of effective samples that are used in the vernier task has about doubled. This use of classification images has clarified the mechanism of one instance of perceptual learning. This study was a direct precursor to Li, Levi & Klein (2006). .
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169. Yu C, Klein SA, Levi DM (2004) [YKL04]. Perceptual learning in contrast discrimination and the (minimal) role of context. Journal of Vision 4,169-182.
174. Kuai SG, Zhang JY, Klein SA, Levi DM, Yu C. (2005) [KZKL05]. The essential role of stimulus temporal patterning in enabling perceptual learning. Nat. Neurosci. 8 1497-1499.
YKL04 and KZKL05 on learning in a contrast discrimination task initiated an important new direction for our lab, while building on our earlier research demonstrating the important role of contrast discrimination for a wide variety of visual processing tasks. The abstracts of this pair of papers do an excellent job of introducing the topic and in presenting the details of our findings, so there is no need to repeat those details here. Rather, this commentary will comment on how this research got started and some highlights. We were motivated by surprising reports from Dov Sagi's group that contrast discrimination was a task resistant to learning unless reference flankers were present ("context enabled learning"). Our intuition differed from those reported results so we attempted to replicate them. The replication failed since we demonstrated strong learning under conditions similar to Sagi's, without the need for context. In recent publications Sagi's results have come closer to ours. The most interesting aspect of our studies is that in agreement with Sagi learning can be eliminated by roving the reference contrast. In YKL04 we used a 2AFC paradigm randomly intermixing reference contrasts of 20%, 30%, 47% and 63% and found no learning. KZKL05 found that when the same four contrast levels were intermixed in a repeating pattern, learning was restored. This is a surprising result and has become the platform for many of our follow-up studies. One of the other directions that these studies have taken is the question of how learning along one dimension (like stimulus contrast or location or orientation or eye of origin) transfers to other dimensions. The most interesting case of non-transfer is that we found that learning at one contrast level has only partial transfer to other contrasts. Most neural mechanism based models of learning would have full transfer in the contrast domain. A modeling section of YKL04 explores several intriguing mechanisms that would produce the non-transfer. We especially liked the idea of mechanisms tuned in contrast. We plan to resolve competing models of contrast processing using electrophysiological approaches.
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EEG and Brain Imaging
178. Carney T, Ales J & Klein SA (2006). Advances in multifocal methods for imaging human brain activity. Human Vision and Electronic Imaging XI, Bernice Rogowitz, Thrasyvoulos Pappas, Scott Daly, Editors SPIE 6057.
Carney, Ales & Klein (2006) describes our new stimulation methods that overcome past limitations. Our previous lookup table "movies" limited the stimulus to 128 dartboard patches each with only two luminance levels. The new method allows very rapid presentation of highly compressed images with almost no restrictions on the number of patches and the content of each patch. This paper presents high quality data obtained using 192 dartboard patches (8 rings of 24 spokes). This is the type of data that we are presently using for our high quality early vision source localization. We demonstrate responses with high signal to noise not only from the 192 separate patches but also from the 8*22=176 within ring edges between patches (cross-kernels). We present data showing that the edge generated topographies are similar (thank goodness) to those from the adjacent patches. The new stimulus technique also allows multiplexing multiple stimulus attributes in each patch. For example independent m-sequences controlling horizontal and vertical gratings or spatial frequencies in each patch allow one to stimulate independent groups of neurons so that in the same recording session we are able to carry out two experiments at the same time. There is a time efficiency in this method to the degree that the multiple neural populations are independent and saturating.
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179. Baker SL, Baseler H, Carney T & Klein SA (2006). Localizing sites of activation in primary visual cortex using visual evoked potentials and functional magnetic resonance imaging. Journal of Clinical Neurophysiology, 23, 404 - 415.
Baker, Baseler, Carney & Klein (2006) presents a comparison of single dipole EEG source localization with what would be expected if the dipole were assumed to come from V1 based on MRI/fMRI maps of the same individual. One might worry about the one dipole per patch assumption. Luckily, with m-sequence rapid stimulation we (and Don Hood and Andrew James) have shown, using principal components analysis that typically, more than 50% of the response variance can be accounted for by a single dipolar source. What our paper is the first to do is to make detailed comparisons between the dipoles found from VEP data and what would be expected from the MRI/fMRI maps. We showed that the fit is quite good. We used a permutation test to calculate that there was a negligible chance p<10-6 that the agreement between the VEP dipoles and the MRI/fMRI maps occurred by chance.
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