Human observers can bisect a space with an accuracy which far exceeds the retinal grain. How spat... more Human observers can bisect a space with an accuracy which far exceeds the retinal grain. How spatial information is sampled to provide such hyperacuity thresholds has been of interest since Hering’s (1899) proposal that local signs are averaged along the length of the lines. We investigated this question in central and peripheral vision of human observers by measuring bisection thresholds for stimuli comprised of discrete samples, each ~1′ long. The number of samples and the intersample spacing were systematically varied. The results show that (1) the critical variable is not the total length of the pattern (i.e., length of the samples plus interspaces) but rather the number of samples; (2) central and peripheral vision differ qualitatively in their sampling characteristics. In central vision, only a small number of samples (5) are needed to provide optimum performance; increasing the number of samples from 1 to 5 results in only a slight improvement in bisection thresholds. The periphery, on the other hand, requires more samples for optimal performance, and thresholds improve in proportion to the square root of the number of samples. The data of strabismic amblyopes show the same n behavior as the normal periphery. The results suggest that in strabismic amblyopia, and in the normal periphery, spatial information is undersampled.
Amblyopia represents a developmental abnormality of the “spatial sense” resulting from image degr... more Amblyopia represents a developmental abnormality of the “spatial sense” resulting from image degradation and/or binocular image misregistration early in life. Clinicians generally consider spatial vision in terms of Snellen acuity, with a limiting acuity of about 20/20 (i.e. critical detail of about 1′); however, the visual system is capable of making much finer spatial discriminations. For example, relative position, size and orientation can be judged with an accuracy of 3 to 6 arc seconds or better (Klein and Levi, 1985). These low spatial thresholds are 5 to 10 times finer than either the cutoff spatial frequency or the intercone spacing. For this reason, Westheimer (1975) has coined the term “hyperacuity” to describe a variety of tasks that involve sensing the direction of spatial offset of a line or point relative to a reference.
This study was concerned with what stimulus information humans with amblyopia use to judge the sh... more This study was concerned with what stimulus information humans with amblyopia use to judge the shape of simple objects. We used a string of four Gabor patches to define a contour. A fifth, center patch served as the test pattern. The observersÕ task was to judge the location of the test pattern relative to the contour. The contour was either a straight line, or an arc with positive or negative curvature. We asked whether phase shifts in the inner or outer pairs of patches distributed along the contour influence the perceived shape. That is, we measured the phase shift influence function. Our results, consistent with previous studies, show that amblyopes are imprecise in shape discrimination, showing elevated thresholds for both lines and curves. We found that amblyopes often make much larger perceptual errors (biases) than do normal observers in the absence of phase shifts. These errors tend to be largest for curved shapes and at large separations. In normal observers, shifting the phase of inner patches of the string by 0.25 cycle results in almost complete phase capture (attraction) at the smallest separation (2k), and the capture effect falls off rapidly with separation. A 0.25 cycle shift of the outer pair of patches has a much smaller effect, in the opposite direction (repulsion). While several amblyopic observers showed reduced capture by the phase of the inner patches, to our surprise, several of the amblyopes were sensitive to the phase of the outer patches. We used linear multiple regression to determine the weights of all cues to the task: the carrier phase of the inner patches, carrier phase of the outer patches and the envelope of the outer patches. Compared to normal observers, some amblyopes show a weaker influence of the phase of the inner patches, and a stronger influence of both the phase and envelope of the outer patches. We speculate that this may be a consequence of abnormal ''crowding'' of the inner patches by the outer ones.
In normal foveal vision, visual space is accurately mapped from retina to cortex. However, the no... more In normal foveal vision, visual space is accurately mapped from retina to cortex. However, the normal periphery, and the central field of strabismic amblyopes have elevated position discrimination thresholds, which have often been ascribed to increased 'intrinsic' spatial disorder. In the present study we evaluated the sensitivity of the human visual system (both normal and amblyopic) to spatial disorder, and asked whether there is increased 'intrinsic' topographical disorder in the amblyopic visual system. Specifically, we measured thresholds for detecting disorder (two-dimensional Gaussian position perturbations) either in a horizontal string of N equally spaced samples (Gabor patches), or in a ring of equally spaced samples over a wide range of feature separations. We also estimated both the 'equivalent intrinsic spatial disorder' and sampling efficiency using an equivalent noise approach. Our results suggest that both thresholds for detecting disorder, and equivalent intrinsic disorder depend strongly on separation, and are modestly increased in strabismic amblyopes. Strabismic amblyopes also show markedly reduced sampling efficiency. However, neither amblyopic nor peripheral vision performs like ideal or human observers with added separation-independent positional noise. Rather, the strong separation dependence suggests that the 'equivalent intrinsic disorder' may not reflect topographic disorder at all, but rather may reflect an abnormality in the amblyopes' Weber relationship.
Journal of the Optical Society of America, Aug 1, 1987
Performance of three-dot bisection was determined as a function of orientation for a variety of f... more Performance of three-dot bisection was determined as a function of orientation for a variety of feature separations and field meridians at eccentricities of 0-10 deg for two observers. The dot stimuli and separations were scaled in size to compensate for eccentricity. The precision of three-dot bisection was found to depend on the direction of test-feature offset. In the fovea, horizontal and vertical bisections were better than oblique bisections, while at eccentricities of 5-20 deg, isoeccentric (on a tangent to a circle of a given eccentricity) bisection was better than radial bisection. The direction of offset was more important than the orientation of the stimulus. Large separations showed a stronger effect than small separations. The anisotropy of bisection appears different from the meridional effect for resolution and is unlikely to be simply related to a local anisotropy of the cortical magnification factor.
We measured resolution of edge (the line) blur as a function of edge (and line) contrast. Previou... more We measured resolution of edge (the line) blur as a function of edge (and line) contrast. Previous attempts to predict resolution thresholds involved many modeling assumptions concerning the visual system’s sensitivity and/or the retinal sampling density. Our goal is to avoid assumptions by measuring the visibility of those multipoles that are used in the resolution task. The task of discriminating edge (or line) blur is equivalent to the task of detecting a dipole (or quadrupole) test pattern in the presence of the edge (or line) pedestal. The multipole test threshold can be related to the variance of the blur by using the relationship P v + ε ( x ) = P v ( x ) + 0.5 ε P v ′ ′ ( x ) + O ( ε 2 ) , where P v (x) is an edge or line with a blur of variance v and where ϵ (with units of min2) is the ratio of test threshold to pedestal strength. A sample result is that a dipole of 4 % min2 strength was visible on a 100 % contrast edge pedestal, corresponding to a blur variance of 0.04 min2 (equal to a standard deviation of 0.2 min or a 0.28-min separation between a pair of lines). This small resolution threshold would be surprising in terms of the retinal sampling density but is not surprising in terms of our test-pedestal approach.
ABSTRACT Amblyopia results in a loss of contrast sensitivity and position acuity. Here we report ... more ABSTRACT Amblyopia results in a loss of contrast sensitivity and position acuity. Here we report the results of experiments using noise to try to better understand the nature of the neural losses in amblyopia. In the first experiment, we used noise to derive the template or classification image used to detect a target and to discriminate its position. We found that some amblyopic observers show markedly abnormal templates for the position task and moderately abnormal classification images for the detection task; however, the abnormal template could not fully account for the loss of performance (efficiency). Reduced efficiency in the amblyopic visual system may reflect a poorly matched template, a high fraction of internal to external noise, or both. Comparison of the observers' performance with that of their template suggests that the amblyopes have a high fraction of internal (relative to external) noise. To analyze the internal noise further, we used a "double-pass" technique, in which observers performed the identical experiment twice. The amount of disagreement between the two experiments provides another estimate of the fraction of internal noise. Amblyopes show a much higher fraction of stimulus-dependent internal noise than do normal observers. We conclude that the loss of efficiency in amblyopia is attributable in part to a poorly matched template, but to a greater degree, to a high fraction of internal (relative to external) noise.
We used Gaussian blurred lines of same-and opposite-polarity to measure the effects of blur on 3-... more We used Gaussian blurred lines of same-and opposite-polarity to measure the effects of blur on 3-line spatial interval discrimination (bisection). The results of our experiments can be summarized as follows. Spatial interval discrimination (3-line bisection) thresholds are proportional to the separation of the lines (i.e. Weber's law). At the optimal separation, spatial interval discrimination thresholds for same-polarity lines represent a "hyperacuity" as small as 2 set arc. For same-polarity Gaussian blurred lines, over a wide range of the blur standard deviations (u), the optimal thresbold occurs when the separation is approx. 2 u, and the optimal threshold is about 0.02 a, or a Weber fraction (b/s) of 0.01. For opposite-polarity lines, under conditions where same-polarity stimuli yield the best thresholds (at a separation 22 a), spatial interval thresholds are an order of magnitude worse than that for same-polarity lines, suggesting that the localization of stimili of opposite-polarity is much worse than that of same-polarity stimuli over a wide range of spatial scales. At large separations, greater than about 5 u, spatial interval discrimination thresholds are more or less independent of both contrast and polarity. While hyperacuity is generally thought of in terms of the tiny spatial thresholds which are obtained at small separations with stimuli comprised of thin lines, the present results, and those of others, suggest that for same-polarity stimuli, hyperacuity thresholds are a general property of the visual system, occurring at many spatial scales. The present results also suggest that the poor localization of opposite-polarity lines occurs at multiple spatial scales, when the line separation is less than about five times the stimulus spread. We consider several models which can account for particular features of our data. Psychophysics Spatial interval discrimination Bisection Hyperacuity Blur Gaussian blur Intrinsic blur Modelling Weber's law Spatial vision ' dmrimimtion under photopic and scotopic conditions.
Abnormal visual development in strabismic amblyopia drastically affects visual perception and pro... more Abnormal visual development in strabismic amblyopia drastically affects visual perception and properties of neurons in primary visual cortex (V1). To test the notion that amblyopia also has consequences for higher visual areas, we asked humans with amblyopia to count briefly presented features. Using the amblyopic eye, strabismic amblyopes counted inaccurately, markedly underestimating the number of features. This inaccuracy was not due to low-level considerations (blur, visibility, crowding, undersampling or topographical jitter), as they also underestimated the number of features missing from a uniform grid. Rather, counting deficits in strabismic amblyopes reflected a higher-level limitation in the number of features the amblyopic visual system can individuate.
Humans with amblyopia show marked deficits in positional judgments. We measured Vernier acuity fo... more Humans with amblyopia show marked deficits in positional judgments. We measured Vernier acuity for edges and lines over a wide range of contrast. Our results suggest that in both amblyopic and normal eyes, the spatial localization of abutting edges or lines improves with increasing stimulus contrast (with a slope of about -0.6 on log-log coordinates).
Recent estimates of the cortical magnification factor suggest that the area of the cortex devoted... more Recent estimates of the cortical magnification factor suggest that the area of the cortex devoted to the fovea is considerably higher than previously estimated. Hyperacuity is thought to reflect cortical processing and for Vernier acuity, foveal and peripheral performance has been shown to differ only in terms of the area of cortex devoted to the task (Levi and Klein, 1984). Performance on a different spatial discrimination task, 3-dot bisection, was measured in the fovea and inferior peripheral field at eccentricities of 2.5°, 5°, and 10° of two subjects using a rating scale signal detection paradigm with feedback. By scaling the stimulus size in proportion to recent estimates of the cortical magnification factor at each eccentricity, the functions of s/s over a wide range of separations of reference dots were shown to remain constant in cortical units from 0° to 10°. Further experiments comparing performance for horizontal, vertical, and oblique orientations of the stimulus in different meridians of the visual field revealed performance to be more dependent on the orientation than the location of a stimulus at a given eccentricity. Specifically, position discrimination was better for tangentially than radially oriented stimuli.
Henry Stapp studied with the founders of quantum mechanics and has been one of the most forceful ... more Henry Stapp studied with the founders of quantum mechanics and has been one of the most forceful defenders of a version of what is known as the orthodox interpretation. Upon completion of his PhD under Emilio Segrè and Owen Chamberlain, Stapp was invited to work with Pauli, who unfortunately died prematurely the same year. Stapp was then invited to work with Werner Heisenberg, and then with J. A. Wheeler, on the foundations of quantum mechanics-one of the main topics on which Stapp has focused his remarkable career. These facts alone make Henry Stapp an icon in the field of physics, particularly the foundations of physics, but there is a lot more to say about Stapp and his work. In this paper, we discuss Stapp's legacy, as well as his views about the connection between the observer, quantum measurements, and the mind/body problem.
Human observers can bisect a space with an accuracy which far exceeds the retinal grain. How spat... more Human observers can bisect a space with an accuracy which far exceeds the retinal grain. How spatial information is sampled to provide such hyperacuity thresholds has been of interest since Hering’s (1899) proposal that local signs are averaged along the length of the lines. We investigated this question in central and peripheral vision of human observers by measuring bisection thresholds for stimuli comprised of discrete samples, each ~1′ long. The number of samples and the intersample spacing were systematically varied. The results show that (1) the critical variable is not the total length of the pattern (i.e., length of the samples plus interspaces) but rather the number of samples; (2) central and peripheral vision differ qualitatively in their sampling characteristics. In central vision, only a small number of samples (5) are needed to provide optimum performance; increasing the number of samples from 1 to 5 results in only a slight improvement in bisection thresholds. The periphery, on the other hand, requires more samples for optimal performance, and thresholds improve in proportion to the square root of the number of samples. The data of strabismic amblyopes show the same n behavior as the normal periphery. The results suggest that in strabismic amblyopia, and in the normal periphery, spatial information is undersampled.
Amblyopia represents a developmental abnormality of the “spatial sense” resulting from image degr... more Amblyopia represents a developmental abnormality of the “spatial sense” resulting from image degradation and/or binocular image misregistration early in life. Clinicians generally consider spatial vision in terms of Snellen acuity, with a limiting acuity of about 20/20 (i.e. critical detail of about 1′); however, the visual system is capable of making much finer spatial discriminations. For example, relative position, size and orientation can be judged with an accuracy of 3 to 6 arc seconds or better (Klein and Levi, 1985). These low spatial thresholds are 5 to 10 times finer than either the cutoff spatial frequency or the intercone spacing. For this reason, Westheimer (1975) has coined the term “hyperacuity” to describe a variety of tasks that involve sensing the direction of spatial offset of a line or point relative to a reference.
This study was concerned with what stimulus information humans with amblyopia use to judge the sh... more This study was concerned with what stimulus information humans with amblyopia use to judge the shape of simple objects. We used a string of four Gabor patches to define a contour. A fifth, center patch served as the test pattern. The observersÕ task was to judge the location of the test pattern relative to the contour. The contour was either a straight line, or an arc with positive or negative curvature. We asked whether phase shifts in the inner or outer pairs of patches distributed along the contour influence the perceived shape. That is, we measured the phase shift influence function. Our results, consistent with previous studies, show that amblyopes are imprecise in shape discrimination, showing elevated thresholds for both lines and curves. We found that amblyopes often make much larger perceptual errors (biases) than do normal observers in the absence of phase shifts. These errors tend to be largest for curved shapes and at large separations. In normal observers, shifting the phase of inner patches of the string by 0.25 cycle results in almost complete phase capture (attraction) at the smallest separation (2k), and the capture effect falls off rapidly with separation. A 0.25 cycle shift of the outer pair of patches has a much smaller effect, in the opposite direction (repulsion). While several amblyopic observers showed reduced capture by the phase of the inner patches, to our surprise, several of the amblyopes were sensitive to the phase of the outer patches. We used linear multiple regression to determine the weights of all cues to the task: the carrier phase of the inner patches, carrier phase of the outer patches and the envelope of the outer patches. Compared to normal observers, some amblyopes show a weaker influence of the phase of the inner patches, and a stronger influence of both the phase and envelope of the outer patches. We speculate that this may be a consequence of abnormal ''crowding'' of the inner patches by the outer ones.
In normal foveal vision, visual space is accurately mapped from retina to cortex. However, the no... more In normal foveal vision, visual space is accurately mapped from retina to cortex. However, the normal periphery, and the central field of strabismic amblyopes have elevated position discrimination thresholds, which have often been ascribed to increased 'intrinsic' spatial disorder. In the present study we evaluated the sensitivity of the human visual system (both normal and amblyopic) to spatial disorder, and asked whether there is increased 'intrinsic' topographical disorder in the amblyopic visual system. Specifically, we measured thresholds for detecting disorder (two-dimensional Gaussian position perturbations) either in a horizontal string of N equally spaced samples (Gabor patches), or in a ring of equally spaced samples over a wide range of feature separations. We also estimated both the 'equivalent intrinsic spatial disorder' and sampling efficiency using an equivalent noise approach. Our results suggest that both thresholds for detecting disorder, and equivalent intrinsic disorder depend strongly on separation, and are modestly increased in strabismic amblyopes. Strabismic amblyopes also show markedly reduced sampling efficiency. However, neither amblyopic nor peripheral vision performs like ideal or human observers with added separation-independent positional noise. Rather, the strong separation dependence suggests that the 'equivalent intrinsic disorder' may not reflect topographic disorder at all, but rather may reflect an abnormality in the amblyopes' Weber relationship.
Journal of the Optical Society of America, Aug 1, 1987
Performance of three-dot bisection was determined as a function of orientation for a variety of f... more Performance of three-dot bisection was determined as a function of orientation for a variety of feature separations and field meridians at eccentricities of 0-10 deg for two observers. The dot stimuli and separations were scaled in size to compensate for eccentricity. The precision of three-dot bisection was found to depend on the direction of test-feature offset. In the fovea, horizontal and vertical bisections were better than oblique bisections, while at eccentricities of 5-20 deg, isoeccentric (on a tangent to a circle of a given eccentricity) bisection was better than radial bisection. The direction of offset was more important than the orientation of the stimulus. Large separations showed a stronger effect than small separations. The anisotropy of bisection appears different from the meridional effect for resolution and is unlikely to be simply related to a local anisotropy of the cortical magnification factor.
We measured resolution of edge (the line) blur as a function of edge (and line) contrast. Previou... more We measured resolution of edge (the line) blur as a function of edge (and line) contrast. Previous attempts to predict resolution thresholds involved many modeling assumptions concerning the visual system’s sensitivity and/or the retinal sampling density. Our goal is to avoid assumptions by measuring the visibility of those multipoles that are used in the resolution task. The task of discriminating edge (or line) blur is equivalent to the task of detecting a dipole (or quadrupole) test pattern in the presence of the edge (or line) pedestal. The multipole test threshold can be related to the variance of the blur by using the relationship P v + ε ( x ) = P v ( x ) + 0.5 ε P v ′ ′ ( x ) + O ( ε 2 ) , where P v (x) is an edge or line with a blur of variance v and where ϵ (with units of min2) is the ratio of test threshold to pedestal strength. A sample result is that a dipole of 4 % min2 strength was visible on a 100 % contrast edge pedestal, corresponding to a blur variance of 0.04 min2 (equal to a standard deviation of 0.2 min or a 0.28-min separation between a pair of lines). This small resolution threshold would be surprising in terms of the retinal sampling density but is not surprising in terms of our test-pedestal approach.
ABSTRACT Amblyopia results in a loss of contrast sensitivity and position acuity. Here we report ... more ABSTRACT Amblyopia results in a loss of contrast sensitivity and position acuity. Here we report the results of experiments using noise to try to better understand the nature of the neural losses in amblyopia. In the first experiment, we used noise to derive the template or classification image used to detect a target and to discriminate its position. We found that some amblyopic observers show markedly abnormal templates for the position task and moderately abnormal classification images for the detection task; however, the abnormal template could not fully account for the loss of performance (efficiency). Reduced efficiency in the amblyopic visual system may reflect a poorly matched template, a high fraction of internal to external noise, or both. Comparison of the observers' performance with that of their template suggests that the amblyopes have a high fraction of internal (relative to external) noise. To analyze the internal noise further, we used a "double-pass" technique, in which observers performed the identical experiment twice. The amount of disagreement between the two experiments provides another estimate of the fraction of internal noise. Amblyopes show a much higher fraction of stimulus-dependent internal noise than do normal observers. We conclude that the loss of efficiency in amblyopia is attributable in part to a poorly matched template, but to a greater degree, to a high fraction of internal (relative to external) noise.
We used Gaussian blurred lines of same-and opposite-polarity to measure the effects of blur on 3-... more We used Gaussian blurred lines of same-and opposite-polarity to measure the effects of blur on 3-line spatial interval discrimination (bisection). The results of our experiments can be summarized as follows. Spatial interval discrimination (3-line bisection) thresholds are proportional to the separation of the lines (i.e. Weber's law). At the optimal separation, spatial interval discrimination thresholds for same-polarity lines represent a "hyperacuity" as small as 2 set arc. For same-polarity Gaussian blurred lines, over a wide range of the blur standard deviations (u), the optimal thresbold occurs when the separation is approx. 2 u, and the optimal threshold is about 0.02 a, or a Weber fraction (b/s) of 0.01. For opposite-polarity lines, under conditions where same-polarity stimuli yield the best thresholds (at a separation 22 a), spatial interval thresholds are an order of magnitude worse than that for same-polarity lines, suggesting that the localization of stimili of opposite-polarity is much worse than that of same-polarity stimuli over a wide range of spatial scales. At large separations, greater than about 5 u, spatial interval discrimination thresholds are more or less independent of both contrast and polarity. While hyperacuity is generally thought of in terms of the tiny spatial thresholds which are obtained at small separations with stimuli comprised of thin lines, the present results, and those of others, suggest that for same-polarity stimuli, hyperacuity thresholds are a general property of the visual system, occurring at many spatial scales. The present results also suggest that the poor localization of opposite-polarity lines occurs at multiple spatial scales, when the line separation is less than about five times the stimulus spread. We consider several models which can account for particular features of our data. Psychophysics Spatial interval discrimination Bisection Hyperacuity Blur Gaussian blur Intrinsic blur Modelling Weber's law Spatial vision ' dmrimimtion under photopic and scotopic conditions.
Abnormal visual development in strabismic amblyopia drastically affects visual perception and pro... more Abnormal visual development in strabismic amblyopia drastically affects visual perception and properties of neurons in primary visual cortex (V1). To test the notion that amblyopia also has consequences for higher visual areas, we asked humans with amblyopia to count briefly presented features. Using the amblyopic eye, strabismic amblyopes counted inaccurately, markedly underestimating the number of features. This inaccuracy was not due to low-level considerations (blur, visibility, crowding, undersampling or topographical jitter), as they also underestimated the number of features missing from a uniform grid. Rather, counting deficits in strabismic amblyopes reflected a higher-level limitation in the number of features the amblyopic visual system can individuate.
Humans with amblyopia show marked deficits in positional judgments. We measured Vernier acuity fo... more Humans with amblyopia show marked deficits in positional judgments. We measured Vernier acuity for edges and lines over a wide range of contrast. Our results suggest that in both amblyopic and normal eyes, the spatial localization of abutting edges or lines improves with increasing stimulus contrast (with a slope of about -0.6 on log-log coordinates).
Recent estimates of the cortical magnification factor suggest that the area of the cortex devoted... more Recent estimates of the cortical magnification factor suggest that the area of the cortex devoted to the fovea is considerably higher than previously estimated. Hyperacuity is thought to reflect cortical processing and for Vernier acuity, foveal and peripheral performance has been shown to differ only in terms of the area of cortex devoted to the task (Levi and Klein, 1984). Performance on a different spatial discrimination task, 3-dot bisection, was measured in the fovea and inferior peripheral field at eccentricities of 2.5°, 5°, and 10° of two subjects using a rating scale signal detection paradigm with feedback. By scaling the stimulus size in proportion to recent estimates of the cortical magnification factor at each eccentricity, the functions of s/s over a wide range of separations of reference dots were shown to remain constant in cortical units from 0° to 10°. Further experiments comparing performance for horizontal, vertical, and oblique orientations of the stimulus in different meridians of the visual field revealed performance to be more dependent on the orientation than the location of a stimulus at a given eccentricity. Specifically, position discrimination was better for tangentially than radially oriented stimuli.
Henry Stapp studied with the founders of quantum mechanics and has been one of the most forceful ... more Henry Stapp studied with the founders of quantum mechanics and has been one of the most forceful defenders of a version of what is known as the orthodox interpretation. Upon completion of his PhD under Emilio Segrè and Owen Chamberlain, Stapp was invited to work with Pauli, who unfortunately died prematurely the same year. Stapp was then invited to work with Werner Heisenberg, and then with J. A. Wheeler, on the foundations of quantum mechanics-one of the main topics on which Stapp has focused his remarkable career. These facts alone make Henry Stapp an icon in the field of physics, particularly the foundations of physics, but there is a lot more to say about Stapp and his work. In this paper, we discuss Stapp's legacy, as well as his views about the connection between the observer, quantum measurements, and the mind/body problem.
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Papers by Stanley Klein