A model of sensitivity to binary local image statistics ...jdvicto/vps/sfn13_corztg.pdf · sym1...
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Supported by EY7977 825.17 SFN2013 [email protected] θ β_ β / +0.4 -0.4 +0.4 -0.4 +0.8 -0.8 θ β_ β / θ β_ β / L fraction correct S: MC S: DT coordinate value 0 -1 0 +1 0 -1 0 +1 0 -1 0 +1 Coordinate Axes α α γ γ θ θ θ θ θ θ θ θ θ θ θ θ β \ β / β_ β | β \ β \ β / β / β_ β_ β | β | # checks in correlation: +1 -1 L L L L 0 1st order 2nd order 3rd order 4th order Each strip shows the textures generated by varying one coordinate across its entire range, from -1 to +1. A coordinate value of 0 corresponds to a random texture. Methods and Psychometric Functions SUBJECTS 6 subjects VA: 20/20, with correction if needed Practice: approx 1600 trials CONDITIONS 8 repeats of 20 on-axis points 16 repeats of 8 off-axis points 288 trials per block, random order 15 blocks = 4320 trials per plane Feedback during practice only STIMULI Pixel Size: 14 min Display Size: 14.8 deg 2 Binocular viewing at 1m Contrast: 1.0 Duration: 120 ms (followed by mask) Target: 16 x 64 pixels on a 64 x 64 array Trials either have a structured target on a random background, or random target on structured background TASK Find the location of the target stripe (4-AFC, top, right, bottom, left) In this sample stimulus, the target stripe (defined by ) is on the bottom on a random background. Here, the target stripe (on the left) is random on a structured ( ) background. θ L Thresholds were not significantly different for these two conditions and did not depend on target location. θ L Plots show fraction correct for stimuli that vary along a single texture coordinate. Performance is similar for positive and negative excursions of a coordinate, and was highly consistent across subjects (MC and DT). Curves are maximum-likelihood fits to Weibull functions (shape parameter range: 2.2 - 2.6). Error bars are 95% confidence limits. Isodiscrimination Contours in Selected Coordinate Planes γ α γ α S: MC S: AA S: DT θ γ θ γ L S: MC S: AA S: RM β \ β / β \ β / S: JB S: JD S: DT θ θ θ θ L L S: DT S: KP S: MC Note the consistent deviation from an elliptical contour. Ellipsoid model for discrimination in the entire 10-D space = ∑ 2 , , ij i j ij d Q cc Q i,j are the elements of a symmetric, positive-definite matrix c i are the texture coordinates d is the perceptual distance from the random texture (d=1 corresponds to threshold) Thresholds and Model Fits in All 15 Unique Coordinate Planes The ellipsoid model and psychophysical data are in good agreement for each subject. We next use the ellipsoid model to compare across subjects (next column), and then show that it correctly predicts sensitivities to directions in the texture space not used to fit the model (final column). Subject MC DT DF Mean 0.031 0.031 0.047 0.038 0.065 0.086 0.091 0.085 Corrected Raw Goodness of Fit (rmse) JD 0.043 0.099 The raw rmse is the root- mean-squared deviation between the predictions of the ellipsoid model and the measured thresholds. The corrected rmse compares the predictions of the ellipsoid model with the best possible predictions of any opponent model, i.e., any model that predicts equal thresholds for positive and negative deviations of the image statistics. 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 - + m 4 m 8 m 4 + m 8 s y m1 s y m2 s y m3 s y m4 s y m 5 h v i1 h v i2 m 4 - - m 8 m 6 L-m6R Ellipsoid Model Predicts Sensitivities in Multiple Directions in the Texture Space Consistency Across Subjects normalized sensivity first order second order third order fourth order MC DT JD DF mean - + sym1 sym2 sym3 sym4 sym5 hvi1 hvi2 dii rotB rotA Example textures representing the 10 principal axes. On each axis, texture samples are shown in both directions from the origin (which corresponds to the random texture). Correlations strengths, which correspond to distance from the origin, are 0.18 (for sym1 and sym2), and 0.36 (for the remaining textures). The pie charts show the contributions of first-, second-, third-, and fourth-order correlations to each direction. Sensitivity positive direction negative direction prediction CONCLUSIONS MC DT SR KP For each subject, model prediction and measured sensitivities are shown for 12 directions. The first seven directions are principal axes of the ellipsoid. (Only seven principal axes are tested, because the other three axes are in the coordinate planes, and therefore not out- of-sample.) The last five directions are Minkowski directions, which correspond to textures that have maximum or minimum porosity, as quantified by the number of holes per unit area. Psychophysical sensitivity to image statistics of low and high order can be modeled by ellipsoidal isodiscrimination contours. This model accurately predicts sensitivities to combinations of image statistics, including combinations that are predicted to be maximally salient, and combinations predicted to be undetectable. S:MC data +/ - 95%CL fit γ β _ β _ β / θ γ β \ θ β \ α γ θ α θ θ γ α β \ θ θ β _ β | β \ β _ β _ β / β \ θ θ α L L L L L L L L L γ β _ β _ β / θ γ β \ θ β \ α γ θ α θ θ γ α β \ θ θ β _ β | β \ β _ β _ β / β \ θ θ α L L L L L L L L L S:DF data +/ - 95%CL fit A model of sensitivity to binary local image statistics: Testing the predictions Mary M. Conte, Syed M. Rizvi, Daniel J. Thengone, Jonathan D. Victor Brain & Mind Research Institute, Weill Cornell Medical College, NY Motivation and Overview Early cortical stages of visual analysis rely on processing of local correlations, as these define the elements (lines, edges, and texture) that must be extracted for scene segregation and object identification. In natural images, these correlations are of low and high order, and occur together in complex mixtures. To analyze how they are processed, we synthesize image sets in which they vary independently – thus generating a 10-dimensional “texture space”. Stimuli drawn from this space enable characterization of perceptual sensitivities to many kinds of individual image statistics, alone and in combinations. We made measurements of perceptual sensitivities along all 10 axes of the space, and in planes determined by their pairs. In each of the planes, the contours are nearly elliptical, and the shapes and orientations of the ellipses were similar across subjects. The elliptical contour shape suggests that sensitivity in the full 10-d space is described by an ellipsoid. Since the 10-d ellipsoid is uniquely determined by in-plane measurements, the model predicts visual sensitivity to complex combinations of image statistics. As we show, these predictions are accurate. The planar plots show all of the experimentally determined thresholds in each of the coordinate planes tested, along with 95% confidence limits (via bootstrap), and fits of the ellipsoid model. Some predicted contours deviate slightly from ellipses because they take into account the values of out-of-plane parameters.
Transcript of A model of sensitivity to binary local image statistics ...jdvicto/vps/sfn13_corztg.pdf · sym1...
Supported by EY7977
825.17SFN2013
+0.4-0.4 +0.4-0.4 +0.8-0.8
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coordinate value0 -1 0 +1 0 -1 0 +1 0 -1 0 +1
Coordinate Axesααγγ θθθ θθθθθθθ θθβ\ β/β_ β| β\β\ β/β/β_β_ β|β|
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1st order 2nd order 3rd order 4th order Each strip shows the textures generated by varying one coordinate across its entire range, from -1 to +1. A coordinate value of 0 corresponds to a random texture.
Methods and Psychometric FunctionsSUBJECTS6 subjectsVA: 20/20, with correction if neededPractice: approx 1600 trials
CONDITIONS8 repeats of 20 on-axis points16 repeats of 8 off-axis points
288 trials per block, random order15 blocks = 4320 trials per planeFeedback during practice only
STIMULI Pixel Size: 14 min Display Size: 14.8 deg2
Binocular viewing at 1m Contrast: 1.0Duration: 120 ms (followed by mask)Target: 16 x 64 pixels on a 64 x 64 arrayTrials either have a structured target on a random background, or random target on structured background
TASKFind the location of the target stripe (4-AFC, top, right, bottom, left)
In this samplestimulus, the target stripe (defined by )is on the bottomon a randombackground.
Here, the target stripe (on the left)is random on astructured ( )background.
θ L
Thresholds were not significantly different for these two conditionsand did not depend on target location.
θ L
Plots show fraction correct for stimuli that vary along a single texturecoordinate. Performance is similar for positive and negative excursions of acoordinate, and was highly consistent across subjects (MC and DT). Curvesare maximum-likelihood fits to Weibull functions (shape parameter range: 2.2- 2.6). Error bars are 95% confidence limits.
Isodiscrimination Contours in Selected Coordinate Planes
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Note the consistent deviationfrom an elliptical contour.
Ellipsoid model for discriminationin the entire 10-D space
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Qi,j are the elements of a symmetric, positive-definite matrix
ci are the texture coordinates
d is the perceptual distance from the random texture(d=1 corresponds to threshold)
Thresholds and Model Fits in All 15 Unique Coordinate Planes
The ellipsoid model and psychophysical data are ingood agreement for each subject. We next use theellipsoid model to compare across subjects (nextcolumn), and then show that it correctly predictssensitivities to directions in the texture space notused to fit the model (final column).
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CorrectedRawGoodness of Fit (rmse)
JD 0.0430.099
The raw rmse is the root-mean-squared deviationbetween the predictions ofthe ellipsoid model and themeasured thresholds. Thecorrected rmse comparesthe predictions of theellipsoid model with the
best possible predictions of any opponent model, i.e., anymodel that predicts equal thresholds for positive andnegative deviations of the image statistics.
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Ellipsoid Model Predicts Sensitivities in Multiple Directions in the Texture Space
Consistency Across Subjects
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Example textures representing the 10 principal axes.On each axis, texture samples are shown in both directionsfrom the origin (which corresponds to the random texture).Correlations strengths, which correspond to distance fromthe origin, are 0.18 (for sym1 and sym2), and 0.36 (for theremaining textures). The pie charts show the contributionsof first-, second-, third-, and fourth-order correlations toeach direction.
Sen
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positive directionnegative directionprediction
CONCLUSIONS
MC
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For each subject, model prediction and measured sensitivities areshown for 12 directions. The first seven directions are principal axesof the ellipsoid. (Only seven principal axes are tested, because theother three axes are in the coordinate planes, and therefore not out-of-sample.) The last five directions are Minkowski directions, whichcorrespond to textures that have maximum or minimum porosity, asquantified by the number of holes per unit area.
Psychophysical sensitivity to image statistics of low andhigh order can be modeled by ellipsoidal isodiscriminationcontours.
This model accurately predicts sensitivities to combinationsof image statistics, including combinations that arepredicted to be maximally salient, and combinationspredicted to be undetectable.
S:MC
data +/ - 95%CL
fit
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A model of sensitivity to binary local image statistics: Testing the predictions Mary M. Conte, Syed M. Rizvi, Daniel J. Thengone, Jonathan D. Victor
Brain & Mind Research Institute, Weill Cornell Medical College, NY
Motivation and OverviewEarly cortical stages of visual analysis rely on processing of localcorrelations, as these define the elements (lines, edges, and texture)that must be extracted for scene segregation and objectidentification. In natural images, these correlations are of low andhigh order, and occur together in complex mixtures. To analyze howthey are processed, we synthesize image sets in which they varyindependently – thus generating a 10-dimensional “texture space”.Stimuli drawn from this space enable characterization of perceptualsensitivities to many kinds of individual image statistics, alone and incombinations.
We made measurements of perceptual sensitivities along all 10 axesof the space, and in planes determined by their pairs. In each of theplanes, the contours are nearly elliptical, and the shapes andorientations of the ellipses were similar across subjects. The ellipticalcontour shape suggests that sensitivity in the full 10-d space isdescribed by an ellipsoid. Since the 10-d ellipsoid is uniquelydetermined by in-plane measurements, the model predicts visualsensitivity to complex combinations of image statistics. As we show,these predictions are accurate.
The planar plots show all of the experimentally determined thresholdsin each of the coordinate planes tested, along with 95% confidencelimits (via bootstrap), and fits of the ellipsoid model. Some predictedcontours deviate slightly from ellipses because they take into accountthe values of out-of-plane parameters.
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