1999 ARVO Talk Outline
  • Title

  • Introduction

  • Beard & Ahumada (1999 JOSA)

    Brooke Ashley Beard, born on March 23, 1999.







    • Summary

    A "reverse correlation" or response correlation analysis of the noises in a detection task can reveal relevant stimulus features.





    Introduction
    The response correlation image method has clarified observer classification rules for discrimination tasks. Here we apply the method to detection. If detection is based on a single filter output, the method should show an image of the filter.





    Experimental Methods
  • Stimuli:
    Duration: 0.5 sec
    White Noise:
    50% contrast
    2 deg square, 64 pixels/deg
    Gabor Signals:

    Circular Gaussian window, 1/e diameter: 0.31 deg

    Horizontal sine phase grating, 2 or 16 cycles/deg

    Fixation marks:
    1 deg from signal, noise center
    Horizontal, vertical pairs
    Always present
  • Task:
    Yes-No, "signal present" or "signal absent"
  • Observers:
    GP, CS, BLB, AA
  • Procedure:
    Blocks of 100 trials.
    Number of blocks: 
         2 cpd  16 cpd
 GP   48     82
 CS   59     80
 BLB  23     26
 AA   15     20
    2 cpd blocks run first.
    Each noise appeared twice within the same block with the same signal condition.






    • Response Correlation Images
    6 Stimulus/Response trial types:

    No-Signal or Signal:
    S0, S1
    0, 1, or 2 "Signal Present" responses:
    R0, R1, R2

    Average noise for trial type Si, Rj:
    AveNoise(Si,Rj)

    Response Correlation Images:

    No-Signal:
    Image(S0) = AveNoise(S0,R2) - AveNoise(S0,R0)
    Signal:
    Image(S1) = AveNoise(S1,R2) - AveNoise(S1,R0)
    Results

    Trial Type Frequency Table 
                        2 cpd
            S0               S1
      R0    R1   R2     R0   R1    R2
GP    557  443  209    136  344   711
CS    911  417  149    180  352   941
BLB   377  155   60     90  128   340
AA    212  102   47     44   85   260

                   16 cpd
            S0               S1
      R0    R1   R2     R0   R1    R2
GP   1246  650  217    305  805   877
CS   1290  552  115    370  657  1016
BLB   452  145   42    128  189   344
AA    290  160   52     49  131   318
    Response Correlation Images: 
    

    

    
2 cpd:   S0           S1

    

    
 GP  

    
 CS  

    
BLB  

    
 AA  

    

    

    
16 cpd:   S0          S1

    

    
 GP  

    
 CS  

    
BLB  

    
 AA






    Reduced Dimension Correlation Images

    Reduced dimension components are normalized to have unit variance.

    The N by 1 column "image" element j is formed by cross-multiplying image row j with the signal Gaussian window and summing: 

    ColumnImage  = Sum Image   Gauss
           j    k       j,k     k

    Figure Below. Column images for 4 observers GP, CS, BLB, and AA for 2 cpd. No-Signal image on left, Signal image on right. No-Signal and Signal images themselves at bottom. Absissa is noise row position, top to bottom. Ordinate is response correlation score normalized to have unit variance.

    Figure Below. Column images for 16 cpd.

    The 1 by 1 signal "image" is formed by cross-multiplying the correlation image with the Gabor signal image and summing: 

    SignalImage = Sum Image   Gabor
              j,k      j,k     j,k

    The phase-independent signal amplitude "image" is formed by computing signal "images" and signal quadrature "images" for each noise sample and then summming their squares to get the phase-independent amplitudes. The correlation image calculation is then applied with these "images" in place of the noise. 

    SigPhase =  Sum Image   Gabor
            j,k      j,k     j,k


    QuadPhase =  Sum Image   Gabor
             j,k      j,k     j+1,k


                       2           2
SigAmp = SigPhaseIm + QuadPhase






    Signal Component "Images" 

              2 cpd          16 cpd
       S0      S1      S0      S1 
GP    8.94   11.91    0.88    6.85
CS    9.11   19.34    2.33   19.86
BLB   5.17   12.92   -1.59   12.61
AA    6.91    9.47    3.08    6.47

    Signal Phase-Independent Amplitude "Images" 

            16 cpd
      S0      S1 
GP   0.43    0.14
CS   5.46    4.42
BLB  3.99    0.29
AA   3.72   -0.64






    • Result Summary

  • 2 cpd:
    Signal and No-Signal images resemble signal
    No-Signal images have lower amplitude

  • 16 cpd:
    Signal images resemble signal
    No-Signal images are featureless.
    No-Signal responses correlate with phase-independent signal amplitude
  • Conclusions

  • References

    aa0202.gif corim02.htm gab162.gif line16u.gif stim.htm aa0212.gif corim16.htm gp0202.gif pairs.htm tb0202.gif aa1602.gif corimcal.htm gp0212.gif proc.htm tb0212.gif aa1612.gif cs0202.gif gp1602.gif tb1602.gif bab.htm cs0212.gif gp1612.gif resp.htm tb1612.gif colim02.htm cs1602.gif intro.htm respfreq.htm colim16.htm cs1612.gif line02.gif ressumm.htm colimcal.htm gab02.gif line02u.gif sigimcal.htm gab022.gif line16.gif sigimtab.htm