Multipole-Based CSF Estimates Predict Crack Detection Individual Differences

Albert J. Ahumada and Bettina L. Beard

NASA Ames Research Center

http://vision.arc.nasa.gov/personnel/al/ahumada.html

Introduction: For an airframe crack detection project (Beard, Jones, Chacon, and Ahumada, 2005), we wanted to measure the contrast sensitivity functions (CSFs) of the inspectors. We wanted to use the same equipment, so we wanted to use stimuli that did not require special techniques to present the threshold stimuli, so we decided against windowed gratings. Klein (1989) had proposed using multi-pole stimuli to estimate CSFs. Line segments (monopoles) are similar to the cracks that the inspectors were asked to detect in airframe images. Figure 1 shows an airframe crack image; Figure 2 shows the multipole experiment stimuli.

Figure 1. Example airframe crack detection images: (above or left) image with crack, (below or right) image with crack removed.

Method: For our Sony Trinitron CRT gamma function, it was possible to choose a line width (0.5 arc min) length (8 arc min), and duration (0.25 sec) such that below-threshold lines were easily presented. Dipoles and quadapoles require matching positive and negative levels, a condition not met exactly, but the unwanted line components were well below threshold. Thresholds were estimated for 9 observers.

Figure 2. Multipole experiment images: square, line, dipole, and quadrapole.

Results: Two parameters were estimated for each observer, the overall sensitivity factor and the Difference-of-Gaussian CSF center frequency cutoff. These same two parameters were estimated for each observer using contrast thresholds from crack detection in actual airframe images. There was agreement among the two sets of parameters (Figures 3a and 3b, but there was a strong correlation between the two crack detection parameters (Figure 3c), suggesting a single variable was the source of the individual differences.

Figure 3. Scatter plots and rank correlations among estimates. 3a) DoG center standard deviation estimates for the two experiements. 3b) Contrast sensitivity estimates for the two experiments. 3c) The two parameters for the crack image detection experiment.

Question: For the Modelfest (2001) data, what happens when you estimate the observer CSFs, from the multipole-like stimuli separately and also estimate them from the fixed-width Gabors?

Methods: For each of the 16 observer, the difference-of-Gaussian CSF center spread was estimated for three subsets of the images:

1.The 10 fixed-width Gabors (Figure 4).

2.Seven non-periodic images: 4 Gaussian blobs and a Gaussian-windowed edge, line, and dipole (Figure 5).

3.The line and the dipole.

Figure 4. The first 7 of the 10 fixed-width Gabors (the higher frequencies aliased badly).

Figure 5. Modelfest images 26-32, four sizes of Gaussian blobs and Gaussian-windowed edge, line, and dipole.

Results: The median DoG CSF center standard deviations in arc min for the 10 fixed-width Gabors were clustered close to 1.5 min. The estimates based on the 7 non-periodic images (26-32) were more spread out and had a larger median (Figure 6a). The estimates based on the line and the dipole (31, 32) were also larger (Figure 6b), suggesting that the mediating variable is not simply spatial uncertainty.

Figure 6. Gabor image based estimates of DoG center standard deviation for 16 Modelfest observers plotted against estimates based on a) images 26-32 and b) the line and dipole images.

Conclusions:

Within the context of visible contrast energy based CSF estimation, multipoles with higher spatial frequency content are not as visible as one would expect from the Gabor-derived CSFs.

Individual differences in multipole-derived CSFs seem likely to be strongly affected by variables other than CSF shape.

References

Ahumada & Beard (1998) A simple vision model for inhomogeneous image quality assessment, SID Digest 29, 641-644.

Beard, Jones, Chacon, and Ahumada (2005) Detection of blurred cracks: A step towards an empirical vision standard, Final Report for FAA Agreement DTFA-2045.

Klein (1989) Visual multipoles and the assessment of visual sensitivity to displayed images, SPIE Proc. 1077, 83-92.

ModelFest (2001) http://vision.arc.nasa.gov/modelfest/

Watson & Ahumada (2005) A standard model for foveal detection of spatial contrast, Journal of Vision (accepted).

Acknowledgement: Support provided by NASA Aerospace Systems and the FAA.