Modeling the detection of blurred visual targets

in non-homogeneous backgrounds

Albert J. Ahumada¹, Bettina L. Beard¹, and Karen M. Jones²

¹NASA Ames Research Center, Moffett Field, CA 94035-1000,

²San Jose State University Foundation, San Jose, CA

ABSTRACT

Detection models work well for targets on uniform or homogeneous backgrounds. How well do they work for the detection of airframe cracks in their natural setting by actual inspectors? How well do they predict the performance when the images are blurred?

We measured crack detection performance for 7 experienced inspectors and 2 non-inspectors.* Signal images were formed by subtracting a crack-removed image from the original image. An attenuated-crack image at a desired contrast level was generated by attenuating the difference image and adding it back to the crack-removed image. The visual resolution was 70 pixels per deg. The display background screen had a luminance of 40 cd/m². The images were Gaussian blurred with spreads of 0, 1.1, 1.7, and 2.3 arc min. Contrast attenuation thresholds were obtained using a 2IFC staircase. The crack-removed image remained on for the duration of a block of trials. At least 3 replications were obtained. Attenuation thresholds for 75% correct were estimated by probit analysis.

Two measures of contrast energy were computed, the visible contrast energy in the signal and that energy attenuated by local visible contrast energy (gain-control masking). Local contrast was computed from a local luminance image computed by blurring the luminance image with the surround of a DoG CSF. The same 8 min spread was used to compute an average local masking energy image. The visible energy of the un-blurred signals correlated well with the average contrast thresholds over the 15 cracks (r = -0.89). Including masking raised the correlation (r = -0.95). Blur raised the thresholds much more than the loss in visible contrast energy. For the images with the greatest loss in visible contrast energy (4.7 dB) at the 1.7 min blur, the average threshold loss was 10 dB. This 5.3 dB discrepancy may result from a lack of experience with blur, or the blur may affect higher order processes such as edge extraction.

Models can predict target detection on homogeneous backgrounds

Mean threshold prediction error for each ModelFest target for the Contrast Energy Model (Watson, 2000).

The reported RMS error was 2.3 dB.

Here we report error adjusted by the number of parameters estimated, which increases this error to 2.8 dB.

The Difference-of-Gaussian CSF Contrast Energy Model (below) has an error of 3.0 dB with the parameters, fc = 14.9 cycle/deg and fs = 1.35 cycle/deg.

Homogeneous Background Model

Contrast from luminance image I and background L0:

C(x,y) = I(x,y) / L0 – 1

Visible contrast from Difference-of-Gaussian filtering:

V(x,y) = C(x,y) * (e^{-(f/fc)^2} – e^{-(f/fs)^2} )

Visible contrast energy is constant at threshold: S V(x,y) ² = k

Can models predict the detection of airframe cracks?

Image with crack (above)

Image with crack removed in Photoshop (below).

What if the images are blurry?

Image (with crack) blurred with a Gaussian filter with a standard deviation of 2.4 arc min.

We assume that the 20/20 observer has a blur standard deviation of 1.4 arc min.

The combined spread will double that of the 20/20 observer and result in an equivalent acuity of 20/40.

Non-homogeneous background model

(Ahumada & Beard, 1998)

No Masking Version

‘Optical’ blur: B(x,y) = I(x,y) * e^{-(f/fc)^2}

Local luminance: L(x,y) = B(x,y) * e^{-(f/fs)^2}

Visible contrast: V(x,y) = B(x,y) / L(x,y) – 1

Difference signal: D(x,y) = V_S (x,y) –V_N (x,y)

Signal energy is constant at threshold: S D(x,y) ² = k

Contrast Gain Masking

Masked visible contrast: M(x,y) = V(x,y) / (1 + m V(x,y)² * e^{-(f/fs)^2} )^0.5

Difference signal: D(x,y) = M_S (x,y) – M_N (x,y)

Signal energy is constant at threshold: S D(x,y) ² = k

Methods

Signal images were formed by subtracting a crack-removed image from the original image.

An attenuated-crack image at a desired contrast level was generated by attenuating the difference image and adding it back to the crack-removed image.

The images were Gaussian blurred, giving nominal acuities of 20/20 (no blur), 20/30, 20/40 and 20/50.

Crack detection contrast thresholds were measured for 7 experienced inspectors and 2 non-inspectors.

The non-inspectors collected data on 10 images.

Three inspectors saw subsets of these images.

Four inspectors used another set of 5 images.

Contrast attenuation thresholds were obtained using a 2IFC staircase.

The crack-removed image remained on for the duration of a block of trials.

Attenuation thresholds for 75% correct were estimated by probit analysis.

The score for an observer and an image was the median of 3 or 4 replications.

Results

Prediction error pooled over observers and images:

No-Masking Model (fc = 17 cpd, fs = 2.1 cpd): 4.0 dB

Masking Model (m = 400): 3.5 dB

When the ModelFest error is pooled in the same way rather than averaged, it gives a value of 3.9 dB

[ModelFest scores are the mean of four replications, the staircases were more efficient, and the parameters were optimized.]

The effect of the blur on observer detectability was larger than that predicted by the model, consistent with the finding that classification images for Gaussian blobs are smaller than the blob itself (Abbey and Eckstein, 2002).

The median contrast sensitivity on the no-blur images of the 7 maintenance inspector observers was 3.3 dB worse than that of the ModelFest observers (7 dBB).

The other 2 observers had more experience with the task and were negligibly (0.2 dB) worse than the ModelFest observers.

Conclusions

The model for non-homogeneous backgrounds with contrast gain masking predicted as well as the corresponding uniform background detection model predicted detection threshold for the ModelFest stimuli.

The model under-predicts the effect of blur.

This may result from a lack of experience with blur, inefficient templates, or the blur may affect higher order processes such as edge extraction.

References

Abbey, C.K. Eckstein, M.P. (2002) Classification image analysis: Estimation and statistical inference for two-alternative forced-choice experiments Journal of Vision 2(1), 66-78.

Ahumada, A.J., Beard, B.L. (1997). Image discrimination models predict detection in fixed but not random noise. Journal of the Optical Society of America A 14, 2471-2476.

Ahumada, A.J., Beard, B.L. (1998) A simple vision model for inhomogeneous image quality assessment, Society for Information Display Digest 29, 641-644.

Beard, B.L., Frank, T.A., Ahumada, A.J. (2003) Using vision modeling to define occupational vision standards, Human Factors and Ergonomics Society Annual Meeting (October 15, Denver, CO).

Watson, A.B. (2000) Visual detection of spatial contrast patterns: Evaluation of five simple models, Optics Express 6(1), 12-33.

Acknowledgments

Supported by FAA/NASA Agreement DTFA-2045 and the HMP Project of NASA's Airspace Systems Program.

We appreciate the assistance of Cynthia Chacon.