A Local Luminance Metric

Albert J. Ahumada, NASA-Ames Research Center, al.ahumada@nasa.gov

Question. The contrast image C(x,y) is usually computed from the luminance image L(x,y) and the background luminance L₀ as C(x,y) = (L(x,y) – L₀)/L₀.

What should L₀ be to compute the contrast of the crack in this image?

A Simple Answer. The luminance L₀(x,y) for the contrast of a point (x,y) is the average luminance near that point, the blurred image L₀(x,y) = L(x,y) * S_L(x,y).

A convenient blur function is the Gaussian

S_L(x,y) = (1/(2p s_L²)) exp(- (x² + y²)/(2 s_L²)).

What should we use for the standard deviation s_L?

Estimation Strategy. Ahumada and Beard (1998) computed “visible” contrast on a slowly varying background by first using an “optical blur” low-pass filter S_B(x,y) to get a blurred luminance image B(x,y), then a “luminance-spread” low-pass filter S_L(x,y) to get a local luminance image L₀(x,y). The “visible” contrast at each point was then C_V(x,y) = (B(x,y) - L₀(x,y)) / L₀(x,y).

What value of s_L best predicts target detection?

Computational Simplification: For targets on a uniform background, very similar “visible” contrast values are obtained by first computing luminance contrast from the uniform background (paragraph 1) and then filtering with a contrast sensitivity function computed as the difference between the two low pass filters,

CSF = S_B(x,y) - S_L(x,y).

Method. To estimate the local luminance spread function S_L(x,y), two-component CSFs were fit to the uniform-background Modelfest detection thresholds from 16 observers. Thresholds were predicted by visible contrast energy.

Balanced Surround CSF. For the 10 constant-width, cosine-phase Gabor images, these thresholds were fit by the above equal-volume or zero-DC-response Difference-of-Gaussian CSF. Using one value of s_L for all observers gave a good fit to the thresholds (error standard deviation = 3 dB). The estimated s_L = 0.56 deg.

Unbalanced Surround CSF. When all 43 Modelfest images were included in the analysis, an unbalanced CSF of the form S_B(x,y) – a S_L(x,y) fit better, where a is about 0.8. The estimated s_L depends somewhat on the function used to represent S_B(x,y). Watson and Ahumada (2005) estimated s_L = 0.42 deg for the Gaussian S_B(x,y), but values ranged from 0.28 deg to 0.32 deg for the better fitting S_B(x,y) functions.

Discussion. While the high frequency limb of the CSF is the result of optics and a cascade of neural factors, the low frequency limb is purely neural and can be thought of as defining local luminance. This local luminance spread can be used for predicting detection on non-uniform backgrounds. In the corresponding local luminance model, L₀(x,y) is the blurred weighted average of the image and the background that preceded the image, L₀(x,y) = (a L(x,y) + (1- a) L₀) * S_L (x,y).

The DC response parameter 1- a may represent the contribution of the background prior to the stimulus on a uniform background.

Acknowledgement. Support provided by NASA Aerospace Systems.

References

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

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

Bowen and Wilson (1994) A two-process analysis of pattern masking, Vision Research 34, 645–657.

ModelFest URL: http://vision.arc.nasa.gov/modelfest/.

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