Miller and Bernard argue that photoreceptor sampling occurs at the inner rather than outer segments. Foveal inner segments form a lattice-like array that should create visible Moiré patterns when frequencies above 60 c/deg are image by interferometry. Despite a checkered past, this prediction is confirmed by recent experiments. Extrafoveally, frequencies above the nominal Nyquist limits of the cones are routinely present in the retinal image. Spectral analysis shows that the inner segments there form optimally irregular sampling arrays that avoid Moiré distortion by scattering supra-Nyquist frequencies into broadband noise. Thus is appears that topological disorder in the receptor mosaic prevents aliasing outside the fovea--the only place it could occur in normal vision.

Sometimes a solid object seen with both eyes can seem to reverse perspective. A study of this geometrically irrational experience suggests that ordinary depth perception is somewhat precarious

Optical transforms were used to compute the power spectra of rhesus cones treated as arrays of image sampling points. Spectra were obtained for the central fovea, parafovea, periphery, and far periphery. All were consistent with a novel spatial sampling principle that introduces minimal noise for spatial frequencies below the Nyquist limits implied by local receptor densities, while frequencies above the nominal Nyquist limits are not converted into conspicuous moiré patterns, but instead are scattered into broadband noise. This sampling scheme allows the visual system to escape aliasing distortion despite a large mismatch between retinal image bandwidth and the Nyquist limits implied by extrafoveal cone densities.

Constant volume (CV) operators are nonlinear image processing operators in which the area covered by the pointspread function around each point in the input image varies inversely with the light intensity at that point. This operation is designed to make spatial resolution increase with retinal illuminance, but it proves to have unexpected side-effects that mimic other important properties of human spatial vision, including Mach bands and Weber’s law. Mach bands are usually attributed to lateral inhibition in the retina, and when retinal image processing is modeled by a linear operator they imply such inhibition, since they cannot be produced by a nonnegative impulse response. CV operators demonstrate that Mach bands and other high-pass filter effects can be created by purely positive pointspread functions, i.e., without inhibition. This paper shows in addition that if one attempts to combine lateral inhibition with a CV operation, the results are dramatically wrong: the edge response always contains Mach bands that bulge in the wrong direction. Thus within the nonlinear theoretical framework provided by CV operators, lateral inhibition is neither necessary nor sufficient for modeling Mach bands and other high-pass filter properties of spatial vision. © 1989.

In choice reaction time tasks, response latency varies as the subject changes his bias for speed vs accuracy; this is the speed-accuracy tradeoff. Ollman’s Fast Guess model provides a mechanism for this tradeoff by allowing the subject to vary his probability of making a guess response rather than a stimulus controlled response (SCR). It is shown that the mean latency of SCR’s (μs) in two-choice experiments can be estimated from a single session, regardless of how the subject adjusts his guessing probability. Three experiments are reported in which μs apparently remained virtually constant despite tradeoffs in which accuracy varied from chance to near-perfect. From the standpoint of the Fast Guess model, this result is interpreted to mean that the tradeoff here was produced almost entirely by mixing different proportions of fast guesses and constant (mean) latency SCR’s. The final sections of the paper discuss the question of what other models might be compatible with μs invariance. © 1971.

Holman and Marley have shown that Thurstone’s Case V model becomes equivalent to the Choice Axiom if its discriminal processes are assumed to be independent double exponential random variables instead of normal ones. It is shown here that for pair comparisons, this representation is not unique; other discriminal process distributions (specifiable only in terms of their characteristic functions) also yield a model equivalent to the Choice Axiom. However, none of these models is equivalent to the Choice Axiom for triple comparisons: There the double exponential representation is unique. It is also shown that within the framework of Thurstone’s theory, the double exponential distribution, and hence the Choice Axiom, is implied by a weaker assumption, called "invariance under uniform expansions of the choice set.". © 1977.

If f and g are nonvanishing characteristic functions the functional equation g(s)g(t)g(-s - t) = f(as)f(at)f(-as - at) implies g(s) = eibsf(as), i.e., f and g corresponding to probability distributions of the same type. It is shown here that when f and g are allowed to vanish this equation also has solutions in which f and g correspond to distributions of different types. The practical implication is that there are nonequivalent. Thurstone models which cannot be discriminated by any choice experiment with three objects. © 1978.

Additional theoretical and experimental results are presented for a choice reaction time performance model described by Oilman (1966). A formula is given for estimating the latency distribution of true recognition responses from the results of a single session; the estimate is invariant with respect to changes in the proportion of “guess” responses and with respect to fluctuations in the latency distribution of guesses. © 1967, Psychonomic Press. All rights reserved.