From the light that falls on the retina, the visual system must extract meaningful information about what is where in our environment. At an early stage in this process, it analyzes the incoming ...sensory data along many dimensions of pattern vision. This book describes the current knowledge about this stage of visual processing, focusing both on psychophysical experiments measuring the detection and identification of near-threshold patterns and on the mathematical models used to draw inferences from such experimental results. Neurophysiological evidence is presented and compared critically to the psychophysical evidence. Orientation, spatial frequency, direction of motion, and eye of origin are among the many dimensions of spatiotemporal pattern vision for which experimental results and mathematical models are reviewed. Introductory material on psychophysical methods, signal detection theory, and the mathematics of Fourier analysis is also given. The preface gives a guide to the organization of the book and to what parts of the book can be read independently of one another. The last two chapters contain lists of references organized by dimensions of pattern vision. An appendix at the end of the book lists the assumptions used in the models both in order of appearance and in groups according to function.
Intrinsic uncertainty arises from sources intrinsic to the observer, in particular from the observer's inability to attend to only the relevant information (attention limitations) and inability to ...remember the set of possible stimuli (memory limitations). This intrinsic uncertainty can be incorporated into the models based on multiple independent analyzers that were presented in the previous chapter for cases of extrinsic uncertainty. This chapter considers the interaction of uncertainty assumptions with the transducer function (output versus input function) of individual analyzers; the overall transducer function of all the analyzers used by the decision rule; the psychometric function for the observer; and the ROC curves. The control of attention and individual differences is discussed.
The seventeen dimensions of pattern vision considered in this book are mutually independent in the following sense: specifying the stimulus value on any one dimension does not give the value on any ...other. They are not, however, mutually independent in another important sense: if two patterns differ only along certain dimensions, the two sub-populations of analyzers they excite differ not only along that dimension but also along others. These dimensional interdependencies dramatically complicate interpretation of experiments designed to reveal multiple visual analyzers or similar entities. This chapter summarizes these interdependencies, as well as other factors complicating the interpretation of analyzer-revealing experiments. Their implications for the results on each pattern vision dimension are discussed. The complications in interpretation apply to many other domains as well as to pattern vision.
Some Mathematics Graham, Norma van Surdam
Visual Pattern Analyzers,
12/1989
Book Chapter
This chapter provides the mathematical background for using Fourier Analysis (Linear Systems Analysis) to study visual pattern analyzers. It introduces sinusoidal, Gabor, and delta functions as ...applied to descriptions of neurons' receptive fields and visual stimuli. It describes how a linear system's responses to simple stimuli can predict the system's responses more generally. Bandwidth is the range of values along a dimension to which a system can respond and is represented in the system's Fourier Transform. The chapter provides insight into how bandwidth depends on the particular properties of a system's weighting function (receptive field) and presents a table of the relationships. Because different investigators have described bandwidth using different measures, a table of conversions among the bandwidth measures is provided. An appendix at the end of the chapter presents the material more formally.
Summation experiments using patterns that are far apart along any dimension (e.g., two lines of very different orientations) can answer the question of whether there are multiple analyzers along that ...dimension. Two classes of models are presented: probabilistic models in which variability in analyzers' outputs causes increased performance (probability summation); and deterministic models that predict increased performance without assuming variability by incorporating nonlinear pooling (Minkowski, Quick) into decision rules. This chapter presents the results on the spatial-frequency dimension (and their possible dependence on retinal inhomogeneity). An appendix derives convenient formulas in terms of observable quantities to allow easy use of the models in many situations. This chapter together with Chapters 7 through 10 cover what is sometimes called multidimensional signal detection theory.
Parametric experiments measure an observer's contrast sensitivity as a function of value along any dimension. These parametric experiments are not very useful for distinguishing between ...single-analyzer and multiple-analyzer models, nor do they give useful information about the peak sensitivities of multiple analyzers or the sensitivity function of individual analyzers. Rather, these experiments tell us about the overall (envelope) sensitivity of the whole set of multiple analyzers. This chapter describes parametric contrast sensitivity on the seventeen visual pattern dimensions. Two issues in the chapter are of particular theoretical interest: the description of sensitivity changes with spatial position in the visual field (size-scaling models, cortical magnification factors) and with mean luminance (adaptation, constant-flux models). A list of references to parametric experiments organized by visual pattern dimension is presented.
This chapter continues Chapter 9's description of identification experiments by describing three more paradigms: simple detection and identification; the 2x2 paradigm; and concurrent identification. ...The models of Chapter 9 are used with new decision rules added for two of the additional paradigms. It discusses the effects of relaxing the assumptions (e.g., allowing correlation among analyzer outputs) and how one can measure these effects in the identification paradigm. It also discusses transducer functions and imperfect attention as they affect results of identification experiments. This and the preceding chapter are illustrated with results of experiments on the spatial-frequency dimension.
This chapter considers the uncertainty arising from sources extrinsic to the observer, in particular from the observer's ignorance on any given trial as to which of several alternative stimuli will ...be presented. Explanations based on multiple independent analyzers are presented, and their predictions for uncertainty experiments and summation experiments are calculated. These models differ in their assumptions about the probability distribution characterizing each analyzer's output and in their assumptions about how the multiple analyzer's outputs are combined to form the observer's decision rule. Several generalization are presented, e.g., probability distributions predicting shallower ROC slopes predict larger blocked-summation effects but smaller uncertainty effects. Further, these models provide some insight into and justification for the quick nonlinear pooling model presented in Chapter 4.
This chapter provides the necessary background for the study of visual pattern analyzers (e.g., spatial frequency and orientation-selective channels, direction-selective mechanisms). It briefly ...describes known properties of neurons in cortical areas V1 and V2, which may be the physiological substrate for the visual pattern analyzers. It introduces seventeen spatiotemporal dimensions of pattern vision along which neurons, and visual patterns and analyzers can differ. Several psychophysical paradigms are introduced that use near-threshold visual patterns. The chapter describes the models appropriate for interpreting results from these near-threshold paradigms and speculates about why these results have been particularly useful in uncovering the multiple-analyzer stage of visual processing.
This chapter summarizes available evidence from the four kinds of near-threshold analyzer-revealing experiments presented in previous chapters — adaptation, summation, uncertainty, and identification ...— for each of the seventeen pattern-vision dimensions along which multiple analyzers might exist. The effects of several factors, like age of observer and psychophysical procedure are also described. For each dimension, the chapter asks whether multiple analyzers exist on that dimension, and if they do, asks further questions: what is the analyzers' bandwidth? Are their outputs labeled? Are their outputs probabilistically independent or correlated? Is there inhibition among them? Occasional references are given in the course of the summary, but the majority of the references are to be found in a list of references at the end of the chapter organized by the type of analyzer-revealing experiment and by the patterns dimensions studied.
