123Vision is very important for human survival. It involves many important and complex tasks.45A typical natural sub-task.6Another typical natural sub-task. Image contours can occur for a number of entirely different physical reasons. They can be the result of surface boundaries, surface markings or shading. There can be little doubt that many perceptual tasks depend critically upon identifying whether a contour is a surface boundary, a marking or a shadow.78Here is another example where the red value at each pixel location is estimated from the blue and green values, using the average statistics of natural images.The brain exploits this type of statistical regularity to improve the accuracy of our perceptions.9There is much statistical regularity in natural stimuli. For example, each pixel in an image has a value of red, green and blue. But the color in images is so predictable that it is possible to guess a missing color value pretty well if you know the other two values. In the bottom image the blue value at each pixel location has been guessed from the red and green values, using knowledge of the average statistics of natural images.101112An example of absolute statistics. Distribution of edge orientation in images collected in different environments.13Example of across-domain statistics. From range-finder measurements, one can determine the probability of different distances given different image locations (relative to a line in the horizontal plane). The range image in A and probability distributions in B are from Huang, Lee and Mumford (2000). The plot in C is from Yang and Purves (2003).1415Cross section of the human retina. In this figure, light would reach the receptors from below (i.e., through the other cells in the retina). Dowling, J. E. (1987). The Retina: An approachable part of the brain. Cambridge, MA, Belknap Press.1617Major connections between visual cortical areas. The width of the connection is proportional to the number of axon fibers. The upper side (warm colors) is the so-called “where pathway” and the bottom side (cool colors) is the so-called “what pathway.” These pathways have been determined from anatomical measurements (including injecting different areas with tracers).1819There many different types of neurons but they share important features.20An electrode next to a pyramidal cell (a projection neuron) in the visual cortex.2122Some basics of single neuron behavior and single neuron recording.23Electrical activity of a muscle reflex: from the stretch receptor to muscle contraction.242526PET images demonstrating how localization of activity can change depending on the task.27Demonstration of how fMRI can be used to quantify brain activity in specific brain locations in humans.28Optical imaging of primary visual cortex while a monkey performed a simple reaction time detection task. An hour long talk could easily be devoted to this study.Records summed membrane potentials in the superficial (output layers of the cortex). Response distributed over a large population.2930Different perceptual tasks can be classified by picking one attribute from each column.31Example of an objective identification task with feedback. If there are just two alternatives, then such tasks are often called a discrimination tasks; if one of the alternatives is “uniform” in some fashion, then such tasks are often called a detection tasks. A typical stimulus presentation sequence for a single interval two-alternative forced choice experiment.32In the two interval task the observer must decide whether a target pattern is in the first temporal interval or the second temporal interval.33Illustration of the two-interval two-alternative forced choice task and the concept of the psychometric function.34A real example of a psychometric function. Each data point represents the proportion correct for a block of 30 trials.35The logic of measuring discrimination thresholds. The measurements are focused on the transition zone between the indistinguishable and the trivially easy to distinguish.An objective identification task with no feedback. The illusion in this example is called the Müller-Lyer illusion. Such illusions have also been studied with descriptive methods (the phenomenological approach).363738394041424344Example psychometric function for an objective task with no feedback.45Example of an objective estimation task with no feedback. The gray scale (luminance) is the same for the two squares in the checkerboard; in fact, it is exactly the same gray shown at the tails of the arrows. One way to estimate the difference in apparent luminance is to adjust the luminance of a comparison patch (against a same fixed background) to match the brightness of the squares in the two regions of the image. The luminance of the lighter comparison patch has an apparent luminance more similar to the square in the “shadow.” The difference in the physical luminance of the comparison gives a precise measure of the apparent (psychological) luminance difference.4647The likelihood of a particular sequence of responses from an observer, assuming statistical independence across trials. Maximum likelihood parameter estimation is to find parameter values that maximize the likelihood of the observed data.4849The likelihood of a particular sequence of correct and incorrect responses from an observer, assuming statistical independence across trials. Maximum likelihood parameter estimation is to find parameter values that maximize the likelihood of the observed data.50Table of possible stimulus response outcomes in a 2AFC or a Yes/No task. For a summary of basic signal detection theory see Wickens, T. (2002) Elementary Signal Detection Theory. Oxford University Press (available online through the UT library).51Derivation of signal detection theory model of 2AFC data for the case of 1D Gaussian sensory input. The same final result is obtained with nD Gaussian sensory input.5253Z is the decision variable, d’ is the number of standard deviations separating the means of the two distributions, and c* is the decision criterion.54Rewriting in terms of d’.55Now rescale the axes into units of standard deviation. This is the standard representation for signal detection theory. Within this representation, the proportions of hits and false alarm rates are used to estimate d’ and c.5657Signal detection theory in for two-dimensional distributions. (A,B,C) Synthetic data