Abstract
When detecting targets under natural conditions, the visual system almost always faces multiple, simultaneous dimensions of extrinsic uncertainty. Many of these dimensions (like orientation and scale) result from random variation in object pose or observer viewpoint. To understand the fundamental limits to performance set by simultaneous dimensions of uncertainty, it is useful to determine the performance of ideal observers, which provide the appropriate benchmark for evaluating the performance of human observers and sub-optimal model observers. Unfortunately, even for a small number of dimensions, simulating ideal-observer performance can be prohibitively time consuming. We describe an efficient method for simulating the effects of high levels of uncertainty on detection of additive targets in white noise backgrounds. This method is based on equations that make it possible to precompute many of the quantities needed in the simulation of ideal and sub-ideal observers. We demonstrate the method by simulating the exact ideal observer, and the maximum-template-response (MAX) observer, with the simultaneous extrinsic uncertainty about the target scale and 2D orientation. The task is to detect a target which might appear in any of 359 different orientations and 51 different scales (total of 18,360 template shapes). The method was able to simulate 36,720 trials for the exact ideal observer in less than a minute, with an average office computer. (This is equivalent to simulating with 4 dimensions of uncertainty with 10 levels along each dimension.) For various single dimensions of uncertainty, the MAX observer has been shown to closely approximate the ideal observer. Here, we find it approximates ideal performance only if the templates are normalized by their total energy. When not properly normalized, the hit rate of MAX observer as a function of scale systematically deviates from that of the ideal observer. We are currently testing these predictions in psychophysical experiments.