Geisler Wilson S
Center for Perceptual Systems and Department of Psychology, University of Texas at Austin, Austin, TX, USA.
J Vis. 2018 Feb 1;18(2):1. doi: 10.1167/18.2.1.
This theoretical note describes a simple equation that closely approximates the psychometric functions of template-matching observers with arbitrary levels of position and orientation uncertainty. We show that the approximation is accurate for detection of targets in white noise, 1/f noise, and natural backgrounds. In its simplest form, this equation, which we call the uncertain normal integral (UNI) function, has two parameters: one that varies only with the level of uncertainty and one that varies only with the other properties of the stimuli. The UNI function is useful for understanding and generating predictions of uncertain template matching (UTM) observers. For example, we use the UNI function to derive a closed-form expression for the detectability (d') of UTM observers in 1/f noise, as a function of target amplitude, background contrast, and position uncertainty. As a descriptive function, the UNI function is just as flexible and simple as other common descriptive functions, such as the Weibull function, and it avoids some of their undesirable properties. In addition, the estimated parameters have a clear interpretation within the family of UTM observers. Thus, the UNI function may be the better default descriptive formula for psychometric functions in detection and discrimination tasks.
本理论说明描述了一个简单方程，该方程能紧密近似具有任意位置和方向不确定性水平的模板匹配观察者的心理测量函数。我们表明，对于在白噪声、1/f噪声和自然背景中检测目标，这种近似是准确的。以其最简单的形式，这个我们称为不确定正态积分（UNI）函数的方程有两个参数：一个仅随不确定性水平变化，另一个仅随刺激的其他属性变化。UNI函数有助于理解和生成不确定模板匹配（UTM）观察者的预测。例如，我们使用UNI函数推导出UTM观察者在1/f噪声中的可检测性（d'）的闭式表达式，它是目标幅度、背景对比度和位置不确定性的函数。作为一个描述函数，UNI函数与其他常见描述函数（如威布尔函数）一样灵活和简单，并且它避免了它们的一些不良特性。此外，估计的参数在UTM观察者家族中有明确的解释。因此，对于检测和辨别任务中的心理测量函数，UNI函数可能是更好的默认描述公式。
