Showing papers by "Craig K. Abbey published in 1998"

Objective assessment of image quality. III. ROC metrics, ideal observers, and likelihood-generating functions

Abstract: We continue the theme of previous papers [J. Opt. Soc. Am. A 7, 1266 (1990); 12, 834 (1995)] on objective (task-based) assessment of image quality. We concentrate on signal-detection tasks and figures of merit related to the ROC (receiver operating characteristic) curve. Many different expressions for the area under an ROC curve (AUC) are derived for an arbitrary discriminant function, with different assumptions on what information about the discriminant function is available. In particular, it is shown that AUC can be expressed by a principal-value integral that involves the characteristic functions of the discriminant. Then the discussion is specialized to the ideal observer, defined as one who uses the likelihood ratio (or some monotonic transformation of it, such as its logarithm) as the discriminant function. The properties of the ideal observer are examined from first principles. Several strong constraints on the moments of the likelihood ratio or the log likelihood are derived, and it is shown that the probability density functions for these test statistics are intimately related. In particular, some surprising results are presented for the case in which the log likelihood is normally distributed under one hypothesis. To unify these considerations, a new quantity called the likelihood-generating function is defined. It is shown that all moments of both the likelihood and the log likelihood under both hypotheses can be derived from this one function. Moreover, the AUC can be expressed, to an excellent approximation, in terms of the likelihood-generating function evaluated at the origin. This expression is the leading term in an asymptotic expansion of the AUC; it is exact whenever the likelihood-generating function behaves linearly near the origin. It is also shown that the likelihood-generating function at the origin sets a lower bound on the AUC in all cases.

Stabilized estimates of Hotelling-observer detection performance in patient-structured noise

Abstract: This paper addresses the question of how to determine the performance of the optimum linear or Hotelling observer when only sample images are available. This observer is specified by a template from which a scalar test statistic is computed for each image. It is argued that estimation of the Hotelling template is analogous to problems in image reconstruction , where many difficulties can be avoided through judicious use of prior information. In the present problem, prior information is enforced by choice of the representation used for the template. We consider specifically a representation based on Laguerre-Gauss functions, and we discuss ways of estimating the coefficients in this expansion from sample images for the problem of detection of a known signal. The method is illustrated by two experiments, one based on simulated nonuniform fields called lumpy backgrounds, the other on real coronary angiograms.

Human vs model observers in anatomic backgrounds

Abstract: Model observers have been compared to human performance detecting low contrast signals in a variety of computer generated backgrounds including white noise, correlated noise, lumpy backgrounds, and two component noise. The purpose of the present paper is to extend this work by comparing a number of previously proposed model observers (non-prewhitening matched filter, non-prewhitening matched fitler model with an eye filter, Hotelling observer and channelized-Gabor Hotelling observer model) to human visual detection performance in real anatomic backgrounds (x-ray coronary angiograms). Human and model observer performance are compared as a function of increasing added white noise. Our results show that three of the four models (the non-prewhitening matched filter, the Hotelling and channelized-Gabor Hotelling) are good predictors of human performance.

Some unlikely properties of the likelihood ratio and its logarithm

Abstract: It is well known that the optimum way to perform a signal-detection or discrimination task is to compute the likelihood ratio and compare it to a threshold. Varying the threshold generates the receiver operating characteristic (ROC) curve, and the area under this curve (AUC) is a common figure of merit for task performance. AUC can be converted to a signal-to-noise ratio, often known as d a , using a well-known formula involving an error function. The ROC curve can also be determined by psychophysical studies for humans performing the same task, and again figures of merit such as AUC and d a can be derived. Since the likelihood ratio is optimal, however, the d a values for the human must necessarily be less than those for the ideal observer, and the square of the ratio of d a (human)/d a (ideal) is frequently taken as a measure of the perceptual efficiency of the human. The applicability of this efficiency measure is limited, however, since there are very few problems for which we can actually compute d a or AUC for the ideal observer. In this paper we examine some basic mathematical properties of the likelihood ratio and its logarithm. We demonstrate that there are strong constraints on the form of the probability density functions for these test statistics. In fact, if one knows, say, the density on the logarithm of the likelihood ratio under the null hypothesis, the densities of both the likelihood and the log-likelihood are fully determined under both hypotheses. Moreover, the characteristic functions and moment-generating functions for the log-likelihood under both hypotheses are specified in terms of a likelihood-generating function. From this single function one can obtain all moments of both the likelihood and the log-likelihood under both hypotheses. Moreover, AUC is expressed to an excellent approximation by a single point on the function. We illustrate these mathematical properties by considering the problem of signal detection with uncertain signal location.