Hotelling trace criterion and its correlation with human-observer performance

Abstract

The Hotelling trace criterion (HTC) is used to find a set of linear features that optimally separate two classes of objects. The objects used in our study were simulated livers with and without tumors, with noise, blur, and object variability. Using the receiver-operating-characteristic parameter da as our measure, we have found that the ability of the HTC to separate these objects into their correct classes, by detecting the presence or absence of a tumor, has a correlation of 0.988 with the ability of humans to separate the same two classes of objects. This suggests, therefore, that the HTC can be used as a figure of merit for optimizing system parameters, since it calculates a single, scalar figure of merit that has a high correlation with human-observer performance.

Application of the Hotelling and ideal observers to detection and localization of exoplanets

“…The expression for t Hot (g | r p ) in Eq. (16), which requires the knowledge of the mean vectors and covariance matrix under the two hypotheses, is the socalled Hotelling observer [1,7,15,34,35] and is a linear function of g. As pointed out in [36], the Hotelling observer is still analytically tractable in realistic cases (for example, when the background can be described by a stationary random process), whereas computing the likelihood ratio in practical cases is, in general, a difficult problem. The derivation above shows that, if the data are normally distributed, the Hotelling observer is equivalent to the likelihood ratio, in the sense that they differ by an additive or positive multiplicative constant.…”

Impact of Acquisition Geometry, Image Processing, and Patient Size on Lesion Detection in Whole-Body 18F-FDG PET

“…The reason for using BMI instead of partial patient weight is a practical one: when deciding whether to perform 2D or 3D imaging, one needs to know before starting the scan what protocol to use, and one cannot compute the sum of LACs before scanning the patient but can easily compute the patient BMI. The task considered in this work was lesion detection, measured by SNR CHO (15,19,20). Although lesion detection performance is best assessed using human observer studies (e.g., receiver operating (5)), the numeric observer approach allows more rapid assessment.…”

Statistical characterization of radiological images: basic principles and recent progress

“…A common recourse is then the ideal linear or Hotelling observer, [10][11][12] for which the test statistic is the linear discriminant that maximizes the SNR defined in (4.1). This optimal linear discriminant is given by (4.5) where the superscript t denotes transpose, the angle brackets denote averages over all sources of randomness (background object, signal to be detected, system and measurement noise) and Δ〈g〉 ≡ 〈g〉 1 − 〈g〉 0 is the difference between the mean data vectors under the two hypotheses.…”