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RDI – an efficient model observer for quality assurance in the field of X-ray computed tomography (CT)

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Mathematical model observers are used to determine the image quality of computed tomography (CT) scanners. In a joint research project of two of the Physikalisch‑Technische Bundesanstalt’s (PTB’s) divisions – Ionizing Radiation and Medical Physics and Metrological Information Technology – a novel model observer was developed. This is based on a regression procedure in which especially correlations in the images are taken into account. Joint research activities with scientists from the Netherlands have shown that the results of the new model observer correlate very well with the assessments of radiologists. Furthermore, the new model observer requires significantly fewer images for assessing the image quality of the CT scanner than the model observers used so far.

In a cross‑divisional cooperation project of departments 6.2 and 6.4 at the Physikalisch‑Technische Bundesanstalt (PTB) in Braunschweig and department 8.4 in Berlin, PTB has developed an efficient tool for assessing the quality of X‑ray computed tomography (CT) images. The motivation for this cooperation project is that, on the one hand, the methods that were previously used for image quality determination are based on the assumption of a linear, shift‑invariant imaging system, but this assumption is violated in many modern image reconstruction procedures. On the other hand, the established methods which are also able to assess non‑linear imaging systems are highly time‑consuming. In the so‑called task‑specific quality assessment, a simplified radiological task, such as the detection of a lesion in a CT image, is solved by a so‑called model observer. The model observer is a mathematical object that converts the image into a numeric value (a test statistic) and uses this value to carry out a classification. The measure for image quality is, for example, the so‑called detectability obtained from the ratio of the difference between the test statistics for two image classes (with or without a lesion) and the averaged width of the distributions of the test statistics. In this context, reference is often made to the low‑contrast detectability (LCD) that indicates how well low‑contrast objects can be detected in the CT image, such as in abdominal images.

Under certain conditions, the detectability can be converted into the so‑called area under curve (AUC, i.e., the area under the receiver operating characteristic curve). To put it very simply, this is the probability that the classification will be carried out correctly.

Two established model observers are the channelized Hotelling observer (CHO), which represents a realizable variant of the ideal linear observer, and the nonprewhitening matched filter with eye filtering (NPWE). Both observers model properties of the human visual system (in different ways); this is why both correlate well with the results of human observers. What both of these observers have in common, however, is that they require a high number of training and test images: Typically, several hundred images of the object to be detected (targets) are needed.

PTB’s newly developed observer [1], the so-called regression detectability index (RDI), combines the properties of the CHO and of the NPWE with a new approach. The application of the RDI is initially limited to technical phantoms that usually contain circular objects as targets for the detection task. This preliminary information is used to generate a simple model of the image so that only two model functions have to be adapted to the respective CT images. The RDI is calculated from the coefficients of the adaption. The model is chosen in a way that takes into account the limited resolving power of the human eye. Figure 1 shows an example of the adaption of the model function to real image data.

The second important component of the new observer is the modelling of the covariance matrix. In the case of the CHO, an estimate of the covariance matrix is obtained by using so‑called channels. The image is projected onto a lower dimension with the help of these channels which correspond (or may correspond) to the input channels of human perception. This makes it possible to estimate the high‑dimensional covariance matrix. The covariance matrix is particularly relevant in the case of nonlinear image reconstruction methods; the nonlinearity results in more correlations between the individual pixels. In the case of the RDI, the problem of the high dimension of the covariance matrix (for an image with 64x64 pixels, the covariance matrix has the dimension 4096x4096) is solved by choosing a simple model also for the dependence of the covariance on the distance between two pixels. This model is adapted to the data. Figure 2 shows an example of the adaption of a model function to the values of the covariance matrix as a function of the distance between the image elements.

The “double modeling” of the image and the covariance matrix significantly reduces the need for image data. Although the processing time is slightly longer compared to conventional observers, this is not significant when compared to the work required to generate larger numbers of images. It is observed that the value of the detectability of the RDI does not depend on the number of available images. It is only that the uncertainty decreases when the number of images increases. The required number of images consequently results from the desired uncertainty of detectability.

Within the scope of a cooperation project with the Department of Radiology of the Leiden University Medical Center (LUMC, The Netherlands), the properties of the RDI could be investigated on the basis of low‑contrast module images of the so‑called Catphan phantom. The results of human observers were also available for these image data. In order to be able to compare the different observers, a threshold value Dlim was determined for the detectability. Dlim is the diameter of a target with a detection probability (correct classification) higher than 75 %. Figure 3 shows the results for the standard filtered back projection (FBP). It illustrates that the detectability of the NPWE and the RDI can be scaled in such a way that the thresholds resulting for the target diameter are in a sufficiently good agreement with those determined by human observers. Only 21 images per setting were needed for the evaluation with the aid of the RDI, whereas the NPWE required 168; that is, eight times as many.

Figure 1: Model of an image. Left: square region of interest (ROI) with the target in the center – model function m1 shown in gray‑scale values; center: cross section through the model functions m0 and m1; right: cross section through an image with adaption of the model functions.

Figure 2: Covariance normalized to its maximum value for images of a circular target of the PTB low-contrast phantom as a function of the distance from pixel to pixel. The dots show the mean values from 40 images, the solid line represents the simplifying model function.

Figure 3: Threshold value Dlim for the detectability as a function of the current-time product (proportional to the dose) for images of targets with 1 % contrast of the low-contrast module of the Catphan phantom. CT images: Toshiba Aquilion ONE (LUMC); image reconstruction using FBP. To obtain satisfactory agreement with the results of human observers, the detectability values were scaled with √ η, assuming η for NPWE is 0.44 and 0.6 for RDI. The data marked with (HG) are taken from [1]. Error bars and the area shaded in gray indicate the 95 % coverage intervals.


(1)   M. Anton, W.J.H. Veldkamp, I. Hernandez-Giron, C. Elster: RDI – a regression detectability index for quality assurance in x-ray imaging. Submitted to Physics in Medicine and Biology on 2 October 2019

(2)   I. Hernandez-Giron, A. Calzado, J. Geleijns, R.M.S. Joemai, und W.J.H. Veldkamp: Comparison between human and model observer performance in low-contrast detection tasks in CT images: application to images reconstructed with filtered back projection and iterative algorithms. The British Journal of Radiology (2014), 87, 20140014


Opens local program for sending emailM. Anton, Department 6.2, Working Group 6.24

Opens local program for sending emailC. Elster, Department 8.4, Working Group 8.42


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