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Extending the RDI model observer to images with an anatomic background

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In mammography, raw images are processed by means of sophisticated procedures before being used for diagnosis. According to the protocols that are presently valid, only raw images of technical phantoms are used for quality assurance in Europe today. In the medium term, however, it is planned to use anthropomorphic phantoms, that is to say, phantoms that have realistic anatomic structures. To be able to check processed images, procedures of “task-specific quality assessment” are required. In such procedures, the images are assessed by a model observer instead of a human observer.

Currently, technical phantoms – such as the contrast-detail mammography (CDMAM) phantom – are still used in mammography to guarantee the quality of mammograms [1]. CDMAM is based on a contrast-detail curve, which is obtained by means of a number of small objects that have different thicknesses and different diameters. This curve must remain below a fixed threshold that has been defined in a European standard. It is only then that the quality control is considered to have been “passed” [2]. Raw images (which are known as “for processing images”) are used for this purpose.

In practice, however, radiologists do not determine whether or not a lesion is suspected by using raw (that is to say, for processing) images, but by using processed images (also called “for presentation images”). Image processing is, of course, optimized for anatomic structures. Checking the quality of images on the basis of processed images of technical phantoms is therefore not sufficient. For this reason, these technical phantoms will, in the medium term, be replaced by 3D-printed phantoms which have realistic anatomic structures.

In such cases, the image quality is quantified by task-specific quality assessment. Here, mathematical models (model observers) are used as a substitute for human observers (radiologists). One disadvantage of these procedures is that they require a large number of images (typically: 200 images with the signature of a lesion and 200 images with a similar background, but without the signature of a lesion) to simulate a classification process (lesion visible/not visible). In this case, a measure for the image quality is what is called detectability [3].

Last year, PTB developed the regression detectability index (RDI) – a new model observer that enables reliable statements to be made about the image quality, but requiring fewer images. To be able to apply this new observer, however, the background must be devoid of structure. In its currently published form [4], the RDI is therefore not suitable for images which exhibit an anatomic structure.

It has, however, been possible to solve this problem by modeling the anatomic background prior to applying the RDI observer and by deducting it afterwards. This is done by means of thin plate splines – a special form of radial basis functions that represent a two-dimensional generalization of the known splines [5]. The form of the two-dimensional surface is obtained analogously to the deformation of a thin metal plate (which gives the method its name) that is fixed at defined sampling points. The fit depends on the number and distribution of the sampling points as well as on the rigidity of the plate (which has to be selected as well).

The modified RDI has been successfully used not only on simulated images, but also on mammograms of 3D-printed phantoms. Our cooperation partners – LRCB, the Dutch Expert Center for Screening, and RUMC, the Radboud University Medical Center (both located in Nijmegen, Netherlands) – provided us with images obtained with devices of two different manufacturers (FUJI and HOLOGIC). These images contained circular objects of 0.1 mm and 0.25 mm in diameter. In the mammogram, these objects were embedded in a phantom exhibiting an anatomic structure [6].

The detectability value obtained by means of the RDI could be compared both with the detectability of an established model observer (that is to say, the channelized Hotelling observer – CHO) and with data obtained from human observers. The latter data were also provided by our cooperation partners from Nijmegen. Here, the detectability values of the RDI, of the CHO and of human observers are linked by linear relations. The correlation of the detectability values of the RDI and of human observers is excellent. To do this, the RDI only requires 25 % of the number of images needed before and provides a comparable uncertainty in terms of the quality measure.

Our work is not yet completed. The parameters of the background fit remain to be optimized. However, the preliminary results obtained to date are promising. We therefore expect that it will be possible to use the modified RDI for modern quality assurance measurements in mammography.


Figure 1: Mean values over 25 images with an edge length of 65 pixels (left) and the corresponding covariance of the gray-scale values as a function of the distance from one pixel to the next. Top: prior to subtraction of the background with thin plate splines; bottom: after subtracting the background. As an example: Sections of mammograms of an anatomic phantom [6], HOLOGIC, object diameter: 0.25 mm (for processing).

Figure 2: Detectability d' as a function of the product of the time-current product (which is proportional to the dose), as an example of images recorded by means of a HOLOGIC mammography screening device (resolution: 0.07 mm), diameter of the object to be detected: 0.25 mm, processed images (for presentation). Filled circles: CHO; filled triangles: RDI with background deduction; ope.n triangles: three human observers. The error bars reflect the 95 % coverage intervals. The solid lines are polynomial fits, to guide the eye only.

Figure 3: Detectability d' of the RDI as a function of the mean detectability of the three human observers (h.o.). HOLOGIC, for presentation, object diameters: 0.1 mm and 0.25 mm. Correlation coefficient r = 0.99; p value: 3.2e-7.



[1]       Karssemeijer, N. & Thijssen, M.: Determination of contrast-detail curves of mammography systems by automated image analysis. Digital mammography (1996) 96, 155-160

[2]       Van Engen, R.; Bosmans, H.; Dance, D.; Heid, P.; Lazzari, B.; Marshall, N.; Schopphoven, S.; Thijssen, M.; Young, K. & others: Digital mammography update. European protocol for the quality control of the physical and technical aspects of mammography screening. S1, Part 1: Acceptance and constancy testing. European guidelines for quality assurance in breast cancer screening and diagnosis, European Commission, Office for Official Publications of the European Union (2013)

[3]       ICRU Report No. 54: Medical imaging - the assessment of image quality. Journal of the ICRU (2006)

[4]       Anton, M.; Veldkamp, W.; Hernandez-Giron, I. & Elster, C.:  RDI - a regression detectability index for quality assurance in x-ray imaging. Physics in Medicine & Biology, (2020) 65, 085017

[5]       Reginatto, M. & Behrens, R.: Multi-parameter interpolation of beta radiation dose rates using radial basis functions. Radiation protection dosimetry, (2016) 171, 463-469

[6]       Balta, C.; Bouwman, R. W.; Sechopoulos, I.; Broeders, M. J. M.; Karssemeijer, N.; van Engen, R. E. & Veldkamp, W. J. H.: Can a channelized Hotelling observer assess image quality in acquired mammographic images of an anthropomorphic breast phantom including image processing? 
Medical Physics, (2019) 46, 714-725


M. Anton, M. Reginatto, C. Elster (8.42), R. van Engen (LRCB, NL), Ioannis Sechopoulos (RUMC, NL)


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