A Non-Parametric Approach to Detecting Microcalcifications Marius George Linguraru and J. Michael Brady University of Oxford, Medical Vision Laboratory, Ewert House, Ewert Place, Summertown, Oxford OX2 7BZ, UK [email protected]

Abstract. Microcalcifications are the first and smallest signs of breast cancer and some of the most predominant non-palpable breast lesions. We are developing an automated detection method to assist the clinician in the diagnosis process. Our method is based on processed normalised hint images [2] and uses filters based on Gaussian derivative and anisotropic diffusion [4] to differentiate microcalcifications from breast tissue. Tests are performed on samples of real Standard Mammogram Format (SMF) images by a single-scale non-parametric algorithm with encouraging results. We detect 91.3% of the individual calcifications, whether isolated or clustered, which draws the attention of the radiologist to all the clusters.

1. Background We have previously presented a new approach for mammographic image normalisation offering a quantitative representation of the breast tissue, the hint [2]. There is a drawback however, the extremely noisy appearance of these images that makes their analysis very difficult. Although the signal-to-noise ratio (SNR) of the mammogram is slightly improved by the generation of hint (without glare removed), by glare removal, to reduce the number of false positives (FPs), the SNR decreases drastically due to the amplification of high frequency noise. Yam et al. [5] introduce a de-noising algorithm, which attempts to remove radiographic mottle, a source of false positives in detecting microcalcifications. The SNR is increased and the overall appearance of the hint image improved. In our previous work, we used the scale-space and edge detection characteristics of anisotropic diffusion [4] to filter hint images and highlight microcalcifications and shot-noise [3]. We used the difference in shape of a microcalcification (hill-shape with slightly blurred edges) versus noise (spikes with sharp edges) as the major property in the detection algorithm. The parametric format of anisotropic diffusion makes this process highly dependent on the fine-tuning of its input parameters. There are three parameters to be considered when attempting to blur an image using anisotropic diffusion: k - the contrast, t - the time or number of iterations and σ - the standard deviation or scale. In our previous work, we adopted a multi-scale approach in which we varied a single parameter, namely the number of iterations [3]. This is undesirable in clinical practice.

2. Method and Results Since t is not an image characteristic, we choose to vary k, which is image dependent Now we can iterate the blurring filter for a constant number of iterations over the image, but this raises the question: how do we choose the right contrast parameter to determine the values of the eigenvalues? [3]. To solve this, we have designed an adaptive Gaussian derivative filter. The result of applying this filter to a de-noised, glare-removed, hint image results in a gradientmap that highlights suspicious regions as regards microcalcification detection. Furthermore, the same filter outputs the value of k for the subsequent diffusion. We apply the anisotropic diffusion filter [3] to the hint image with the corresponding value of k for a fixed number of iterations. Note the emphasised outline of the microcalcifications, while most of the background is seriously blurred. A new filtering step is introduced at this stage to actually depict the microcalcifications in the processed image. It is based on the same computation as the anisotropic diffusion, but also incorporates some adaptive thresholding suited to the image characteristics and the properties of microcalcifications. This last filtering process concludes with a black-and-white map of detection (BWMD), as in Fig.1.

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Fig. 1. (a) The hint image (contrast enhanced) of a microcalcification cluster; (b) the corresponding gradient map of the image; (c) the diffused image of (a) after using the computed value of k; (d) the corresponding BWDM of the image; (e), (f), (g) and (h) show two more examples of detection.

We applied the method to a database comprising 35 samples of digital mammograms at a resolution of 50µm with the size of 500x500 pixels. The hint images were in a 32-float format and contained a total of 23 isolated microcalcifications previously labeled by an experienced radiologist. The overall ratio of detection is 91.3% true positives (TPs) for a number of 0.32 FPs per image. One source of FPs in our detection algorithm is the curvilinear structures, due to the relatively high contrast they have against the average background. In Fig.2. we show an image where our algorithm detected an FP. To avoid these erroneous results, we removed the CLS from the images with FPs [1] and then applied the algorithm again on the CLS-free hint images. The number of FPs/image was reduced to 0.2.

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Fig. 2. (a) An hint image (contrast enhanced) containing one subtle microcalcifications and a prominent CLS; (b) the BWMD of image (a) showing an FP; (c) the image (a) after CLS removal; (d) the BWMD of image (b) with the correct detection of the microcalcification.

4. Discussions and Conclusion The spread of the detected clusters is well defined in the BWMD, although some of the subtle calcifications are missed. We must therefore refine the algorithm so that will be more sensitive to local rather than global variability. A major source of errors can be the breast edge and the shot-noise. The solution would be the breast edge correction together with bringing the background to a hint value similar to that of the average breast tissue and the local interpolation at shot-noise location. Although we have not tested any image of a breast during HRT treatment, we expect similar difficulties in such cases. We presented an automated method to detect microcalcifications in digital mammography based on a series of subsequent filters and computations designed to output for the user a map of detection showing the regions where salts of calcium are detected. The method uses the facilities and improvements in medical image normalisation offered by the hint image representations. The results we showed are generated by a single-scale non-parametric algorithm. A multi-scale approach would obviously improve our results considerably, but the scope of our work is to develop a robust detection method that could be easily used in clinical conditions. This requires minimal or no intervention from the clinician in the algorithm settings.

References 1. Evans, C.J.: Detecting and Removing Curvilinear Structures from Mammograms. Internal Report, Department of Engineering Science, University of Oxford (2001) 2. Highnam, R.P. Brady, J.M.: Mammographic Image Analysis. Kluwer Academic Publishers, Dordrecht Boston London (1999) 3. Linguraru, M.G. Brady, J.M. Yam, M.: Filtering hint Images for the Detection of Microcalcifications. In Niessen, W. Viergever, M. (eds.): Medical Image Computing and Computer-Assisted Intervention 2001, Lecture Notes in Computer Science, Vol. 2208. Springer-Verlag, Berlin Heidelberg New York (2001) 629-636 4. Weickert, J.: Anisotropic Diffusion in Image Processing. B.G. Teubner, Stuttgart (1998) 5. Yam, M. Brady, J.M. Highnam, R.P. English, R.: Denoising hint Surfaces: a Physics-based Approach. In Medical Image Computing and Computer-Assisted Intervention 1999, Springer-Verlag, Berlin Heidelberg New York (1999) 227-234