Improved Fuzzy Entropy Algorithm for X-Ray Pictures ... - Springer Link

Improved Fuzzy Entropy Algorithm for X-Ray Pictures Preprocessing Mariusz Korkosz1, Marzena Bielecka2 , Andrzej Bielecki3 , Marek Skomorowski3, Wadim Wojciechowski4, and Tomasz W´ojtowicz3 1

Division of Rheumatology, Departement of Internal Medicine and Gerontology, Jagiellonian University Hospital, ´ Sniadeckich 10, 31-531 Cracow, Poland [email protected] 2 Department of Geoinformatics and Applied Computer Science, Faculty of Geology, Geophysics and Environmental Protection, AGH University of Science and Technology, Mickiewicza 30, 30-059 Cracow, Poland [email protected] 3 Institute of Computer Science, Faculty of Mathematics and Computer Science, Jagiellonian University, L  ojasiewicza 6, 30-348 Cracow, Poland {bielecki,skomorowski,tomasz.wojtowicz}@ii.uj.edu.pl 4 Department of Radiology, Jagiellonian University Hospital, Kopernika 19, 31-531 Cracow, Poland [email protected]

Abstract. The fuzzy entropy algorithm was designed for preprocessing of photos taken in the visible spectrum of light. However it did not produce satisfying results when it is directly applied to X-ray pictures. In this paper we present significant improvements of this approach and apply it to hand radiographs. The noise elimination and the bone contourisation is the task which is studied in this paper. Not only is the algorithm modified but also it is combined with using of median and minimum filters. The presented approach allows us to obtain satisfying noise elimination and clear bone contourisation.

1

Introduction

X-ray pictures are one of the most important diagnostic tools in contemporary medicine - see, for instance, [7,9,13,22]. Despite competition from computer tomography and magnetic resonance, X-ray pictures remain popular due to low cost and simplicity. The application of computer power in the field of automatic or semi-automatic processing makes X-ray imaging even more attractive. However such approach requires good preprocessing of the medical image [1,21,25]. In the field of rheumatology there are several diseases, of both inflammatory and non-inflammatory nature, detectable on X-ray pictures, especially in palm region [22]. Numerical processing have been proposed on various levels, beginning L. Rutkowski et al. (Eds.): ICAISC 2012, Part II, LNCS 7268, pp. 268–275, 2012. c Springer-Verlag Berlin Heidelberg 2012 

Improved Fuzzy Entropy Algorithm for X-Ray Pictures Preprocessing

269

from preprocessing [1,8,12,26,27]. Then, recognition of interesting features like contour or joints detection [4,8,11,14], and detection of pathological changes in joint spaces and bone contours are done [2,3,5,6,17,18,20]. Further research employs pattern recognition and image understanding [16,23,24] in order to create computer-aided medical diagnostic system [15]. Processing of X-ray pictures is more difficult than pictures taken in visible spectrum for various reasons which have been discussed in the paper [25] and are also a subject of this paper. High noise level, low contrast between soft tissue and background and high variability in the level of gray due to differences in tissue thickness between finger area and wrist area are the main issues associated with X-ray pictures. On the level of preprocessing, important goal is to extract the hand itself from raw image. Low contrast between soft tissue and background and high variability in luminance cause problems with binarisation whereas high noise level causes failing of direct application of visible spectrum pictures preprocessing algorithm to X-ray images. A certain algorithm, called fuzzy entropy direction feature image edge detection, designed for visible spectrum images (see [10,19]), is the starting point of our studies. The adaptation of this algorithm to X-ray pictures processing is presented in this paper. The algorithm, called shortly fuzzy entropy is a multi-stage algorithm consisting of four steps. In the previous paper [25] only its first step was analyzed. This issue and the whole algorithm is briefly described in Section 2. In the paper [25], the aspect of noise filtering is also discussed. It is shown there that if this algorithm is used to X-ray images processing, it must be supported by external noise filter. The filtering must be done even twice, between steps of fuzzy entropy algorithm. This problem is discussed in Section 3 whereas in Section 4 the fourth step of fuzzy entropy algorithm is discussed in the aspect of possible algorithm improvements. The last Section is a final conclusion.

2

Fuzzy Entropy

The fuzzy entropy algorithm, consisting of four steps, is introduced in the paper [10]. The entropy calculation is its first step. For each pixel of image the value of entropy, depending on the level of gray of this pixel and its neighbourhood , is calculated. Let p be the pixel and N (p) be its neighborhood, and let #N (p) denotes the number of elements in the set N (p). The entropy value of p is given as E(p) =

 1 H(U (v, p)), #N (p)

(1)

v∈N (p)

where U (v, p) =

1 , 1 + |λ(v) − λ(p)|

(2)

and H(x) = −x · log2 x − (1 − x) · log2 (1 − x).

(3)

270

M. Korkosz et al.

The symbol λ() denotes the level of gray of a given pixel. Let us observe that the function U returns 1 when both analyzed pixels are identical whereas the function H is incomputable for arguments equal to 0 and 1. It has been proposed to replace the function H with a less troublesome one. In the paper [25] various aspects of such replacements are discussed. It was finally decided that a polynomial, 4 · x · (1 − x) is the best replacement. First of all, there are no points in the function domain for which the function value can not be calculated. Secondly, computations are less time-consuming which is crucial according to the huge number of pixels in a radiograph. In the second step of the algorithm the direction of possible edge around each pixel is calculated. For each pixel 3×3 neighborhood possibility of creation of the fragment of the edge is analyzed. The outlined edge must satisfy three following conditions: 1. the edge goes through center pixel, 2. the edge starts on any border pixel and goes straight or turns maximally of 45 degrees, 3. the edge is undirected. This produces twelve possible edge contours on the 3 × 3 mask, four straight and eight bent. In this step all twelve possibilities are examined in such a way that entropy values, calculated in the first step of the algorithm, are summed along the supposed edge. Then the largest sum is taken and direction on which it was calculated is assumed to be an edge. The third step of the algorithm, named Non-Maxima Supression, is aimed to reduce a certain type of noise. However, it does not remove properly the noise associated with X-ray pictures, and because of that other solutions of filtering have been proposed in Section 3. The last step is binarisation, discussed with details in Section 4.

3

Noise

As it has been already mentioned in Section 1, X-ray pictures have high level of noise. This noise causes a problem to the fuzzy entropy algorithm. Due to the fact that the algorithm is sensitive to weak edges, the noise can be treated as such edges - see Fig.1. In the paper [25] two noise filtering algorithms have been proposed - the median filter (4) and the minimum filter (5). For given image pixel p there is his 3 × 3 neighborhood N (p) such that p ∈ N (p): λ(p) = median{λ(v) : v ∈ N (p)},

(4)

λ(p) = min{λ(v) : v ∈ N (p)}.

(5)

Improved Fuzzy Entropy Algorithm for X-Ray Pictures Preprocessing

271

It has been proved that the best results can be received when filtering is applied twice - first before the step 1 of fuzzy entropy algorithm, and second after the step 1 and before steps 2,3,4, hence the fuzzy entropy algorithm must be stopped after step 1 and be restarted once again.

Fig. 1. Pure fuzzy entropy algorithm applied without filtering. The left picture presents the result after step 1. Noise is very much visible, what results in poor overall contrast. The right picture presents the final result. It is noticeable that the algorithm has done its best, yet the effect is not acceptable for further calculation.

From all execution possibilities, the following seem to produce interesting results (digits 1-4 indicate algorithm steps 1-4): – median–1–2–3–4 (see Fig.2) – median–1–median–2–3–4 (see Fig.3) – median–1–minimum–2–3–4 (see Fig.4)

Fig. 2. Median filter applied only once, before step 1. Result after step 1. (left) and final result (right).

272

M. Korkosz et al.

Fig. 3. Median filter applied twice - before and after step 1. Result after second median filtering on the left. Note the image is more blurry than corresponding image in Fig.2. On the right final result. Note that important features appear stronger than in Fig.2.

Fig. 4. Median filter applied before and minimum filter applied after step 1. The left picture presents the result of minimum filter applied after step 1. The right picture presents the final result. It does not look much useful because the median filter has “eaten” too much, yet in Section 4 this problem is discussed in details.

4

Binarisation

Another interesting aspect is adaptive threshold control situated in the step 4 of fuzzy entropy algorithm. The threshold value T determines whether a pixel will be finally black or white, what depends whether its level of gray is below or above the threshold, which is calculated in the following way: T = J + k · σ,

(6)

J is an arithmetic mean of all pixels’ value, σ is a variance, and k is a special tuning value, the “expert’s knob”. The authors of [10] propose the usage of k for noise suppression. However,this works well with visible-spectrum images and poorly with X-ray images. The problem is, that the contrast between anatomical features and noise is too small to sort it out in such a simple way. For this reason this other means of filtering are proposed in this paper - see Section 3.

Improved Fuzzy Entropy Algorithm for X-Ray Pictures Preprocessing

273

Fig. 5. Four different values of k in process where median filter was applied twice. From left: 0.5, 1.1, 2.1, 3.0.

Fig. 6. Four different values of k : 0.5, 0.8, 1.1, 2.1 in process where median and then minimum filter were applied

Nevertheless the ability to tweak the value of k may help the filtering from step 3 to achieve optimal result. Let us observe that in Fig.5 tests show that optimal value of k is in a wide range from 1.0 to 2.0. If k = 0.5 white bones in the picture are in fact of black-white mosaic and the background noise is not well visible. If k = 3.0 then certain anatomical features around fingers disappeared, which means that the value of k is too high. In the case presented in Fig.6 the optimum value is in narrow range around the value of 0.8. The picture obtained for k = 2.1 is absolutely unacceptable as a result.

5

Conclusion

It has been shown that the algorithm designed for visible spectrum images can be adapted for X-ray images preprocessing. One important achievement is that various combination of filters, combined with setting of k value in the proposed algorithm, produces results useful but differing one from another. Therefore this algorithm can be utilized to produce results which will be useful in various context for higher-level algorithms which refer to medical image recognition and understanding. These topics are outside of scope of this paper, but their effectiveness is intrinsically depended on results of preprocessing.

274

M. Korkosz et al.

References 1. Bielecki, A., Korkosz, M., Zieli´ nski, B.: Hand radiographs preprocessing, image representation in the finger regions and joint space width measurements for image interpretation. Pattern Recognition 41, 3786–3798 (2008) 2. Bielecka, M., Skomorowski, M., Zieli´ nski, B.: A Fuzzy Shape Descriptor and Inference by Fuzzy Relaxation with Application to Description of Bones Contours at Hand Radiographs. In: Kolehmainen, M., Toivanen, P., Beliczynski, B. (eds.) ICANNGA 2009. LNCS, vol. 5495, pp. 469–478. Springer, Heidelberg (2009) 3. Bielecka, M., Bielecki, A., Korkosz, M., Skomorowski, M., Wojciechowski, W., Zieli´ nski, B.: Application of Shape Description Methodology to Hand Radiographs Interpretation. In: Bolc, L., Tadeusiewicz, R., Chmielewski, L.J., Wojciechowski, K. (eds.) ICCVG 2010. LNCS, vol. 6374, pp. 11–18. Springer, Heidelberg (2010) 4. Bielecki, A., Korkosz, M., Wojciechowski, W., Zieli´ nski, B.: Identifying the Borders of the Upper and Lower Metacarpophalangeal Joint Surfaces on Hand Radiographs. In: Rutkowski, L., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2010. LNCS, vol. 6113, pp. 589–596. Springer, Heidelberg (2010) 5. Bielecka, M., Bielecki, A., Korkosz, M., Skomorowski, M., Wojciechowski, W., Zieli´ nski, B.: Modified Jakubowski Shape Transducer for Detecting Osteophytes ˇ and Erosions in Finger Joints. In: Dobnikar, A., Lotriˇc, U., Ster, B. (eds.) ICANNGA 2011, Part II. LNCS, vol. 6594, pp. 147–155. Springer, Heidelberg (2011) 6. Bottcher, J., et al.: Digital X-ray radiogrammetry combined with semiautomated analysis of joint space widths as a new diagnostic approach in rheumatoid arthritis: a cross-sectional and longitudal study. Arthritis and Rheumatism 52, 3850–3859 (2006) 7. Choi, S., Lee, Y., Hong, S., Lee, G., Kang, S., Park, J., Park, J., Park, H.: Evaluation of inflammatory change and bone erosion using a murine type II collageninduced arthritis model. Rheumatology International 31, 595–603 (2011) 8. Choi, S., Lee, G.J., Hong, S.J., Park, K.H., Urtnasan, T., Park, H.K.: Development of a joint space width measurement method based on radiographic hand images. Computers in Biology and Medicine 41, 987–998 (2011) 9. Choi, S., Su-Jin Chae, S., Kang, S., Cheong, Y., Hong, S., Park, H.: Non-invasive screening of progressive joint defects in the type II collagen - induced arthritis animal model using radiographic paw images. Inflammation Research 60, 447–456 (2011) 10. Chun, H., Jun, L., Junwei, H.: Image edge detection method based on the direction feature of fuzzy entropy. In: Proc. 6th International Conference on Natural Computation, pp. 3581–3584 (2010) 11. Davis, L., Theobald, B.J., Toms, A., Bagnall, A.: On the Extraction and Classification of Hand Outlines. In: Yin, H., Wang, W., Rayward-Smith, V. (eds.) IDEAL 2011. LNCS, vol. 6936, pp. 92–99. Springer, Heidelberg (2011) 12. He, X.Q., Ran, L.K., Tan, P.C., Jin, J.: Hand radiographs preprocessing and improved k-cosine algorithm in location method for phalangeal key points. Journal of Clinical Rehabilitative Tissue Engineering Research 15, 4817–4820 (2011) 13. Jantan, S., Hussain, A., Mustafa, M.M.: Distal radius bone age estimation based on fuzzy model. In: Proceedings of Conference on Biomedical Engineering and Sciences, IECBES, pp. 427–432 (2010) 14. Kaufmann, J., Slump, C.H., Bernelot Moens, H.J.: Segmentation of hand radiographs by using multi-level connected active appearance models. In: Proceedings of the SPIE, vol. 5747, pp. 1571–1581 (2005)

Improved Fuzzy Entropy Algorithm for X-Ray Pictures Preprocessing

275

15. Klooster, R., Hendrics, E.A., Watt, I., Kloppenburg, M., Reiber, J.H.C., Stoel, B.C.: Automatic quantification of osteoarthritis in hand radiographs: validation of a new method to measure joint space width. Osteoarthritis and Cartilage 16, 18–25 (2008) 16. Ogiela, M.R., Tadeusiewicz, R., Ogiela, L.: Image languages in intelligent radiological palm diagnostics. Pattern Recognition 39, 2157–2165 (2006) 17. Pfeil, A., et al.: Computer-aided joint space analysis of the metacarpal-phalangeal and proximal-interphalangeal finger joint: normative age-related and genderspecific data. Skeletal Radiology 36, 853–864 (2007) 18. Pfeil, A., et al.: Normative Reference Values of Joint Space Width Estimated by Computer-aided Joint Space Analysis (CAJSA): The Distal Interphalangeal Joint. Journal of Digital Imaging 21(suplement 1), 104–112 (2008) 19. Qi, B., Tang, L., Zhang, J.: Research on measurement of hydrophobocity of insulators. Proceedings of the CSEE 26, 120–124 (2008) 20. Sharp, J., Gardner, J., Bennett, E.: Computer-based methods for measuring joint space and estimating erosion volume in the finger and wrist joints of patients with rheumatoid arthritis. Arthritis and Rheumatism 43, 1378–1386 (2000) 21. Szostek, K., Gronkowska-Serafin, J., Pi´ orkowski, A.: Problems of corneal endothelial image binarization. Schedae Informaticae 20, 211–218 (2011) 22. Staniszewska-Varga J., Szyma´ nska-Jagiello W., Luft S., Korkosz M.: Rheumatic diseases atlas. Medycyna Praktyczna, Krak´ ow (2003) (in Polish) 23. Tadeusiewicz, R., Ogiela, M.R.: Medical image understanding technology. STUDFUZZ. Springer, Heidelberg (2004) 24. Tadeusiewicz, R., Ogiela, M.R.: Picture languages in automatic radiological palm interpretation. International Journal of Applied Mathematics and Computer Science 15, 305–312 (2005) 25. W´ ojtowicz, T.: An improvement in fuzzy entropy edge detection for X-ray imaging. Schedae Informaticae 20, 159–166 (2011) 26. Zieli´ nski, B.: A fully automated algorithm dedicated to computing metacarpophalangeal and interphalangeal joint cavity widths. Schedae Informaticae 16, 47–67 (2007) 27. Zieli´ nski, B.: Hand radiograph analysis and joint space location improvement for image interpretation. Schede Informaticae 17/18, 45–61 (2009)