Wavelet. Coefficients. Fmicros() (micros) Wavelet. Wavelet Coefficients. Fmasses() (masses) Wavelet Coefficients (stellate) Fstellate()

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1 Enhanceent via Fusion of Maographic Features Iztok oren y, Andrew Laine z, and Fred Taylor y y Dept. of Electrical and Coputer Engineering z Center for Bioedical Engineering University of Florida, Gainesville, FL Colubia University, New York, NY Abstract Maographic iage enhanceent ethods are typically aied at either iproveent of the overall visibility of features or enhanceent of a specific sign of alignancy. In this paper, we present a synthesis of the two paradigs by eans of iage fusion. After a redundant B-spline wavelet transfor decoposition is carried out, the transfor coefficients are processed for enhanceent of icrocalcifications, circuscribed asses, and stellate lesions. The odified coefficients are then fused for reconstruction of an enhanced iage with iproved visualization of alignancies. Both processing for enhanceent of selected features and fusion of the resultant iages are accoplished within a single wavelet transfor fraework which contributes to the coputational efficiency of the described ethod. The devised algorith not only allows for efficient cobination of specific features of iportance in the contrast enhanced iages, but also provides a flexible fraework for incorporation of different enhanceent ethods and their independent optiization. 1 Introduction Maography is the best ethod for early detection of breast cancer at a tie when approxiately 80 percent of woen diagnosed with breast cancer have no identifiable risk factors for this disease. The early detection of breast cancer is essential since therapeutic actions are ore likely to be successful in the early stages. Finding sall alignancies and subtle lesions is often difficult with false-negative rate being due both to difficulty with discerning subtle features on the coplex noral anatoy background and oversight of abnoralities. Contrast enhanceent can ake ore obvious unseen or barely seen features of a aogra without requiring additional radiation. Better visibility of suspicious structures can increase effectiveness and efficiency, and thus iprove the diagnostic perforance of aography. Existing ethods of aographic iage enhanceent can be divided roughly into two categories: (1) ethods aied at better visualization of all features present in an iage [1, 2, 10, 12], and (2) ethods that target specific features of iportance (e.g., icrocalcifications [13, 14, 16], stellate lesions [8]). Methods fro the first category are not optiized for a specific type of cancer and soeties not even for aography. Rather, they try to iprove the perceptual quality of the entire iage and are often developed with a fraework ore general than aography alone in ind. The second category ethods concentrate on revelation of particular signs of alignancy. They can be very successful in their area of specialization; however, in order to process aogra for presence of various features, one would need to apply different algoriths independently resulting in both larger nuber of iages to be interpreted by a radiologist and increased coputational coplexity of such a procedure. In this paper, we present an approach which overcoes these shortcoings and probleatic liitations via synthesis of the two paradigs by eans of iage fusion. 2 Methodology The goal of our ethod is to adapt specific enhanceent schees for distinct aographic features, and then cobine the set of processed iages into an enhanced iage. The aographic iage is first processed for enhanceent of icrocalcifications, asses, and stellate lesions. Fro the resulting enhanced iages, the final enhanced iage is synthesized by eans of iage fusion [7]. based iage enhanceent and fusion are erged into a unified fraework, so that there is no need for carrying out the two operations independently (i.e., coputing wavelet decopositions, odifying wavelet coefficients for enhanceent of specific features, reconstructing the enhanced iages, perforing wavelet transfors of the enhanced iages, fusing transfor coefficients, and obtaining the final result by reconstruction fro fused wavelet coefficients). Both enhanceent and fusion are therefore iplicit (i.e., perfored in the wavelet doain only).

2 Ficros() (icros) Input Maogra Decoposition Fasses() (asses) Fusion of Enhanced Maogra Fstellate() (stellate) Figure 1: Overview of the algorith. Figure 1 presents a block schee of the overall algorith. The algorith consists of two ajor steps: (1) wavelet coefficients are odified distinctly for each type of alignancy; (2) the obtained ultiple sets of wavelet coefficients are fused into a single set fro which the reconstruction is coputed. The devised schee allows efficient deployent of an enhanceent strategy appropriate for clinical screening protocols: enhanceent algorith is first developed for each specific type of feature independently, and the results are then cobined using an appropriate fusion strategy. The structure of the algorith also enables independent developent and optiization of enhanceent strategies for individual aographic features as well as the fusion odule. 2.1 B-Spline Transfor Since diagnostic features in aogras appear in a variety of shapes and sizes, traditional iage enhanceent techniques such as histogra equalization and unsharp asking seldo produce satisfactory results and are clearly outperfored by ore sophisticated ethods [10, 12]. Recognizing the benefit of aographic iage processing across different scales have resulted in a variety ofwavelet-based techniques; however, the choice of an appropriate wavelet transfor is of crucial iportance. In enhanceent ofa- ogras, for exaple, it is essential to iprove the visibility of features without distorting their appearance and shape. Algorith introduced artifacts are dangerous since they can lead to isdiagnosis, and lack of translation invariance of the transfor has been identified as a possible source of artifacts. In the light of this ajor shortcoing of orthogonal and biorthogonal wavelet transfors, translation-invariantovercoplete wavelet representations of signals have becoepopular [2, 10, 13,14]. In two diensions, the lack of rotation invariance affects the processing results as well, and several steerable [3] wavelet transfors have been devised to address this proble [1, 8, 9]. Translation and rotation invariance are equally iportant for iage fusion applications, and our experients have shown eliination of orthogonal and biorthogonal wavelet transfor caused artifacts when the steerable dyadic wavelet transfor based fusion ethod [7] has been used. Here, we eploy a generalization of the discrete dyadic wavelet transfor [11] with wavelets being equal to the second derivative of a central B-spline. This ultiscale spline derivative-based transfor [5] has several nice properties: (1) it is translationinvariant and approxiately steerable, (2) it is well suited for incorporating flexibility fro a variety of ethods [1, 2, 4, 8,10,13,14], and (3) it can be ipleented as a filter bank consisting of one-diensional filters only. The wavelets can be expressed as where ψ(x; y) %(x; 2 ; %(x; y) =fi p+2 (x)fi p+2 (y) and fi p (x) denotes a central B-spline of order p 2 N. Since central B-splines can closely approxiate a Gaussian probability density function (in fact, they converge to a Gaussian as their order tends to infinity), %(x; y) can be ade approxiately circularly syetric and, consequently, ψ(x; y) approxiately steerable. A rotation of ψ(x; y) by 0 can therefore be approxiated by ψ 0 (x; y) ' (cos 0 @x + 2 cos 2 0 sin 2 + +(sin 0 2 %(x; y); so that the set of basis functions that approxiately steer the wavelets ψ(x; y) is g. 2 Figure 2 shows the building blocks of a filter bank ipleentation of the transfor which uses the set of

3 G (2 ω ) 2 x G (2 ω ) G (2 ω ) 1 x 1 y G 2(2 ω y) H(2 ω x) (a) H(2 ω y) 2(2 ω x ) L (2 ω y) 1(2 ω x) 1(2 ω y) L (2 ω x) 2(2 ω y) H(2 ω x) H(2 ω y) (b) Figure 2: Filter bank ipleentation of a ultiscale spline derivative-based transfor with a second derivative wavelet. Basic processing odules for (a) decoposition and (b) reconstruction at a scale 2. basis functions needed to approxiately steer ψ(x; y). The filters were specified as G 2 d d (!) j!( =e 2 )! 2j sin 2 d;! H(!) = cos 2 2p; L(!) =jh(!)j 2 ; and 2 d j!( 2 d d (!) = 1 (2j) d e 2 ) sin! 2 P2p 1 =0 cos! 2; 2 where d 2f1; 2g. All the filters are either syetric or antisyetric, a property which enables an additional speedup when a syetric (e.g., irror extended) input signal is used [6]. B-spline approxiations are also well suited for carrying out the proper initialization of the wavelet transfor by eans of siple prefiltering. Such a spline based initialization can significantly iprove the accuracy of processing at finer scales. 2.2 Enhanceent and Fusion After the wavelet decoposition, the obtained coefficients are odified for iproved visualization of features of diagnostic iportance. Local enhanceent of icrocalcifications, circuscribed asses, and stellate lesions has been developed for each type of alignancy separately. An advantage of the ethod represented by Figure 1 is the fact that the entire processing algorith can be split into subprobles which can be tackled independently. For enhanceent of icrocalcifications, second derivatives along directions of x and y-axis are added to for an approxiation to a Laplacian of Gaussian. The obtained coefficients are thresholded, and the original coefficients at the corresponding locations ultiplied by a gain factor. Siilar enhanceent through detection was used by Strickland and Hahn [13, 14]. To reduce the nuber of false-positive elongated saples, the strength of local orientation was coputed by eploying second derivative wavelets in conjunction with their Hilbert transfor pairs for ultiscale orientation analysis. Note that, although not ipleented for the purpose of this paper, it is possible to obtain voices of the transfor as well (e.g., octaves 2.5" and 3.5" [13, 14]); central B-spline properties enable coputation of the transfor at any integer scale [15]. Enhanceent of circuscribed asses is carried out by applying a piecewise linear enhanceent function [2] to wavelet coefficients at scales 2 3 through 2 5. The selection of the scale range was based upon the pixel resolution (116μ) of digitized aogras in the University of Florida database. Stellate lesions are contrast enhanced according to the observation that they introduce a distortion into a radial orientation pattern fro the nipple to the chest wall [4]. The 1-nor of differences between local orientation and average orientation within a sliding window is used as an input to a soft thresholding function at each dyadic scale independently [8]. The choice of enhanceent paraeters controls the aggressiveness/subtleness of each resultant enhanceent (i.e., proinence of the targeted feature with respect to the surrounding tissue). Note also that it is possible to put different weights on features, and exclude certain features fro the final result. 3 Experiental Results Our ethod was applied to digitized aogras fro the University of Florida database, and showed proising results in ters of iproved visibility and detection of subtle features. Figure 3 deonstrates the results of processing using the ultiscale analysis contrast enhanceent algorith [10], and using the proposed fusion of enhanced features ethod. In this exaple, the fusion of enhanced features ephasizes the appearance of a ass which is surrounded by dense parenchya of the breast. Our preliinary results suggest that this type of iage is ore easily interpreted by radiologists copared to iages produced via global enhanceent techniques; however, the ultiscale analysis contrast enhanceent algorith [10] is being refined as well. A powerful aspect of the enhanceent via fusion schee lies in its flexibility: the ultiscale analysis based global contrast enhanceent algorith [10] can be readily incorporated into the schee as one of the branches before the fusion odule.

4 4 Conclusion The described ethod incorporates a variety of properties of aographic iage enhanceent ethods tailored to specific signs of alignancy into a unified coputational fraework. Multiscale spline derivative-based transfor has proved flexible enough for iplicit enhanceent of individual types of aographic features and thus enabled processing within a single wavelet transfor decoposition. In addition to its efficiency, the algorith is also well suited for further refineents; optiizations can be perfored for each type of alignancy alone, and separately for the fusion strategy. Our preliinary experients iply that the enhanceent via fusion approach can provide ore obvious clues for radiologists. Further clinical tests are planned to verify that the versatility of this paradig can provide a better viewing environent for an easier and a ore reliable interpretation of aogras. Acknowledgent This work was supported by the U.S. Ary Medical Research and Materiel Coand under DAMD References [1] C.-M. Chang and A. Laine, Enhanceent of aogras fro oriented inforation," in Proc. IEEE Int. Conf. Iage Process., Santa Barbara, CA, Oct. 1997, vol. 3, pp [2] J. Fan and A. Laine, Multiscale contrast enhanceent and denoising in digital radiographs," in s in Medicine and Biology, A. Aldroubi and M. Unser, Eds., CRC Press, Boca Raton, FL, 1996, pp [3] W. T. Freean and E. H. Adelson, The design and use of steerable filters," IEEE Trans. Pattern Anal. Machine Intell., vol. 13, pp , [4] W. P. egeleyer, J. M. Pruneda, P. D. Bourland, A. Hillis, M. V. Riggs, and M. L. Nipper, Coputer-aided aographic screening for spiculated lesions," Radiology, vol. 191, pp , [5] I. oren, A Multiscale Spline Derivative-Based Transfor for Iage Fusion and Enhanceent, Ph.D. thesis, Departent of Electrical and Coputer Engineering, University of Florida, Gainesville, FL, [6] I. oren and A. Laine, A discrete dyadic wavelet transfor for ultidiensional feature analysis," in M. Akay (Editor), Tie-Frequency and s in Bioedical Signal Engineering, New York, NY: IEEE Press, 1998, pp [7] I. oren, A. Laine, and F. Taylor, Iage fusion using steerable dyadic wavelet transfor," in Proc. IEEE Int. Conf. Iage Process., Washington, D.C., Oct. 1995, vol. 3, pp [8] I. oren, A. Laine, F. Taylor, and M. Lewis, Interactive wavelet processing and techniques applied to digital aography," in Proc. IEEE Int. Conf. Acoust. Speech Signal Process.,Atlanta, GA, May 1996, vol. 3, pp [9] A. Laine, I. oren, W. Yang, and F. Taylor, A steerable dyadic wavelet transfor and interval wavelets for enhanceent of digital aography," in Applications II, H. H. Szu, Ed., Proc. SPIE, Orlando, FL, Apr. 1995, vol. 2491, pp [10] A. F. Laine, S. Schuler, J. Fan, and W. Huda, Maographic feature enhanceent by ultiscale analysis," IEEE Trans. Med. Iaging, vol. 13, pp , [11] S. Mallat and S. Zhong, Characterization of signals fro ultiscale edges," IEEE Trans. Pattern Anal. Machine Intell., vol. 14, pp , [12] W. M. Morrow, R. B. Paranjape, R. M. Rangayyan, and J. E. L. Desautels, Region-based contrast enhanceent of aogras," IEEE Trans. Med. Iaging, vol. 11, pp , [13] R. N. Strickland and H. I. Hahn, transfor atched filters for the detection and classification of icrocalcifications in aography," in Proc. IEEE Int. Conf. Iage Process., Washington, D.C., Oct. 1995, vol. 1, pp [14] R. N. Strickland and H. I. Hahn, transfors for detecting icrocalcifications in aogras," IEEE Trans. Med. Iaging, vol. 15, pp , [15] M. Unser, A. Aldroubi, and S. J. Schiff, Fast ipleentation of the continuous wavelet transfor with integer scales," IEEE Trans. Signal Process., vol. 42, pp , [16] H. Yoshida, W. Zhang, W. Cai,. Doi, R. M. Nishikawa, and M. L. Giger, Optiizing wavelet transfor based on supervised learning for detection of icrocalcifications in digital aogras," in Proc. IEEE Int. Conf. Iage Process., Washington, D.C., Oct. 1995, vol. 3, pp

5 (a) (b) (c) Figure 3: (a) Original aogra. (b) Contrast enhanceent by ultiscale analysis [10]. obtained by fusion of enhanced features. (c) Enhanceent