Demons Methods for Digital Mammography Registration

Transcription

1 Demons Methods for Digital Mammography Registration Yago Díez 1, Meritxell Tortajada 1,SergiGanau 2, Lidia Tortajada 2, Melcior Sentís 2, and Robert Martí 1 1 Computer Vision and Robotics Group, University of Girona, Spain {yago,txell,marly}@eia.udg.edu 2 UDIAT-CD, Corporació Sanitària Parc taulí, Sabadell, Spain Abstract. Image registration is regarded as an important tool for the analysis of temporal mammograms, specially for lesion detection. However, it has not been widely adopted due to the complexity of the problem and the limitations of the algorithms. This work evaluates the suitability of Diffeomorphic Demons for temporal mammographic registration. Analysis in a dataset of 440 images from 53 different patients (performing over 3300 registrations) shows a better registration quality using different objective measures compared to standard Rigid and Non-Rigid algorithms. In addition, a study of the effects of lesions in the registration is performed, indicating that registration results (specially for the Demons) can be potentially used for lesion detection. 1 Introduction Medical imaging is one of the most commonly used application areas for image registration, specially for non-rigid paradigms (see for instance the survey in [1]). The analysis of mammographic images is not an exception [2,6]. Most of the published approaches focus on registering image features such as breast boundary or internal regions such as, for example, the pectoral muscle. However, a reduced number of approaches have been proposed using intensity based information only. Moreover, it was reported in [3] that Rigid transformations obtained more robust results compared to Non-Rigid methods in terms of producing less nonrealistic distortions. More recently, the work in [4] where authors evaluate a larger number of Rigid and Non-Rigid intensity based algorithms, shows that although these unrealistic deformations can occur, well parametrized Non-Rigid algorithms obtain a better overall performance. The main goal of this work is to evaluate the suitability of a particular implementation of the Demons algorithm, the Diffeomorphic Demons, for temporal mammographic registration compared to other existing methods. Authors have shown [4] that the conventional Demons algorithm, although obtaining satisfactory results for similarity metrics, is deemed unsuitable for mammography analysis by perceptual studies due to the severe distortions induced. Complementary goals of this research are also the proposal of new measures for evaluating the quality of registration and the study of the effects of breast lesions (masses and J.M. Sanches, L. Micó, and J.S. Cardoso (Eds.): IbPRIA 2013, LNCS 7887, pp , c Springer-Verlag Berlin Heidelberg 2013

2 254 Y. Díez et al. architectural distortions) in the registration of a large database of patients with temporal information (images from the same breast acquired at different times). This paper is structured as follows: in section 2, we briefly describe the image registration algorithms and their implementation. Subsequently, registration results are presented, providing details on the data, experiments and quantitative analysis (Sec. 3). Finally, discussions and conclusions are provided (Sec. 4). 2 Materials and Methods 2.1 Data Base The images used in this study were obtained from our local digital database. We used 440 full-field digital (FFD) mammograms from 53 patients with breast cancer who had at least two mammographic studies, specifically 49 patients have two studies and 4 patients have three studies. Each study contains four mammographic images, two views (cranio-caudal and medio-lateral oblique) of left and right breasts. Mammograms were acquired using a Selenia FFD mammography system, with resolution 70 micron per pixel, size 4096x3328 or 2560x3328, and 12-bit depth. This work is focused on temporal comparison of mammograms, therefore each mammographic image is registered with its homonymous mammogram in posteriors studies using different registration methodologies doing in total more than 3300 temporal registrations. Presence of masses was annotated by expert radiologists and this allowed us to distinguish between those registration instances containing masses and those not containing them. 2.2 Image Preprocessing During the preprocessing stage, the breast skin-line and the pectoral muscle were manually segmented. Background and pectoral muscle areas were eliminated to preserve the breast area. To reduce computation time, images were resized (quarter size image) using bilinear interpolation. In addition, mammograms were flipped when necessary to match the orientation of the breasts in each mammogram. After that, a peripheral enhancement was applied to compensate thickness variations in breast periphery. During mammographic acquisitions, breast is compressed with a tilting compression paddle, so breast thickness can be non uniform, being lower in the periphery and overexposing this area. The peripheral enhancement determines the overexposed area by Otsu s thresholding and applies a correction factor over the detected region. Each pixel is divided by the mean value of its real neighbourhood and multiplied by the mean value of its ideal neighbourhood according continuity constraints [12]. 2.3 Registration Methods The Diffeomorphic Demons [13] algorithm derives from Thyrion s Demons [11]. The authors reformulated the original idea by formalizing Demons optimization

3 Demons Methods for Digital Mammography Registration 255 over the space of displacement fields. The method has been since then used successfully in a variety of registration scenarios including brain magnetic resonance imaging registration [9]. Furthermore, the authors provided different variants corresponding to the operation allowed in the space of deformation field: exponentiation, addition and composition. In this work, we will focus on the additive variant. For comparison purposes, we also considered two widely used methods for mammography registration: Affine and B-splines [4]. Furthermore, we use all these methods to study the role of some commonly used registration aspects such as Affine initialization and multi-resolution (MR). From now on, Additive Difeomorphic Demons with MR but without Affine initialization is noted md. Additive Diffeomorphic Demons without MR but with Affine initialization is noted AD and Additive Diffeomorphic Demons with MR using also MR Affine initialization is noted mamd. As for Non-Demons methods, A stands for plain Affine registration, mb corresponds to MR B-splines without Affine initialization, AB represent single resolution B-splines with Affine initialization and mamb includes both MR Affine initialization and MR B-splines. 2.4 Statistical Analysis We use boxplots as a compact way to describe thousands of data. Specifically, throughout section 3 we will present several multiple boxplots where each box will group the data resulting from a registration method. Although this is a convenient way to visualize data, statistical inference is necessary in order to provide objective backup to observations. As in this paper we compare the performance of several methods. Pairwise t-tests are the natural option, but given the high number of method pairs, their use is impractical. We present selected t-tests to highlight specific comparisons. In order to present pairwise comparisons between methods in a compact way, we use permutation tests. These tests choose pairs of methods and small sets of independent values obtained by them. Then pairwise hypothesis tests are performed. These tests are regarded in [10] to compute the p-value more exactly than usual t-tests. Finally, the number of times when p<0.05 is stored for every method. All these steps are repeated and what we present is the mean and standard deviation (μ, σ) of the times when each method produced significant p-values. Consequently, methods with higher means have passed a higher number of pairwise comparisons using randomly chosen subsets of values. Following [9], methods are presented in ranks determined by the best performing method (with mean and standard deviation noted μ 0,σ 0 ). Ranks are decided in terms of the distance of method means to μ 0.Specifically,rank1 methods are those in (μ 0 σ 0,μ 0 ], rank 2 methods fall in (μ 0 2σ 0,μ 0 σ 0 ]and finally rank 3 methods are those in the interval (μ 0 3σ 0,μ 0 2σ 0 ]. See [9,10] for further details on permutation tests.

4 256 Y. Díez et al. 3 Experimental Study All registration methods were implemented using the Insight Toolkit (itk) libraries [5]. We used 128 histogram bins and samples for metric computations. A minimum step length stopping criteria was also used. For practical reasons we also fixed a maximum number of iterations for all methods to a maximum of 1000 iterations. In combined or MR methods these iterations were evenly distributed between the methods or MR levels. The Diffeomorphic Demons implementation used for the calculations in this paper can be downloaded at [7]. 3.1 Metrics Metric values are the most widely used tool to measure image similarity in computer vision. Concerning their application to intensity-based registration of medical images, their use is twofold: first they provide the aforementioned quantification of similarity between images. Second, the registration process in usually formalized as an optimization problem and metric values determine both stopping conditions and solution update. This is true for B-splines and Affine registration but not for Diffeomorphic Demons, as these methods use an optimization function defined over the space of displacement fields. Consequently, metric measurements provide an objective value on how successful some methods were in terms of optimization and how similar two images are in their own particular terms. Unfortunately, a metric that is able to express exactly what medical experts perceive as a better registration does not yet exist, so other criteria are also necessary. In the results presented, the Mutual Information metric (MI) was used as the function to optimize for Affine and B- splines registration. Data on the Sum of Squared Distances metric (SSD) is also provided in order to gain insight in the two mentioned aspects of the process. Table 1 presents the permutation tests for the two metrics studied: MI and SSD. As is usual with permutation test, only methods that achieve positive test means are presented. The data shows how for both metrics the methods able to achieve the highest positive test means are Demons based methods. The best method in this pairwise comparison is always mamd (combining Affine initialization and MR Demons), other Demons-based methods follow, but their ranks are reversed depending on which metric is considered. Table 1. Permutation test for MI and SSD MI SSD METHOD μ σ METHOD μ σ Rank 1 mamd mamd md AD Rank 2 AD md Rank 3 AB AB

5 A Demons Methods for Digital Mammography Registration 257 The mentioned trends are much more evident when presented visually in terms of metric boxplots. Fig. 1 provides compared performances of Demons and B-splines based methods as well as standalone Affine registration. Data is provided separately for registrations with and without masses. For the sake of concreteness, all data corresponds to MI, although similar trends are observed for SSD. Notice how, the mean values presented in table 1 and figure 1 are not directly related. In the first case, the permutation test deal with how many times a particular method has passed a pairwise hypothesis test against another method while in the second case, the mean MI value presented relates to the degree of success obtained by each method after registration. We observe how Demons based methods do better than other approaches. We also see how combining both Affine initialization and MR works best for Demons and B-splines. If only one of the two improvements is used, Demons methods seem to benefit more from MR while B-splines favour Affine initialization. Concerning the presence of masses, mean values for every method slightly decrease. This is clearer for Demons methods and suggests the possibility of using Demons methods in registration applications such as lesion or mass detection. This possibility will be addressed further in section A BEF md AD (a) mamd mb AB mamb BEF md AD (b) mamd mb AB mamb Fig. 1. Mutual information. Temporal registrations a) without masses and b) with masses. Measurements before registration are noted as BEF. Values correspond to MI, so higher positive values stand for better results. 3.2 Deformation Fields In Non-Rigid registration, every pixel is transformed in a way that does not necessarily be related to its neighbouring pixels. Each of these movements can be expressed by a displacement vector. The union of all these vectors stands for a displacement (or deformation) field that characterises the Non-Rigid transformation. Fig. 2 shows a visual example of a deformation field. For ease of

6 258 Y. Díez et al. (a) (b) (c) Fig. 2. Deformation field example: (a) source image, (b) target image with visible mass and (c) corresponding AD deformation field visualization, only vector norms are presented in the image in the form of a color code. Pixels closer to red correspond to higher norm values and pixels closer to white to lower values. The figure shows the potential of deformation fields for applications such as mass detection. Pixels corresponding to the mass appearing in the second temporal study present the highest norm values in the whole of the image. We study deformation fields corresponding to Demons and B-spline methods. For the automatic study of these fields, several parameters can be considered [8]. We focus on two of them: average and maximum norms of the vectors in the deformation field. Our aim is to provide statistical support to the claim that flexible registration methods, specially Diffeomorphic Demons, can be used for mass detection in digital mammography images. Concerning the average norm of the deformation field of the methods studied, we computed the mean values of this average norm for every method before and after registration. A noticeable increase was observed, specially for Diffeomorphic Demons methods. This behaviour was observed even more clearly for the maximumnormindicator(seetable2). In order to provide inferential backing to these observations of descriptive statistics, a set of pairwise t-tests was performed to check if the maximum norm of a given method was significantly different for registrations with and without masses. The alternative hypothesis (H 1 ) was stated as the maximum norm is higher for registrations with masses than for those without masses. Results showed statistically significant difference for md (p value = ) and for mamd (p value = ). This did not, however, happen, for any of the B-splines methods whose p-values were all over 0.4. This shows the potential of Diffeomorphic Demons methods for mass detection in digital mammography. Results of the maximum norm of the vectors in the deformation field are also visualised in Fig 3. Maximum norms for all Non-Rigid methods studied are presented, data is provided separately for registrations with and without masses.

7 Demons Methods for Digital Mammography Registration 259 Table 2. Statistical summary of deformation fields for all methods. Registrations with and without masses are presented separately. Average Norm Max Norm Without Masses With Masses Without Masses With Masses μ σ μ σ μ σ μ σ md AD mamd mb AB mamb We observe how Demons methods produce deformations with higher maximum norm than B-splines. We also see how, as expected, using Affine initialization decreases the maximum norm. This happens as the initial Affine step helps cover part of the distance that each pixel has to cover in order to reach its corresponding pixel. Furthermore, the increase in maximum norm for registrations with masses is also visible md AD mamd (a) mb AB mamb md AD mamd (b) mb AB mamb Fig. 3. Deformation Field Maximum Norm. Temporal registrations a) without masses and b) with masses. 4 Discussion and Conclusions We have presented results using over 3300 registrations corresponding to breast cancer patients. The analysis of metric data shows how Demons based methods outperform Affine and B-splines based approaches. We have also studied the use of MR and Affine initialization for flexible methods showing how the best results are obtained by the combination of the two techniques. Access to annotations

8 260 Y. Díez et al. from expert radiologist allowed us to discriminate those registrations containing masses from those not containing them. The analysis of differences between both scenarios using deformation fields showed statistically significant differences in behaviour for Demons methods. To sum up, according to our study, not only does Demons provide best results in terms of measures commonly used to evaluate the quality of registration but it also shows application possibilities in specific fieldssuchasmassdetection. Acknowledgment. This work was partially supported by the Spanish Science and Innovation grant TIN C References 1. Zitova, B.: Image registration methods: a survey. Image and Vision Computing 21(11), (2003) 2. Guo, Y., Sivaramakrishna, R., Lu, C.C., Suri, J., Laxminarayan, S.: Breast image registration techniques: a survey. Medical and Biological Engineering and Computing 44(1), (2006) 3. van Engeland, S., Snoeren, P., Hendriks, J., Karssemeijer, N.: A comparison of methods for mammogram registration. IEEE Transactions on Medical Imaging 22(11), (2003) 4. Díez, Y., Oliver, A., Lladó, X., Freixenet, J., Martí, J., Vilanova, J., Martí, R.: Revisiting intensity-based image registration applied to mammography. IEEE Transactions on Information Technology in Biomedicine 15(5), (2011) 5. Ibáñez, L., Schroeder, W., Ng, L., Cates, J.: The ITK Software Guide, 1st edn. Kitware, Inc. (2003), ISBN Díez, Y., Oliver, A., Lladó, X., Martí, R.: Comparison of registration methods using mammographic images. In: IEEE International Conference on Image Processing, pp (2010) 7. Vercauteren, T., Pennec, X., Perchant, A., Ayache, N.: Diffeomorphic Demons Using ITK s Finite Difference Solver Hierarchy, 8. Janssens, G., Jacques, L., Orban de Xivry, J., Geets, X., Macq, B.: Diffeomorphic registration of images with variable contrast enhancement. International Journal of Biomedical Imaging 2011(891585), 16 pages, doi: /2011/ Klein, A., Andersson, J., Ardekani, B.A., Ashburner, J., Avants, B., Chiang, M., Christensen, G.E., Collins, D.L., Gee, J., Hellier, P., Hyun Song, J., Jenkinson, M., Lepage, C., Rueckert, D., Thompson, P., Vercauteren, T., Woods, R.P., Mann, J.J., Parseya, R.V.: Evaluation of 14 nonlinear deformation algorithms applied to human brain MRI registration. NeuroImage 46(3), (2009) 10. Menke, J., Martinez, T.: Using permutations instead of Student s t distribution for p-values in paired difference algorithm comparisons. In: Proceedings of IEEE International Joint Conference on Neural Networks, pp (2004) 11. Thirion, J.: Fast non-rigid matching of 3D medical images. HAL-CCSd-CNR (1995) 12. Tortajada, M., Oliver, A., Martí, R., Vilagran, M., Ganau, S., Tortajada, L., Sentís, M., Freixenet, J.: Adapting breast density classification from digitized to full-field digital mammograms. In: Maidment, A.D.A., Bakic, P.R., Gavenonis, S. (eds.) IWDM LNCS, vol. 7361, pp Springer, Heidelberg (2012) 13. Vercauteren, T., Pennec, X., Perchant, A., Ayache, N.: Diffeomorphic demons: efficient non-parametric image registration. NeuroImage 45(1-1) (2009)