712 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 18, NO. 8, AUGUST 1999 Nonrigid Registration Using Free-Form Deformations: Application to Breast MR Images D. Rueckert,* L. I. Sonoda, C. Hayes, D. L. G. Hill, M. O. Leach, and D. J. Hawkes Abstract— In this paper we present a new approach for the nonrigid registration of contrast-enhanced breast MRI. A hierar- chical transformation model of the motion of the breast has been developed. The global motion of the breast is modeled by an affine transformation while the local breast motion is described by a free-form deformation (FFD) based on B-splines. Normalized mutual information is used as a voxel-based similarity measure which is insensitive to intensity changes as a result of the contrast enhancement. Registration is achieved by minimizing a cost function, which represents a combination of the cost associated with the smoothness of the transformation and the cost associated with the image similarity. The algorithm has been applied to the fully automated registration of three-dimensional (3-D) breast MRI in volunteers and patients. In particular, we have compared the results of the proposed nonrigid registration algorithm to those obtained using rigid and affine registration techniques. The results clearly indicate that the nonrigid registration algorithm is much better able to recover the motion and deformation of the breast than rigid or affine registration algorithms. I. INTRODUCTION C ARCINOMA of the breast is the most common ma- lignant disease in women in the western world. 9.5% of women will develop the disease in the United Kingdom [1]. The major goals of breast cancer diagnosis are early detection of malignancy and its differentiation from other breast disease. Currently, the detection and diagnosis of breast cancer primarily relies on X-ray mammography. For further differentiation of mammographic or clinical abnormalities, ultrasonography, transcutaneous biopsy, and MRI are used. Although X-ray mammography has the advantage of high sensitivity, almost approaching 100%, in fatty breast tissue, high resolution up to 50 m, and low cost, it has a number of disadvantages, such as low sensitivity in dense glandular breast tissue, low specificity, and poor signal-to-noise ratio. Furthermore, the projective nature of the images and the exposure to radiation limit its applicability, especially for Manuscript received November 4, 1998; revised July 6, 1998. the work of D. Rueckert and D. J. Hawkes was supported by in part by the EPSRC Project under Grant GR/L08519. The work C. Hayes and M. O. Leach was supported in part by the MRC under Grant G9600413 and in part by the CRC under Grant SP1780/0103. The Associate Editor responsible for coordinating the review of this paper and recommending its publication was D. Metaxas. Asterisk indicates corresponding author. *D. Rueckert, L. I. Sonoda, D. L. G. Hill, and D. J. Hawkes are with the Division of Radiological Sciences and Medical Engineering, Guy’s, King’s, and St. Thomas’ School of Medicine, King’s College London, Guy’s Hospital, London SE1 9RT, U.K. (e-mail: D.Rueckert@umds.ac.uk). C. Hayes and M. O. Leach are with the CRC Clinical Magnetic Resonance Research Group, Institute of Cancer Research, Royal Marsden Hospital, Sutton SM2 5PT, U.K. Publisher Item Identifier S 0278-0062(99)08508-0. young premenopausal women with a genetic predisposition to develop breast cancer. This has led to the investigation of alternative imaging modalities, such as MRI, for the detection and diagnosis of breast cancer [2]. Even though MRI mammography has disadvantages, such as a low spatial resolution of around 1 mm and the need for contrast agents, it has a number of advantages, including the tomographic, and therefore three- dimensional (3-D) nature, of the images. This allows the application of MRI mammography to breasts with dense tissue, postoperative scarring, and silicon implants. Furthermore, the lack of radiation makes it applicable to young premenopausal women. Typically, the detection of breast cancer in MRI requires the injection of a contrast agent such as Gadolinium DTPA. It is known that the contrast agent uptake curves of malignant disease differ from benign disease and this property can be used to identify cancerous lesions [3]. To quantify the rate of uptake, a 3-D MRI scan is acquired prior to the injection of contrast media, followed by a dynamic sequence of 3-D MRI scans. The rate of uptake can be estimated from the difference between pre- and postcontrast images. Any motion of the patient between scans, or even normal respiratory and cardiac motion, complicates the estimation of the rate of uptake of contrast agent by the breast tissue. To facilitate the analysis of pre- and postcontrast enhanced MRI, Zuo et al. [4] proposed a registration algorithm which minimizes the ratio of variance between images. However, their algorithm is based on the assumption that the breast is only undergoing rigid motion. Kumar et al. [5] proposed a nonrigid registration technique which uses an optical-flow type algorithm, but is based on the assumption that the intensities in the pre- and postcontrast enhanced images remain constant. A similar approach has been suggested by Fischer et al. [6]. To overcome the problems caused by nonuniform intensity change, Hayton et al. [7] developed a pharmacokinetic model, which is combined with an optical-flow registration algorithm. This algorithm has been applied to the registration of two- dimensional (2-D) breast MRI, but relies on the assumption that the change of intensities can be sufficiently explained by the pharmacokinetic model, which is not always the case. Any registration algorithm for the motion correction of contrast-enhanced breast MRI must take into account that the breast tissue deforms in a nonrigid fashion and that the image intensity and contrast will change, due to the uptake of the contrast agent. In recent years, many voxel- based similarity measures have shown promising results for multimodality image registration (for a detailed overview see 0278–0062/99$10.00  1999 IEEE