A nonrigid registration of MR breast images using complex-valued wavelet transform

Abstract

In this paper, a fast, slice-by-slice, nonrigid registration algorithm of dynamic magnetic resonance breast images is presented. The method is based on a multiresolution motion estimation of the breast using complex discrete wavelet transform (CDWT): the pyramid of oriented complex subimages is used to implement a hierarchical phase-matching-based motion estimation algorithm. The resulting motion estimate is nonrigid and pixel-independent. To assess the method performance, we computed the correlation coefficient and the normalized mutual information between pre- and postcontrast images with and without realignment. The indices increased after using our approach and the improvement was superior to rigid or affine registration. A set of clinical scores was also evaluated. The clinical validation demonstrated an increased readability in the subtraction images. In particular, CDWT registration allowed a best definition of breast and lesion borders and greater detail detectability.

Fig 1

The registration algorithm.

Fig 2

Two-dimensional DWT processing block (top). The image (I) is filtered low-pass and high-pass by h₀ and h₁, respectively, and then down-sampled. This operation is firstly applied for columns and then for rows. I^(1,1) represents the input for the next decomposition level. CDWT outputs in frequency domain at level 1 (bottom). I^(1,1) and I^(2,1) are the low-resolution output images, whereas {D^(n,1), n=1,...,6} are the subband images oriented in the six directions defined by Wavelet filters.

Fig 3

Post-contrast image (a) and the correspondent non-registered (b) and registered (c) images. In (d), (e) and (f) the same images in which the same contour around the two significant lesions is put.

Fig 4

A case of multicentric lesion in the left breast. Maximum-intensity projection reconstruction of the images difference after a no registration, b rigid registration, c affine registration, and d wavelet registration. The arrow shows a small medial lesion in the left breast.

Fig 5

Subtraction between precontrast and postcontrast images in a cranial position: a no registration, b rigid registration, c affine registration, and d wavelet registration. In d, the cluster of lesion is better detectable. The right breast is also present to show the small controlateral lesion (arrow) detectable in d.

Fig 6

Performances of wavelet registration (wr) with respect to no registration (nr) and affine registration (ar). The graph represents the mean values of the clinical score for the different clinical aspects (standard deviation bars are superimposed).