Splines and wavelets for medical imaging

Both types of representations are useful when one wishes to consider image data as a continuum rather than a discrete array of pixels. Such a continuous modeling of the data is often required in medical imaging. Interpolation, in particular, plays a crucial role at various stages of processing [18, 24]. For instance, it is present—explicitly or not—for tomographic reconstruction, irrespective of the type of algorithm used (filtered backprojection, inverse Fourier or iterative reconstruction). Another important area is medical image visualization; this involves simple 2D operations such as image zooming, panning, rotation, or 3D manipulations, such as reslicing or maximum intensity projection [21], which are often used by radiologists. Interpolation models are also required for performing various types of image registrations [8, 33]; these include intra-modal registration for rigid-body motion compensation [P3], inter-modal registration of CT, PET and MR data sets of a same subject [10, 25], as well as elastic matching for stereotaxic normalization or distortion correction. Considering an image as a continuously–defined function is often desirable for feature extraction, in particular, contour detection. Likewise, wavelets have been found to be well-suited for multi-scale processing, noise filtration of medical images [36], statistical data analysis (fMRI and PET) [31], and feature extraction (e.g., texture).