Shape registration via the wavelet transform

We present a system for the automatic global registration of voxelized data using the wavelet transform. The huge size of current data sets makes such multi-resolution techniques appealing; however, the traditional discrete wavelet transform has the drawback of variance with translation and rotation. We employ the dualtree complex wavelet transform (Kingsbury, 2003), which carefully adds near invariance to translation and reduced sensitivity to rotation in computationally efficient ways, thus enabling the object matching application. We employ the wavelet transform to accomplish registration by extracting features in a multi-resolutional format, thus rapidly detecting and matching feature points. The method is robust to occlusion, clutter and noise. The efficacy of the algorithm is demonstrated through examples from solid modeling and biomedical applications.