3D Object Modeling

Summary

Range Data Registration in the Frequency Domain

Building 3D models is an important problem in several areas, such as forensic applications, medical applications, industrial inspection, or virtual visits of 3D synthetic environments. One way to build models is by acquiring range data images, by means of laser scanners, and then stitching them together. This implies registering, or aligning range data pairs. (Lucchese et al., 2002) introduces an original method to solve this problem, which operates in the frequency domain. The Fourier transform allows decoupling the estimation of the rotation parameters from the estimation of the translation parameters. The algorithm exploits this well-known property by suggesting a three-step procedure. The performance of the algorithm is assessed through extensive testing with several objects and shows that good and very robust estimates of 3D rigid motion are achievable, and are well suited for unsupervised registration. The algorithm can be used as a pre-alignment tool for more accurate space-domain registration techniques, like the ICP algorithm. These methods have been successfully deployed for building models of cultural heritage objects, and for registering computed tomography data.

Euclidean and Affine Registration in the Frequency Domain

Free-form 3D surfaces registration can be made more robust by integrating the surface albedo. (Cortelazzo et al., 1998) investigates this problem in the Fourier domain and proposes a new technique that uses radial projections of the frequency domain representation of the combined range and intensity data. An interesting extension of the algorithm can be used for the estimation of 3D affine transformations. The obtained results are useful per se in applications targeted to enhancing the visual quality of the models, or can serve as a good starting point for the ICP algorithm when a higher precision is needed.

References

1. TPAMI

   A frequency domain technique for range data registration Lucchese, L., Doretto, G., and Cortelazzo, G. M. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2002. abstract bibTeX pdf doi

   This work introduces an original method for registering pairs of 3D views consisting of range data sets which operates in the frequency domain. The Fourier transform allows the decoupling of the estimate of the rotation parameters from the estimate of the translation parameters, our algorithm exploits this well- known property by suggesting a three-step procedure. The rotation parameters are estimated by the first two steps through convenient representations and projections of the Fourier transforms’ magnitudes and the translational displacement is recovered by the third step by means of a standard phase correlation technique after compensating one of the two views for rotation. The performance of the algorithm, which is well-suited for unsupervised registration, is clearly assessed through extensive testing with several objects and shows that good and robust estimates of 3D rigid motion are achievable. Our algorithm can be used as a prealignment tool for more accurate space-domain registration techniques, like the ICP algorithm.

   @article{luccheseDC02IEEEtpami,
     abbr = {TPAMI},
     author = {Lucchese, L. and Doretto, G. and Cortelazzo, G. M.},
     title = {A frequency domain technique for range data registration},
     journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
     year = {2002},
     volume = {24},
     pages = {1468--1484},
     number = {11},
     month = nov,
     bib2html_pubtype = {Journals},
     bib2html_rescat = {3D Object modeling},
     doi = {10.1109/TPAMI.2002.1046160},
     file = {luccheseDC02IEEEtpami.pdf:doretto\\journal\\luccheseDC02IEEEtpami.pdf:PDF;luccheseDC02IEEEtpami.pdf:doretto\\journal\\luccheseDC02IEEEtpami.pdf:PDF},
     issn = {0162-8828},
     keywords = {Fourier transforms, frequency-domain analysis, image motion analysis,
     	image registration, parameter estimation},
     owner = {doretto},
     timestamp = {2007.01.19}
   }
   

2. ICIP

   Free-form textured surfaces registration by a frequency domaintechnique Cortelazzo, G. M., Doretto, G., and Lucchese, L. In Proceedings of IEEE International Conference on Image Processing, 1998. abstract bibTeX pdf doi

   Free-form 3-D surfaces registration is a fundamental problem in 3-D imaging, typically approached by extensions or variations of the ICP algorithm. This work presents a new frequency domain technique for 3-D view registration, totally different form any other techniques for 3-D motion estimation also, based on the Fourier transform. The proposed method can give a non-feature- based method for unsupervised registration of 3-D views. The obtained results are useful “per se” in applications targeted to visual quality or can serve as good starting point for the ICP algorithm when a higher precision is needed

   @inproceedings{cortelazzoDL98icip,
     abbr = {ICIP},
     author = {Cortelazzo, G. M. and Doretto, G. and Lucchese, L.},
     title = {Free-form textured surfaces registration by a frequency domaintechnique},
     booktitle = {Proceedings of IEEE International Conference on Image Processing},
     year = {1998},
     volume = {1},
     pages = {813--817},
     address = {Chicago, IL, USA},
     month = oct,
     bib2html_pubtype = {Conferences},
     bib2html_rescat = {3D Object Modeling},
     doi = {10.1109/ICIP.1998.723634},
     file = {cortelazzoDL98icip.pdf:doretto\\conference\\cortelazzoDL98icip.pdf:PDF;cortelazzoDL98icip.pdf:doretto\\conference\\cortelazzoDL98icip.pdf:PDF},
     keywords = {Fourier transforms, frequency-domain analysis, image registration,
     	image texture, motion estimation},
     owner = {doretto},
     timestamp = {2007.01.19}
   }