Towards statistically optimal interpolation for 3D medical imaging

The use of a statistical estimation technique called kriging, which produces estimation error measurements and analyzes the volumetric grid to determine sample value variability, is described. The use of interpolation in 3D medical imaging are first reviewed. Several different interpolation techniques, including linear trilinear, and tricubic interpolation techniques, are described and assessed. The kriging statistical estimation process is presented, and the results of applying it to slice interpolation and surface visualization are reported. The results indicate the potential of kriging for interpolation in 3D medical imaging and point out the need for further work.<<ETX>>

[1]  R. Webster,et al.  Kriging: a method of interpolation for geographical information systems , 1990, Int. J. Geogr. Inf. Sci..

[2]  N. Cressie.  The origins of kriging , 1990 .

[3]  Martin R. Stytz,et al.  Three-dimensional medical imaging: algorithms and computer systems , 1991, CSUR.

[4]  Gabor Herman,et al.  Display of 3-D Digital Images: Computational Foundations and Medical Applications , 1983, IEEE Computer Graphics and Applications.

[5]  Jane Wilhelms,et al.  Topological considerations in isosurface generation , 1994, TOGS.

[6]  E LorensenWilliam,et al.  Decimation of triangle meshes , 1992 .

[7]  M R Stytz,et al.  Three-dimensional medical imaging modalities: an overview. , 1990, Critical reviews in biomedical engineering.

[8]  Farrell Ej,et al.  Three-dimensional data visualization and biomedical applications , 1989 .

[9]  N. Cressie.  Kriging Nonstationary Data , 1986 .

[10]  William E. Lorensen,et al.  Marching cubes: A high resolution 3D surface construction algorithm , 1987, SIGGRAPH.

[11]  O. Dubrule.  Comparing splines and kriging , 1984 .

[12]  David Robinson,et al.  Statistically optimal interslice value interpolation in 3D medical imaging: theory and implementation , 1992, [1992] Proceedings Fifth Annual IEEE Symposium on Computer-Based Medical Systems.

[13]  W. Lorensen,et al.  Two algorithms for the three-dimensional reconstruction of tomograms. , 1988, Medical physics.

[14]  J. Udupa,et al.  Shape-based interpolation of multidimensional objects. , 1990, IEEE transactions on medical imaging.

[15]  Craig Upson,et al.  V-buffer: visible volume rendering , 1988, SIGGRAPH.

[16]  William E. Lorensen,et al.  Decimation of triangle meshes , 1992, SIGGRAPH.

[17]  Elliot K. Fishman,et al.  Volumetric rendering of computed tomography data: principles and techniques , 1990, IEEE Computer Graphics and Applications.

[18]  J. Wilhelms,et al.  Topological considerations in isosurface generation extended abstract , 1990, SIGGRAPH 1990.

[19]  G. Matheron.  Principles of geostatistics , 1963 .

[20]  Carolyn A. Bucholtz,et al.  Shape-based interpolation , 1992, IEEE Computer Graphics and Applications.

[21]  E LorensenWilliam,et al.  Marching cubes: A high resolution 3D surface construction algorithm , 1987 .

[22]  Gabor T. Herman,et al.  The theory, design, implementation and evaluation of a three-dimensional surface detection algorithm , 1980, SIGGRAPH '80.

[23]  Alan Watt,et al.  Fundamentals of three-dimensional computer graphics , 1989 .

[24]  Marc Levoy,et al.  Display of surfaces from volume data , 1988, IEEE Computer Graphics and Applications.