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Biometrika 1996 83(1):207-221; doi:10.1093/biomet/83.1.207
© 1996 by Biometrika Trust
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Kriging and splines with derivative information

K. V. MARDIA, J. T. KENT, C. R. GOODALL and J. A. LITTLE

Department of Statistics, University of Leeds Leeds LS2 9JT, U.K.
Department of Statistics, Pennsylvania State University University Park, Pennsylvania 16802, U.S.A.
Division of Radiological Sciences, United Medical and Dental Schools 3rd floor, Guy's Tower, Guy's Hospital, London Bridge, London SE1 9RT, U.K.

Spline fitting is a popular method of interpolating a real-valued function given its values at a set of points in Rd. Other linear constraints such as derivative information can also be incorporated as we show here. Spline fitting is well known to be a special case of kriging. Using the kriging framework we give a full description of the theory including algorithms for computation, and various special cases are discussed. An application is given to the construction of deformations with landmark, tangent and curvature constraints.

Key Words: Conditionally positive definite function • Deformation • Derivative process • Intrinsic process • Object recognition • Radial basis function • Self-similarity • Thin-plate spline


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