Gaussian Process Implicit Surfaces
Oliver J. Williams, Andrew W Fitzgibbon · 2006
Many applications in computer vision and computer graphics require the definition of curves and surfaces. Implicit surfaces [7] are a popular choice for this because they are smooth, can be appropriately constrained by known geometry, and require no special treatment for topology changes. Given a scalar function f: R d ↦ → R, one can define a manifold S of dimension d − 1 wherever f(x) passes through a certain value (e.g., 0) S0 � {x ∈ R d |f(x) = 0}. (1) In this paper we introduce Gaussian processes (GPs) to this area by deriving a covariance function equivalent to the thin plate spline regularizer [2] in which smoothness of a function f(x) is encouraged by the energy � � T 2 E(f) = ∇ ∇f(x) dx (2)