We propose a method for estimating intrasurgical brain shift for image-guided surgery. This method consists of five stages: the identification of relevant anatomical surfaces within the MRI/CT volume, range-sensing of the skin and cortex in the OR, rigid registration of the skin range image with its MRI/CT homologue, non-rigid motion tracking over time of cortical range images, and lastly, interpolation of this surface displacement information over the whole brain volume via a realistically valued finite element model of the head. This paper focuses on the anatomical surface identification and cortical range surface tracking problems. The surface identification scheme implements a recent algorithm which imbeds 3D surface segmentation as the level- set of a 4D moving front. A by-product of this stage is a Euclidean distance and closest point map which is later exploited to speed up the rigid and non-rigid surface registration. The range-sensor uses both laser-based triangulation and defocusing techniques to produce a 2D range profile, and is linearly swept across the skin or cortical surface to produce a 3D range image. The surface registration technique is of the iterative closest point type, where each iteration benefits from looking up, rather than searching for, explicit closest point pairs. These explicit point pairs in turn are used in conjunction with a closed-form SVD-based rigid transformation computation and with fast recursive splines to make each rigid and non-rigid registration iteration essentially instantaneous. Our method is validated with a novel deformable brain-shaped phantom, made of Polyvinyl Alcohol Cryogel.