Shape registration in implicit spaces using information theory and free form deformations (original) (raw)

2000, IEEE Transactions on Pattern Analysis and Machine Intelligence

We present a novel, variational and statistical approach for shape registration. Shapes of interest are implicitly embedded in a higher-dimensional space of distance transforms. In this implicit embedding space, registration is formulated in a hierarchical manner: the Mutual Information criterion supports various transformation models and is optimized to perform global registration; then, a B-spline-based Incremental Free Form Deformations (IFFD) model is used to minimize a Sum-of-Squared-Differences (SSD) measure and further recover a dense local nonrigid registration field. The key advantage of such framework is twofold: 1) it naturally deals with shapes of arbitrary dimension (2D, 3D, or higher) and arbitrary topology (multiple parts, closed/open) and 2) it preserves shape topology during local deformation and produces local registration fields that are smooth, continuous, and establish one-to-one correspondences. Its invariance to initial conditions is evaluated through empirical validation, and various hard 2D/3D geometric shape registration examples are used to show its robustness to noise, severe occlusion, and missing parts. We demonstrate the power of the proposed framework using two applications: one for statistical modeling of anatomical structures, another for 3D face scan registration and expression tracking. We also compare the performance of our algorithm with that of several other well-known shape registration algorithms. Index Terms-Shape registration, mutual information, free form deformations, correspondences, implicit shape representation, distance transforms, partial differential equations. ae 1 INTRODUCTION S HAPE registration is critical to various imaging and vision applications [1]. Global registration, also known as shape alignment, aims to recover a global transformation that brings the pose of a source shape as close as possible to that of a target shape. The alignment has extensive uses in recognition, indexing and retrieval, and tracking. To further account for important local deformations, nonrigid local registration is needed to establish dense correspondences between the basic elements of shapes, such as points, curvature, etc. Medical imaging is a domain that requires local registration such as in building statistical models for internal organs [2], and intrasubject or atlas registration of 2D/3D anatomical structures. There has been a lot of previous research on the shape registration problem [3], [4], [5], as well as on similar problems such as shape matching [6], [2], [7], [8], and point set matching [9]. The algorithms proposed differ in the following three main aspects.