In this paper we introduce the Progressive Forest Split (PFS) representation, a new adaptive refinement scheme for storing and transmitting manifold triangular meshes in progressive and highly compressed form. As in the Progressive Mesh (PM) method of Hoppe, a triangular mesh is represented as a low resolution polygonal model followed by a sequence of refinement operations, each one specifying how to add triangles and vertices to the previous level of detail to obtain a new level. The PFS format shares with PM and other refinement schemes the ability to smoothly interpolate between consecutive levels of detail. However, it achieves much higher compression ratios than PM by using a more complex refinement operation which can, at the expense of reduced granularity, be encoded more efficiently. A forest split operation doubling the number n of triangles of a mesh requires a maximum of approximately 3:5n bits to represent the connectivity changes, as opposed to approximately 5 + log 2 nn bits in PM.We describe algorithms to efficiently encode and decode the PFS format. We also show how any surface simplification algorithm based on edge collapses can be modified to convert single resolution triangular meshes to the PFS format. The modifications are simple and only require two additional topological tests on each candidate edge collapse. We show results obtained by applying these modifications to the Variable Tolerance method of Guéziec.

We describe new methods for rigid registration of a preoperative computed tomography (CT)-scan image to a set of intraoperative X-ray fluoroscopic images, for guiding a surgical robot to its trajectory planned from CT. Our goal is to perform the registration, i.e., compute a rotation and translation of one data set with respect to the other to within a prescribed accuracy, based upon bony anatomy only, without external fiducial markers. With respect to previous approaches, the following aspects are new: 1) we correct the geometric distortion in fluoroscopic images and calibrate them directly with respect to the robot by affixing to it a new calibration device designed as a radiolucent rod with embedded metallic markers, and by moving the device along two planes, while radiographs are being acquired at regular intervals; 2) the registration uses an algorithm for computing the best transformation between a set of lines in three space, the (intraoperative) X-ray paths, and a set of points on the surface of the bone (imaged preoperatively), in a statistically robust fashion, using the Cayley parameterization of a rotation; and 3) to find corresponding sets of points to the X-ray paths on the surfaces, our new approach consists of extracting the surface apparent contours for a given viewpoint, as a set of closed three-dimensional nonplanar curves, before registering the apparent contours to X-ray paths. Aside from algorithms, there are a number of major technical difficulties associated with engineering a clinically viable system using anatomy and image-based registration. To detect and solve them, we have so far conducted two experiments with the surgical robot in an operating room (OR), using CT and fluoroscopic image data of a cadaver bone, and attempting to faithfully simulate clinical conditions. Such experiments indicate that intraoperative X-ray-based registration is a promising alternative to marker-based registration for clinical use with our proposed method.

We describe a system for capturing bump maps from a series of images of an object from the same view point, but with varying, known, illumination. Using the illumination information we can reconstruct the surface normals for a variety of, but not all, surface nishes and geometries. The system allows an existing object to be rerendered with new lighting and surface nish without explicitly reconstructing the object geometry.

ÐMany real-world polygonal surfaces contain topological singularities that represent a challenge for processes such as simplification, compression, and smoothing. We present an algorithm that removes singularities from nonmanifold sets of polygons to create manifold (optionally oriented) polygonal surfaces. We identify singular vertices and edges, multiply singular vertices, and cut through singular edges. In an optional stitching operation, we maintain the surface as a manifold while joining boundary edges. We present two different edge stitching strategies, called pinching and snapping. Our algorithm manipulates the surface topology and ignores physical coordinates. Except for the optional stitching, the algorithm has a linear complexity and requires no floating point operations. In addition to introducing new algorithms, we expose the complexity (and pitfalls) associated with stitching. Finally, several real-world examples are studied.

No abstract