A method represents a shape of an object in an image. Portions of the image interior to a boundary of the object are ordered. A medial axis for the ordered portions of the image is derived. The medial axis is segmented to produce an ordered tree. The ordered tree is transformed to a partial ordered tree to represent the shape of the object.

A method determines a surface of an object in a sequence of images. The method begins by estimating a boundary of the object in each image of the sequence using motion information of adjacent images of the sequence. Then, portions of each image of the sequence are ordered to produce an ordered sequence of images. The ordered portions are exterior to the estimated object boundary. Edges in each ordered image are filtered using the motion information, and each ordered image of the sequence is searched to locate the filtered edges to form a new boundary outside the estimated boundary. The filtering and searching are repeated, while projecting the new object boundaries over the sequence of images, until the new object boundaries converges to a surface of the object.

An adaptive multiscale method approximates shapes with continuous or uniformly and densely sampled contours, with the purpose of sparsely and nonuniformly discretizing the boundaries of shapes at any prescribed resolution, while at the same time retaining the salient shape features at that resolution. In another aspect, a fundamental geometric filtering scheme using the Constrained Delaunay Triangulation (CDT) of polygonized shapes creates an efficient parsing of shapes into components that have semantic significance dependent only on the shapes' structure and not on their representations per se. A shape skeletonization process generalizes to sparsely discretized shapes, with the additional benefit of prunability to filter out irrelevant and morphologically insignificant features. The skeletal representation of characters of varying thickness and the elimination of insignificant and noisy spurs and branches from the skeleton greatly increases the robustness, reliability and recognition rates of character recognition algorithms.

A tracking technique which tracks a structure in three-dimensional data is disclosed. The tracking technique uses a geometric shape to model the structure to be tracked. Tracking is achieved by altering the orientation (and perhaps scale) of the geometric shape at a given three-dimensional point until it best fits the structure being tracked. Using this best fit information, a subsequent point within the structure being tracked can be identified. The tracking continues by thereafter altering the orientation (and perhaps scale) of the geometric shape at or near the subsequent point until a best fit is identified. The invention can be implemented as a digital filter, a tracking system or a method.

A method and system for viewing three-dimensional data which corresponds to a structure that has been tracked throughout the three-dimensional data is disclosed. Typically, structures which require tracking so that they can be followed throughout three-dimensional data are non-planar and, therefore, very difficult to view. Initially, tracking data is obtained by tracking a structure through the three-dimensional data. After the structure has been tracked through the three-dimensional data, the structure is displayed on a monitor or display device such that the portion of the three-dimensional data which is pertinent to the tracked structure is distinguishable from other data. As a result, a user can readily and easily view the data associated with the tracked structure. As an example, when the tracked structure is an artery, the image of the tracked structure displayed on the monitor or display device is not simply a planar slice of the three-dimensional data, instead it is planar perpendicular to the tracked structure and along a spline curve which follows the tracked data points through the three-dimensional data. Consequentially, for this example, the geometry of the displayed image is a ruled spline cutting surface formed from the three-dimensional data corresponding to the tracked structure.