Biomedical subjects

J A Sethian

Publications and source records attributed to J A Sethian.

6 recordsLinked to original sources

PubMed2000

Subjective surfaces: a method for completing missing boundaries.

We present a model and algorithm for segmentation of images with missing boundaries. In many situations, the human visual system fills in missing gaps in edges and boundaries, building and completing information that is not present. This presents a considerable challenge in computer vision, since most algorithms attempt to exploit existing data. Completion models, which postulate how to construct missing data, are popular but are often trained and specific to particular images. In this paper, we take the following perspective: We consider a reference point within an image as given and then develop an algorithm that tries to build missing information on the basis of the given point of view and the available information as boundary data to the algorithm. We test the algorithm on some standard images, including the classical triangle of Kanizsa and low signal/noise ratio medical images.

Journal Article↗

PubMed2000

Fast methods for the Eikonal and related Hamilton- Jacobi equations on unstructured meshes.

The Fast Marching Method is a numerical algorithm for solving the Eikonal equation on a rectangular orthogonal mesh in O(M log M) steps, where M is the total number of grid points. The scheme relies on an upwind finite difference approximation to the gradient and a resulting causality relationship that lends itself to a Dijkstra-like programming approach. In this paper, we discuss several extensions to this technique, including higher order versions on unstructured meshes in Rn and on manifolds and connections to more general static Hamilton-Jacobi equations.

Journal Article↗

PubMed1998

Computing geodesic paths on manifolds.

The Fast Marching Method is a numerical algorithm for solving the Eikonal equation on a rectangular orthogonal mesh in O(M log M) steps, where M is the total number of grid points. In this paper we extend the Fast Marching Method to triangulated domains with the same computational complexity. As an application, we provide an optimal time algorithm for computing the geodesic distances and thereby extracting shortest paths on triangulated manifolds.

Journal Article↗

PubMed1996

An O(N log N) algorithm for shape modeling.

We present a shape-recovery technique in two dimensions and three dimensions with specific applications in modeling anatomical shapes from medical images. This algorithm models extremely corrugated structures like the brain, is topologically adaptable, and runs in O(N log N) time, where N is the total number of points in the domain. Our technique is based on a level set shape-recovery scheme recently introduced by the authors and the fast marching method for computing solutions to static Hamilton-Jacobi equations.

Algorithms↗

PubMed1995

Image processing via level set curvature flow.

We present a controlled image smoothing and enhancement method based on a curvature flow interpretation of the geometric heat equation. Compared to existing techniques, the model has several distinct advantages. (i) It contains just one enhancement parameter. (ii) The scheme naturally inherits a stopping criterion from the image; continued application of the scheme produces no further change. (iii) The method is one of the fastest possible schemes based on a curvature-controlled approach.

Angiography, Digital Subtraction↗

PubMed1984

Search, encounter rates, and the evolution of anisogamy.

We describe analytical and numerical models to study gamete encounters in two and three dimensions between differently sized gametes without assuming pre-existing mating types. Our results indicate that an isogamous population can be successfully invaded by a gametangium if it produces gametes of a different size. The existence of a low adaptive peak for isogamy and a much higher adaptive peak for anisogamy suggests that stochastic forces may be initially important in driving isogamy through the fitness saddle to anisogamy.

Animals↗