In many scientific and technical endeavors, a three-dimensional solid must be reconstructed from serial sections, either to aid in the comprehension of the object's structure or to facilitate its automatic manipulation and analysis. This paper presents a general solution to the problem of constructing a surface over a set of cross-sectional contours. This surface, to be composed of triangular tiles, is constructed by separately determining an optimal surface between each pair of consecutive contours. Determining such a surface is reduced to the problem of finding certain minimum cost cycles in a directed toroidal graph. A new fast algorithm for finding such cycles is utilized. Also developed is a closed-form expression, in terms of the number of contour points, for an upper bound on the number of operations required to execute the algorithm. An illustrated example which involves the construction of a minimum area surface describing a human head is included.
An algorithm is described for obtaining an optimal approximation, using triangulation, of a three-dimensional surface defined by randomly distributed points along contour lines....
This paper proves best known guarantees for exact reconstruction of a sparse signal f from few non-adaptive universal linear measurements. We consider Fourier measurements (rand...
We propose a new model for active contours to detect objects in a given image, based on techniques of curve evolution, Mumford-Shah (1989) functional for segmentation and level ...
We have taken 84 World Wide Standard Seismograph Network recordings of the Alaskan earthquake of 1964 March 28, one of the largest earthquakes in history, and have made an inten...
We have developed a new method for finding and representing dividing surfaces which can, for example, be used to identify “atoms” in molecules or condensed phases based on Bader...
Social media, news, blog, policy document mentions