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On active contour models and balloons

by D. Cohen - CVGIP: Image
"... The use.of energy-minimizing curves, known as “snakes, ” to extract features of interest in images has been introduced by Kass, Witkhr & Terzopoulos (Znt. J. Comput. Vision 1, 1987,321-331). We present a model of deformation which solves some of the problems encountered with the original method. ..."
Abstract - Cited by 588 (43 self) - Add to MetaCart
curve need no longer be close to the solution to converge. The curve passes over weak edges and is stopped only if the edge is strong. We give examples of extracting a ventricle in medical images. We have also made a first step toward 3D object reconstruction, by tracking the extracted contour on a

Principal Curves

by TREVOR HASTIE , WERNER STUETZLE , 1989
"... Principal curves are smooth one-dimensional curves that pass through the middle of a p-dimensional data set, providing a nonlinear summary of the data. They are nonparametric, and their shape is suggested by the data. The algorithm for constructing principal curve starts with some prior summary, suc ..."
Abstract - Cited by 394 (1 self) - Add to MetaCart
Principal curves are smooth one-dimensional curves that pass through the middle of a p-dimensional data set, providing a nonlinear summary of the data. They are nonparametric, and their shape is suggested by the data. The algorithm for constructing principal curve starts with some prior summary

A Signal Processing Approach To Fair Surface Design

by Gabriel Taubin , 1995
"... In this paper we describe a new tool for interactive free-form fair surface design. By generalizing classical discrete Fourier analysis to two-dimensional discrete surface signals -- functions defined on polyhedral surfaces of arbitrary topology --, we reduce the problem of surface smoothing, or fai ..."
Abstract - Cited by 654 (15 self) - Add to MetaCart
, or fairing, to low-pass filtering. We describe a very simple surface signal low-pass filter algorithm that applies to surfaces of arbitrary topology. As opposed to other existing optimization-based fairing methods, which are computationally more expensive, this is a linear time and space complexity algorithm

0.1. Rational Plane Curves Passing Through Points. In the following, we

by Steven Finch
"... Given a complex projective variety V (as defined in [1]), we wish to count the curves in V that satisfy certain prescribed conditions. Let fC denote complex pro-jective -dimensional space. In our first example, V = fC2, the complex projective plane; in the second and third, V is a general hypersurf ..."
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Given a complex projective variety V (as defined in [1]), we wish to count the curves in V that satisfy certain prescribed conditions. Let fC denote complex pro-jective -dimensional space. In our first example, V = fC2, the complex projective plane; in the second and third, V is a general

Connect-The-Dots: How many random points can a regular curve pass through?

by Ery Arias-Castro, David L. Donoho , Xiaoming Huo , Craig Tovey , 2004
"... ..."
Abstract - Cited by 10 (4 self) - Add to MetaCart
Abstract not found

The Band Pass Filter

by Lawrence J. Christiano, Terry J. Fitzgerald , 1999
"... The 'ideal' band pass filter can be used to isolate the component of a time series that lies within a particular band of frequencies. However, applying this filter requires a dataset of infinite length. In practice, some sort of approximation is needed. Using projections, we derive approxi ..."
Abstract - Cited by 106 (2 self) - Add to MetaCart
The 'ideal' band pass filter can be used to isolate the component of a time series that lies within a particular band of frequencies. However, applying this filter requires a dataset of infinite length. In practice, some sort of approximation is needed. Using projections, we derive

Principal Curves Revisited

by Robert Tibshirani - Statistics and Computing , 1992
"... A principal curve (Hastie and Stuetzle, 1989) is a smooth curve passing through the "middle" of a distribution or data cloud, and is a generalization of linear principal components. We give an alternative definition of a principal curve, based on a mixture model. Estimation is carried out ..."
Abstract - Cited by 67 (0 self) - Add to MetaCart
A principal curve (Hastie and Stuetzle, 1989) is a smooth curve passing through the "middle" of a distribution or data cloud, and is a generalization of linear principal components. We give an alternative definition of a principal curve, based on a mixture model. Estimation is carried out

Learning and Design of Principal Curves

by Balázs Kégl, Adam Krzyzak, Tamás Linder, Kenneth Zeger , 2000
"... Principal curves have been defined as ``self consistent'' smooth curves which pass through the ``middle'' of a $d$-dimensional probability distribution or data cloud. They give a summary of the data and also serve as an efficient feature extraction tool. We take a new approach by ..."
Abstract - Cited by 105 (4 self) - Add to MetaCart
Principal curves have been defined as ``self consistent'' smooth curves which pass through the ``middle'' of a $d$-dimensional probability distribution or data cloud. They give a summary of the data and also serve as an efficient feature extraction tool. We take a new approach

Stochastic Completion Fields: A Neural Model of Illusory Contour Shape and Salience

by Lance R. Williams, David W. Jacobs - Neural Computation , 1995
"... We describe an algorithm and representation level theory of illusory contour shape and salience. Unlike previous theories, our model is derived from a single assumption--- namely, that the prior probability distribution of boundary completion shape can be modeled by a random walk in a lattice whose ..."
Abstract - Cited by 210 (14 self) - Add to MetaCart
particle following a random walk will pass through a given position and orientation on a path joining two boundary fragments can be computed directly as the product of two vector-field convolutions. We show that for the random walk we define, the maximum likelihood paths are curves of least energy, that is

Pointed Nodal Plane Curves with the Expected Number of Moduli

by E. Ballico
"... Abstract. Here we describe families of plane curves passing through s fixed points and with the expect number of moduli as s-pointed curves. ..."
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Abstract. Here we describe families of plane curves passing through s fixed points and with the expect number of moduli as s-pointed curves.
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