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- David L. Donoho, Xiaoming Huo, +13 authors Stephen Semmes
- 2001

We describe a framework for multiscale image analysis in which line segments play a role analogous to the role played by points in wavelet analysis. The framework has five key components. The beamlet dictionary is a dyadically-organized collection of line segments, occupying a range of dyadic locations and scales, and occurring at a range of orientations.… (More)

Consider a planar Brownian motion run for nite time. The frontier or \outer boundary" of the path is the boundary of the unbounded component of the complement. Burdzy (1989) showed that the frontier has innnite length. We improve this by showing that the Hausdorr dimension of the frontier is strictly greater than 1. (It has been conjectured that the… (More)

- Stefan Kindermann, Stanley Osher, Peter W. Jones
- Multiscale Modeling & Simulation
- 2005

- Peter W. Jones
- 1991

- Peter W Jones, Mauro Maggioni, Raanan Schul
- Proceedings of the National Academy of Sciences…
- 2008

We use heat kernels or eigenfunctions of the Laplacian to construct local coordinates on large classes of Euclidean domains and Riemannian manifolds (not necessarily smooth, e.g., with (alpha) metric). These coordinates are bi-Lipschitz on large neighborhoods of the domain or manifold, with constants controlling the distortion and the size of the… (More)

We use heat kernels or eigenfunctions of the Laplacian to construct local coordinates on large classes of Euclidean domains and Riemannian manifolds (not necessarily smooth, e.g. with C α metric). These coordinates are bi-Lipschitz on embedded balls of the domain or manifold, with distortion constants that depend only on natural geometric properties of the… (More)

present a randomized algorithm for the approximate nearest neighbor problem in d-dimensional Euclidean space. Given N points {x j } in R d , the algorithm attempts to find k nearest neighbors for each of x j , where k is a user-specified integer parameter. The algorithm is iterative, and its CPU time requirements are proportional to T · N · (d · (log d) + k… (More)

This paper is devoted to the decomposition of an image f into u + v, with u a piecewise-smooth or " cartoon " component, and v an oscillatory component (texture or noise), in a variational approach. The cartoon component u is modeled by a function of bounded variation, while v, usually represented by a square integrable function, is now being modeled by a… (More)

- Peter Wilcox Jones, Andrei Osipov, Vladimir Rokhlin
- Proceedings of the National Academy of Sciences…
- 2011

We present a randomized algorithm for the approximate nearest neighbor problem in d-dimensional Euclidean space. Given N points {x(j)} in R(d), the algorithm attempts to find k nearest neighbors for each of x(j), where k is a user-specified integer parameter. The algorithm is iterative, and its running time requirements are proportional to T·N·(d·(log d) +… (More)

- PETER W. JONES, E W. JONES
- 1994

We consider several results, each of which uses some type of"L 2'' estimate to provide information about harmonic measure on planar domains. The first gives an a.e. characterization of tangent points of a curve in terms of a certain geometric square function. Our next result is an LP estimate relating the derivative of a conformal mapping to its Schwarzian… (More)