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Mercer kernels are used for a wide range of image and signal processing tasks like de-noising, clustering, discriminant analysis etc. These algorithms construct their solutions in terms of the expansions in a high-dimensional feature space F. However, many applications like kernel PCA (principal component analysis) can be used more effectively if a… (More)

- Shawn Lankton, Allen Tannenbaum
- IEEE Transactions on Image Processing
- 2008

In this paper, we propose a natural framework that allows any region-based segmentation energy to be re-formulated in a local way. We consider local rather than global image statistics and evolve a contour based on local information. Localized contours are capable of segmenting objects with heterogeneous feature profiles that would be difficult to capture… (More)

References 197 Preface Striking developments have taken place since 1980 in feedback control theory. The subject has become both more rigorous and more applicable. The rigor is not for its own sake, but rather that even in an engineering discipline rigor can lead to clarity and to methodical solutions to problems. The applicability is a consequence both of… (More)

In this paper, we analyze the geometric active contour models discussed in [6, 181 from a curve evolution point of view and propose some modifications based on gradient flows relative to certain new featurebased Riemannian metrics. This leads to a novel snake paradigm in which the feature of interest may be considered to lie at the bottom of a potential… (More)

- Oleg V. Michailovich, Yogesh Rathi, Allen Tannenbaum
- IEEE Transactions on Image Processing
- 2007

This paper addresses the problem of image segmentation by means of active contours, whose evolution is driven by the gradient flow derived from an energy functional that is based on the Bhattacharyya distance. In particular, given the values of a photometric variable (or of a set thereof), which is to be used for classifying the image pixels, the active… (More)

- Benjamin B. Kimia, Allen Tannenbaum, Steven W. Zucker
- International Journal of Computer Vision
- 1995

We undertake to develop a general theory of two-dimensional shape by elucidating several principles which any such theory should meet. The principles are organized around two basic intuitions: first, if a boundary were changed only slightly, then, in general, its shape would change only slightly. This leads us to propose an operational theory of shape based… (More)

- Allen Tannenbaum
- SIAM Review
- 1993

- Anthony J. Yezzi, Satyanad Kichenassamy, Arun Kumar, Peter J. Olver, Allen Tannenbaum
- IEEE Trans. Med. Imaging
- 1997

In this note, we employ the new geometric active contour models formulated in [25] and [26] for edge detection and segmentation of magnetic resonance imaging (MRI), computed tomography (CT), and ultrasound medical imagery. Our method is based on defining feature-based metrics on a given image which in turn leads to a novel snake paradigm in which the… (More)

- Eugenio Calabi, Peter J. Olver, Chehrzad Shakiban, Allen Tannenbaum, Steven Haker
- International Journal of Computer Vision
- 1998

We introduce a new paradigm, the differential invariant signature curve or manifold, for the invariant recognition of visual objects. A general theorem of É. Cartan implies that two curves are related by a group transformation if and only if their signature curves are identical. The important examples of the Euclidean and equi-affine groups are discussed in… (More)

- Guillermo Sapiro, Allen Tannenbaum
- International Journal of Computer Vision
- 1993

A newaffine invariant scale-space for planar curves is presented in this work. The scale-space is obtained from the solution of a novel nonlinear curve evolution equation which admits affine invariant solutions. This flow was proved to be the affine analogue of the well knownEuclidean shortening flow. The evolution also satisfies properties such… (More)