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Yezzi, Anthony

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    Fast approximate surface evolution in arbitrary dimension
    (Georgia Institute of Technology, 2008-02) Malcolm, James G. ; Rathi, Yogesh ; Yezzi, Anthony ; Tannenbaum, Allen R.
    The level set method is a popular technique used in medical image segmentation; however, the numerics involved make its use cumbersome. This paper proposes an approximate level set scheme that removes much of the computational burden while maintaining accuracy. Abandoning a floating point representation for the signed distance function, we use integral values to represent the signed distance function. For the cases of 2D and 3D, we detail rules governing the evolution and maintenance of these three regions. Arbitrary energies can be implemented in the framework. This scheme has several desirable properties: computations are only performed along the zero level set; the approximate distance function requires only a few simple integer comparisons for maintenance; smoothness regularization involves only a few integer calculations and may be handled apart from the energy itself; the zero level set is represented exactly removing the need for interpolation off the interface; and evolutions proceed on the order of milliseconds per iteration on conventional uniprocessor workstations. To highlight its accuracy, flexibility and speed, we demonstrate the technique on intensity-based segmentations under various statistical metrics. Results for 3D imagery show the technique is fast even for image volumes.
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    Fast approximate curve evolution
    (Georgia Institute of Technology, 2008-01) Malcolm, James G. ; Rathi, Yogesh ; Yezzi, Anthony ; Tannenbaum, Allen R.
    The level set method for curve evolution is a popular technique used in image processing applications. However, the numerics involved make its use in high performance systems computationally prohibitive. This paper proposes an approximate level set scheme that removes much of the computational burden while maintaining accuracy. Abandoning a floating point representation for the signed distance function, we use the integral values to represent the interior, zero level set, and exterior. We detail rules governing the evolution and maintenance of these three regions. Arbitrary energies can be implemented with the definition of three operations: initialize iteration, move points in, move points out. This scheme has several nice properties. First, computations are only performed along the zero level set. Second, this approximate distance function representation requires only a few simple integer comparisons for maintenance. Third, smoothness regularization involves only a few integer calculations and may be handled apart from the energy itself. Fourth, the zero level set is represented exactly removing the need for interpolation off the interface. Lastly, evolution proceeds on the order of milliseconds per iteration using conventional uniprocessor workstations. To highlight its accuracy, flexibility and speed, we demonstrate the technique on standard intensity tracking and stand alone segmentation.
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    Fast Approximate Surface Evolution in Arbitrary Dimension
    (Georgia Institute of Technology, 2008) Malcolm, James ; Rathi, Yogesh ; Yezzi, Anthony ; Tannenbaum, Allen
    The level set method is a popular technique used in medical image segmentation; however, the numerics involved make its use cumbersome. This paper proposes an approximate level set scheme that removes much of the computational burden while maintaining accuracy. Abandoning a floating point representation for the signed distance function, we use integral values to represent the signed distance function. For the cases of 2D and 3D, we detail rules governing the evolution and maintenance of these three regions. Arbitrary energies can be implemented in the framework. This scheme has several desirable properties: computations are only performed along the zero level set; the approximate distance function requires only a few simple integer comparisons for maintenance; smoothness regularization involves only a few integer calculations and may be handled apart from the energy itself; the zero level set is represented exactly removing the need for interpolation off the interface; and evolutions proceed on the order of milliseconds per iteration on conventional uniprocessor workstations. To highlight its accuracy, flexibility and speed, we demonstrate the technique on intensity-based segmentations under various statistical metrics. Results for 3D imagery show the technique is fast even for image volumes.
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    Time-varying Finite Dimensional Basis for Tracking Contour Deformations
    (Georgia Institute of Technology, 2006-12) Vaswani, Namrata ; Yezzi, Anthony ; Rathi, Yogesh ; Tannenbaum, Allen R.
    We consider the problem of tracking the boundary contour of a moving and deforming object from a sequence of images. If the motion of the "object" or region of interest is constrained (e.g. rigid or approximately rigid), the contour motion can be efficiently represented by a small number of parameters, e.g. the affine group. But if the "object" is arbitrarily deforming, each contour point can move independently. Contour deformation then forms an infinite (in practice, very large), dimensional space. Direct application of particle filters for large dimensional problems is impractical, due to the reduction in effective particle size as dimension increases. But in most real problems, at any given time, "most of the contour deformation" occurs in a small number of dimensions ("effective basis") while the residual deformation in the rest of the state space ("residual space") is "small". The effective basis may be fixed or time varying. Based on this assumption, we modify the particle filtering method to perform sequential importance sampling only on the effective basis dimensions, while replacing it with deterministic mode tracking in residual space (PF-MT). We develop the PF-MT idea for contour tracking. Techniques for detecting effective basis dimension change and estimating the new effective basis are presented. Tracking results on simulated and real sequences are shown and compared with past work.
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    Particle Filters for Infinite (or Large) Dimensional State Spaces- Part 1
    (Georgia Institute of Technology, 2006-05) Vaswani, Namrata ; Yezzi, Anthony ; Rathi, Yogesh ; Tannenbaum, Allen R.
    We propose particle filtering algorithms for tracking on infinite (or large) dimensional state spaces. We consider the general case where state space may not be a vector space, we assume it to be a separable metric space (Polish space). In implementation, any such space is approximated by a finite but large dimensional vector, whose dimension may vary at every time. Monte Carlo sampling from a large dimensional system noise distribution is computationally expensive. Also, the number of particles required for accurate particle filtering increases with the number of independent dimensions of the system noise, making particle filtering even more expensive. But as long as the number of independent system noise dimensions is small, even if the total state space dimension is very large, a particle filtering algorithm can be implemented. In most large dim applications, it is fair to assume that "most of the state change" occurs in a small dimensional basis, which may be fixed or slowly time varying (approximated as piecewise constant). We use this assumption to propose efficient PF algorithms. These are analyzed and extended in N. Vaswani, (2006)
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    Particle Filtering for Geometric Active Contours with Application to Tracking Moving and Deforming Objects
    (Georgia Institute of Technology, 2005-06) Rathi, Yogesh ; Vaswani, Namrata ; Tannenbaum, Allen R. ; Yezzi, Anthony
    Geometric active contours are formulated in a manner which is parametrization independent. As such, they are amenable to representation as the zero level set of the graph of a higher dimensional function. This representation is able to deal with singularities and changes in topology of the contour. It has been used very successfully in static images for segmentation and registration problems where the contour (represented as an implicit curve) is evolved until it minimizes an image based energy functional. But tracking involves estimating the global motion of the object and its local deformations as a function of time. Some attempts have been made to use geometric active contours for tracking, but most of these minimize the energy at each frame and do not utilize the temporal coherency of the motion or the deformation. On the other hand, tracking algorithms using Kalman filters or particle filters have been proposed for finite dimensional representations of shape. But these are dependent on the chosen parametrization and cannot handle changes in curve topology. In the present work, we formulate a particle filtering algorithm in the geometric active contour framework that can be used for tracking moving and deforming objects.