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Wallace H. Coulter Department of Biomedical Engineering
Wallace H. Coulter Department of Biomedical Engineering
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ItemDeform PFMT: Particle Filter With Mode Tracker for Tracking Nonaffine Contour Deformations(Georgia Institute of Technology, 201004) Vaswani, Namrata ; Rathi, Yogesh ; Yezzi, Anthony ; Tannenbaum, Allen R.We propose algorithms for tracking the boundary contour of a deforming object from an image sequence, when the nonaffine (local) deformation over consecutive frames is large and there is overlapping clutter, occlusions, low contrast, or outlier imagery. When the object is arbitrarily deforming, each, or at least most, contour points can move independently. Contour deformation then forms an infinite (in practice, very large), dimensional space. Direct application of particle filters (PF) for large dimensional problems is impractically expensive. However, in most real problems, at any given time, most of the contour deformation occurs in a small number of dimensions ("effective basis space") while the residual deformation in the rest of the state space ("residual space") is small. This property enables us to apply the particle filtering with mode tracking (PFMT) idea that was proposed for such large dimensional problems in recent work. Since most contour deformation is low spatial frequency, we propose to use the space of deformation at a subsampled set of locations as the effective basis space. The resulting algorithm is called deform PFMT. It requires significant modifications compared to the original PFMT because the space of contours is a nonEuclidean infinite dimensional space.

ItemA Geometric Approach to Joint 2D RegionBased Segmentation and 3D Pose Estimation Using a 3D Shape Prior(Georgia Institute of Technology, 20100303) Dambreville, Samuel ; Sandhu, Romeil ; Yezzi, Anthony ; Tannenbaum, Allen R.In this work, we present an approach to jointly segment a rigid object in a twodimensional (2D) image and estimate its threedimensional (3D) pose, using the knowledge of a 3D model. We naturally couple the two processes together into a shape optimization problem and minimize a unique energy functional through a variational approach. Our methodology differs from the standard monocular 3D pose estimation algorithms since it does not rely on local image features. Instead, we use global image statistics to drive the pose estimation process. This confers a satisfying level of robustness to noise and initialization for our algorithm and bypasses the need to establish correspondences between image and object features. Moreover, our methodology possesses the typical qualities of regionbased active contour techniques with shape priors, such as robustness to occlusions or missing information, without the need to evolve an infinite dimensional curve. Another novelty of the proposed contribution is to use a unique 3D model surface of the object, instead of learning a large collection of 2D shapes to accommodate the diverse aspects that a 3D object can take when imaged by a camera. Experimental results on both synthetic and real images are provided, which highlight the robust performance of the technique in challenging tracking and segmentation applications.

ItemNonRigid 2D3D Pose Estimation and 2D Image Segmentation(Georgia Institute of Technology, 200906) Sandhu, Romeil ; Dambreville, Samuel ; Yezzi, Anthony ; Tannenbaum, Allen R.In this work, we present a nonrigid approach to jointly solve the tasks of 2D3D pose estimation and 2D image segmentation. In general, most frameworks which couple both pose estimation and segmentation assume that one has the exact knowledge of the 3D object. However, in nonideal conditions, this assumption may be violated if only a general class to which a given shape belongs to is given (e.g., cars, boats, or planes). Thus, the key contribution in this work is to solve the 2D3D pose estimation and 2D image segmentation for a general class of objects or deformations for which one may not be able to associate a skeleton model. Moreover, the resulting scheme can be viewed as an extension of the framework presented in, in which we include the knowledge of multiple 3D models rather than assuming the exact knowledge of a single 3D shape prior. We provide experimental results that highlight the algorithm's robustness to noise, clutter, occlusion, and shape recovery on several challenging pose estimation and segmentation scenarios.

ItemTAC: Thresholding active contours(Georgia Institute of Technology, 200810) Dambreville, Samuel ; Yezzi, Anthony ; Lankton, Shawn ; Tannenbaum, Allen R.In this paper, we describe a regionbased active contour technique to perform image segmentation. We propose an energy functional that realizes an explicit tradeoff between the (current) image segmentation obtained from a curve and the (implied) segmentation obtained from dynamically thresholding the image. In contrast with standard regionbased techniques, the resulting variational approach bypasses the need to fit (a priori chosen) statistical models to the object and the background. Our technique performs segmentation based on geometric considerations of the image and contour, instead of statistical ones. The resulting flow leads to very reasonable segmentations as shown by several illustrative examples.

ItemA variational framework combining levelsets and thresholding(Georgia Institute of Technology, 200709) Dambreville, Samuel ; Niethammer, Marc ; Yezzi, Anthony ; Tannenbaum, Allen R.Segmentation involves separating distinct regions in an image. In this note, we present a novel variational approach to perform this task within the levelsets framework. We propose an energy functional that naturally combines two segmentation techniques usually applied separately: intensity thresholding and geometric active contours. Although our method can deal with more complex statistics, we assume that the pixel intensities of the regions have Gaussian distributions, in this work. The proposed approach affords interesting properties that can lead to sensible segmentation results.

ItemTracking Deforming Objects using Particle Filtering for Geometric Active Contours(Georgia Institute of Technology, 200708) Rathi, Yogesh ; Vaswani, Namrata ; Tannenbaum, Allen R. ; Yezzi, AnthonyTracking deforming objects involves estimating the global motion of the object and its local deformations as a function of time. 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. Geometric active contours provide a framework which is parametrization independent and allow for changes in 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. To the best of our knowledge, this is the first attempt to implement an approximate particle filtering algorithm for tracking on a (theoretically) infinite dimensional state space.

ItemTimevarying Finite Dimensional Basis for Tracking Contour Deformations(Georgia Institute of Technology, 200612) 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 (PFMT). We develop the PFMT 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.

ItemParticle Filters for Infinite (or Large) Dimensional State Spaces Part 1(Georgia Institute of Technology, 200605) 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)

ItemParticle Filtering for Geometric Active Contours with Application to Tracking Moving and Deforming Objects(Georgia Institute of Technology, 200506) Rathi, Yogesh ; Vaswani, Namrata ; Tannenbaum, Allen R. ; Yezzi, AnthonyGeometric 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.

ItemVessel Segmentation Using a Shape Driven Flow(Georgia Institute of Technology, 200409) Nain, Delphine ; Yezzi, Anthony ; Turk, GregWe present a segmentation method for vessels using an implicit deformable model with a soft shape prior. Blood vessels are challenging structures to segment due to their branching and thinning geometry as well as the decrease in image contrast from the root of the vessel to its thin branches. Using image intensity alone to deform a model for the task of segmentation often results in leakages at areas where the image information is ambiguous. To address this problem, we combine image statistics and shape information to derive a regionbased active contour that segments tubular structures and penalizes leakages. We present results on synthetic and real 2D and 3D datasets.