Person:

Yezzi, Anthony

Permanent Link

https://hdl.handle.net/1853/71866

Associated Organization(s)

Organizational Unit

School of Electrical and Computer Engineering

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Publication Search Results

Now showing 1 - 10 of 22

Joint brain parameteric T1-map segmentation and RF inhomogeneity calibration

(Georgia Institute of Technology, 2009) Chen, Ping-Feng ; Steen, R. Grant ; Yezzi, Anthony ; Krim, Hamid

We propose a constrained version of Mumford and Shah’s (1989) segmentation model with an information-theoretic point of view in order to devise a systematic procedure to segment brain magnetic resonance imaging (MRI) data for parametric T1-Map and T1-weighted images, in both 2-D and 3D settings. Incorporation of a tuning weight in particular adds a probabilistic flavor to our segmentation method, and makes the 3-tissue segmentation possible. Moreover, we proposed a novel method to jointly segment the T1-Map and calibrate RF Inhomogeneity (JSRIC). This method assumes the average T1 value of whitematter is the same across transverse slices in the central brain region, and JSRIC is able to rectify the flip angles to generate calibrated T1-Maps. In order to generate an accurate T1-Map, the determination of optimal flip-angles and the registration of flip-angle images are examined. Our JSRIC method is validated on two human subjects in the 2D T1-Map modality and our segmentation method is validated by two public databases, BrainWeb and IBSR, of T1-weighted modality in the 3D setting.
Dynamic shape and appearance modeling via moving and deforming layers

(Georgia Institute of Technology, 2008-08) Jackson, Jeremy D. ; Yezzi, Anthony ; Soatto, Stefano

This model is based on a collection of overlapping layers that can move and deform, each supporting an intensity function that can change over time. We discuss the generality and limitations of this model in relation to existing ones such as traditional optical flow or motion segmentation, layers, deformable templates and deformotion. We then illustrate how this model can be used for inference of shape, motion, deformation and appearance of the scene from a collection of images. The layering structure allows for automatic inpainting of partially occluded regions. We illustrate the model on synthetic and real sequences where existing schemes fail, and show how suitable choices of constants in the model yield existing schemes, from optical flow to motion segmentation, etc.
Coarse-to-Fine Segmentation and Tracking Using Sobolev Active Contours

(Georgia Institute of Technology, 2008-05) Sundaramoorthi, Ganesh ; Yezzi, Anthony ; Mennucci, Andrea C.

Recently proposed Sobolev active contours introduced a new paradigm for minimizing energies defined on curves by changing the traditional cost of perturbing a curve and thereby redefining gradients associated to these energies. Sobolev active contours evolve more globally and are less attracted to certain intermediate local minima than traditional active contours, and it is based on a wellstructured Riemannian metric, which is important for shape analysis and shape priors. In this paper, we analyze Sobolev active contours using scale-space analysis in order to understand their evolution across different scales. This analysis shows an extremely important and useful behavior of Sobolev contours, namely, that they move successively from coarse to increasingly finer scale motions in a continuous manner. This property illustrates that one justification for using the Sobolev technique is for applications where coarse-scale deformations are preferred over fine-scale deformations. Along with other properties to be discussed, the coarse-to-fine observation reveals that Sobolev active contours are, in particular, ideally suited for tracking algorithms that use active contours. We will also justify our assertion that the Sobolev metric should be used over the traditional metric for active contours in tracking problems by experimentally showinghow a variety of active-contour-based tracking methods can be significantly improved merely by evolving the active contour according to the Sobolev method.
Properties of Sobolev-type metrics in the space of curves

(Georgia Institute of Technology, 2008) Mennucci, Andrea C. ; Yezzi, Anthony ; Sundaramoorthi, Ganesh

We define a manifold M where objects c ϵ M are curves, which we parameterize as c : S¹ → R ⁿ (n ≥2, S¹ is the circle). Given a curve c, we define the tangent space TcM of M at c including in it all deformations h : S¹ → R ⁿ of c. We study geometries on the manifold of curves, provided by Sobolev–type Riemannian metrics H[superscript j]. We initially present some mathematical examples to show how the metrics H[superscript j] simplify or regularize gradient flows used in Computer Vision applications. We then provide some basilar results of Hj metrics; and, for the cases j = 1, 2, we characterize the completion of the space of smooth curves; we call this completion(s) “H¹ and H² Sobolev–type Riemannian Manifolds of Curves”. As a byproduct, we prove that the Fréchet distance of curves (see [MM06b]) coincides with the distance induced by the “Finsler L H [superscript ∞] metric” defined in §2.2 in [YM04b].
Vessels as 4-D curves: global minimal 4-D paths to extract 3-D tubular surfaces and centerlines

(Georgia Institute of Technology, 2007-09) Li, Hua ; Yezzi, Anthony

In this paper, we propose an innovative approach to the segmentation of tubular structures. This approach combines all of the benefits of minimal path techniques such as global minimizers, fast computation, and powerful incorporation of user input, while also having the capability to represent and detect vessel surfaces directly which so far has been a feature restricted to active contour and surface techniques. The key is to represent the trajectory of a tubular structure not as a 3-D curve but to go up a dimension and represent the entire structure as a 4-D curve. Then we are able to fully exploit minimal path techniques to obtain global minimizing trajectories between two user supplied endpoints in order to reconstruct tubular structures from noisy or low contrast 3-D data without the sensitivity to local minima inherent in most active surface techniques. In contrast to standard purely spatial 3-D minimal path techniques, however, we are able to represent a full tubular surface rather than just a curve which runs through its interior. Our representation also yields a natural notion of a tube’s “central curve.” We demonstrate and validate the utility of this approach on magnetic resonance (MR) angiography and computed tomography (CT) images of coronary arteries.
A Variational Approach to Problems in Calibration of Multiple Cameras

(Georgia Institute of Technology, 2007-08) Unal, Gozde ; Yezzi, Anthony ; Soatto, Stefano ; Slabaugh, Gregory G.

This paper addresses the problem of calibrating camera parameters using variational methods. One problem addressed is the severe lens distortion in low-cost cameras. For many computer vision algorithms aiming at reconstructing reliable representations of 3D scenes, the camera distortion effects will lead to inaccurate 3D reconstructions and geometrical measurements if not accounted for. A second problem is the color calibration problem caused by variations in camera responses that result in different color measurements and affects the algorithms that depend on these measurements. We also address the extrinsic camera calibration that estimates relative poses and orientations of multiple cameras in the system and the intrinsic camera calibration that estimates focal lengths and the skew parameters of the cameras. To address these calibration problems, we present multiview stereo techniques based on variational methods that utilize partial and ordinary differential equations. Our approach can also be considered as a coordinated refinement of camera calibration parameters. To reduce computational complexity of such algorithms, we utilize prior knowledge on the calibration object, making a piecewise smooth surface assumption, and evolve the pose, orientation, and scale parameters of such a 3D model object without requiring a 2D feature extraction from camera views. We derive the evolution equations for the distortion coefficients, the color calibration parameters, the extrinsic and intrinsic parameters of the cameras, and present experimental results.
Tracking Deforming Objects using Particle Filtering for Geometric Active Contours

(Georgia Institute of Technology, 2007-08) Rathi, Yogesh ; Vaswani, Namrata ; Tannenbaum, Allen R. ; Yezzi, Anthony

Tracking 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.
Global regularizing flows with topology preservation for active contours and polygons

(Georgia Institute of Technology, 2007-03) Sundaramoorthi, Ganesh ; Yezzi, Anthony

Active contour and active polygon models have been used widely for image segmentation. In some applications, the topology of the object(s) to be detected from an image is known a priori, despite a complex unknown geometry, and it is important that the active contour or polygon maintain the desired topology. In this work, we construct a novel geometric flow that can be added to image-based evolutions of active contours and polygons in order to preserve the topology of the initial contour or polygon. We emphasize that, unlike other methods for topology preservation, the proposed geometric flow continually adjusts the geometry of the original evolution in a gradual and graceful manner so as to prevent a topology change long before the curve or polygon becomes close to topology change. The flow also serves as a global regularity term for the evolving contour, and has smoothness properties similar to curvature flow. These properties of gradually adjusting the original flow and global regularization prevent geometrical inaccuracies common with simple discrete topology preservation schemes. The proposed topology preserving geometric flow is the gradient flow arising from an energy that is based on electrostatic principles. The evolution of a single point on the contour depends on all other points of the contour, which is different from traditional curve evolutions in the computer vision literature.
A hybrid Eulerian-Lagrangian approach for thickness, correspondence, and gridding of annular tissues

(Georgia Institute of Technology, 2007-03) Rocha, Kelvin R. ; Yezzi, Anthony ; Prince, Jerry L.

We present a novel approach to efficiently compute thickness, correspondence, and gridding of tissues between two simply connected boundaries. The solution of Laplace’s equation within the tissue region provides a harmonic function whose gradient flow determines the correspondence trajectories going from one boundary to the other. The proposed method uses and expands upon two recently introduced techniques in order to compute thickness and correspondences based on these trajectories. Pairs of partial differential equations are efficiently computed within an Eulerian framework and combined with a Lagrangian approach so that correspondences trajectories are partially constructed when necessary. Examples are presented in order to compare the performance of this method with those of the pure Lagrangian and pure Eulerian approaches. Results show that the proposed technique takes advantage of both the speed of the Eulerian approach and the accuracy of the Lagrangian approach.
Local or global minima: flexible dual-front active contours

(Georgia Institute of Technology, 2007-01) Li, Hua ; Yezzi, Anthony

Most variational active contour models are designed to find local minima of data-dependent energy functionals with the hope that reasonable initial placement of the active contour will drive it toward a “desirable” local minimum as opposed to an undesirable configuration due to noise or complex image structure. As such, there has been much research into the design of complex region-based energy functionals that are less likely to yield undesirable local minima when compared to simpler edge-based energy functionals whose sensitivity to noise and texture is significantly worse. Unfortunately, most of these more “robust” region-based energy functionals are applicable to a much narrower class of imagery compared to typical edge-based energies due to stronger global assumptions about the underlying image data. Devising new implementation algorithms for active contours that attempt to capture more global minimizers of already proposed image-based energies would allow us to choose an energy that makes sense for a particular class of energy without concern over its sensitivity to local minima. Such implementations have been proposed for capturing global minima. However, sometimes the completely-global minimum is just as undesirable as a minimum that is too local. In this paper, we propose a novel, fast, and flexible dual front implementation of active contours, motivated by minimal path techniques and utilizing fast sweeping algorithms, which is easily manipulated to yield minima with variable “degrees” of localness and globalness. By simply adjusting the size of active regions, the ability to gracefully move from capturing minima that are more local (according to the initial placement of the active contour/surface) to minima that are more global allows this model to more easily obtain “desirable” minimizers (which often are neither the most local nor the most global). Experiments on various 2D and 3D images and comparisons with some active contour models and region-growing methods are also given to illustrate the properties of this model and its performance in a variety of segmentation applications.