D. Metaxas. Physics-based Deformable Models: Applications to Computer Vision, Graphics and Medical Imaging. Kluwer Academic Publishers, 1996.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... formulated regularization terms based on physical analogy of a membrane under tension and a thin plate under tension [124] Metaxas and Terzopoulos extended this work into deformable superquadrics and introduced it to the computer vision and computer graphics fields and later to the medical area [82, 81]. The deformable superquadrics of Metaxas and Terzopoulos are based on Lagrangian dynamics. Their sti#ness matrix K combines global and local sti#ness coe#cients. The position of a point on the surface of the model relative to the center depends on the global deformation g and the local ....

D. Metaxas. Physics-Based Deformable Models - Applications to Computer Vision, Graphics and Medical Imaging. Kluwer Academic Publisher, Boston, 1996.

....model recovery, view registration, view integration, and final model recovery from integrated data. A new registration technique based on the recovered deformable superquadrics is also proposed. Although a lot of research has been conducted on recovering globally deformed superquadrics [5] 3] [4], the mathematical expression for bending deformation, proposed in [3] 1] is only suitable for recovering and visualizing bending superquadrics from surface points lying in the first quadrant in the 2 D Cartesian space, i.e. for x 0#y 0. This condition is satisfied by default when ....

D. N. Metaxas. Physics-based Deformable Models: Applications to Computer Vision, Graphics and Medical Imaging. Kluwer Academic Press, U.S, 1997.

....features should be derived from the object shape models in order to generate a unified object database. With hyperquadric representations, each object may have several sets of parameters which will cause serious problems in the matching process of object recognition. Terzopoulos and Metaxas [19 21, 27] formulated deformable superquadrics which incorporate global deformations which represent prominent shape features, and local deformations which capture surface details. Deformable superquadrics are also capable of modeling nonsymmetrical objects. An extension of this work called the blended ....

D. N. Metaxas, Physics-Based Deformable Models: Application to Computer Vision, Graphics and Medical Imaging, Kluwer Academic, Norwell, MA, 1997.

....using genetic algorithms. In other cases the parameters are hand tuned to get reasonable behavior. The di#culty of incorporating accurate material properties is shared by many other methods that have been proposed in the computer graphics literature for real time modeling of deformable bodies (Metaxas, 1997; Platt and Barr, 1988; Terzopoulos and Fleischer, 1988; Gibson, 1997) Linear finite element methods are used by some researchers to obtain models with physically based parameters (Cotin et al. 1996; Martin et al. 1994) Linear models are computationally attractive as it is possible to ....

Metaxas, D. (1997). Physics-Based Deformable Models: Applications to Computer Vision, Graphics, and Medical Imaging. Kluwer Academic, Boston, MA.

....We presented a global registration method, which means that any change in a transformation parameter in uences the transformation of the 3D data set as a whole [40] In a local transformation, such a change in uences only a subset of the data. In the future, we will design deformable models [27] for lung surfaces in order to model local transformations that are due to di erences in patient respiration. We will use the deformable model parameters that register lung border surfaces to address the dicult task of registering structures within the lung. This will require modeling the ....

D. N. Metaxas. Physics-Based Deformable Models: Applications to Computer Vision, Graphics, and Medical Imaging. Kluwer Academic Press, Boston, 1997.

....MERL TR 97 19 November 1997 20 fracture is modeled by breaking connections between mesh points by removing interdependencies in the equations of motion. Details are in [TF88b, TF88a] Terzopoulos and Metaxas proposed deformable superquadric ellipsoids as useful models for image analysis [TM91, Met97] They first parameterize the shape of a (rigid) superquadric ellipsoid by six parameters: a scale parameter a, aspect ratio parameters a 1 ; a 2 , and a 3 , and squareness parameters 1 and 2 . The rigid portion of the representation also includes the standard rigid body degrees of freedom. ....

D. Metaxas. Physics-based Deformable Models: Applications to Computer Vision, Graphics, and Medical Imaging. Kluwer Academic, Boston, 1997.

....values of anthropometric measurements. Since motion tracking is also a goal of this vision system, a motion parameterization is also constructed (by hand) for a small set of facial expressions. The shape and motion estimation of model parameters is realized using a deformable model framework [Met96] This framework uses a parameterized face model, which has parameters for both the shape of the face (the unchanging appearance of an individual) as well as its motion (facial expressions and displays) Shape estimation is performed using 5 edges found in the image, guided by knowledge of where ....

....vector, and R is a rotation matrix given by the quaternion q. The kinematics of the model can be determined in terms of the parameter velocities q. As the shape changes, the velocity at a point u on the model is given by: x(u) L(q;u) q (2. 4) 11 where L = x q is the model Jacobian [Met96] Note that the dependency of L on q is not always written, for reasons of conciseness. For cases where x is defined using a sequence of deformation functions, the Jacobian can be computed using the chain rule as in Appendix A. A good geometric intuition for L(u) is obtained by noting that each ....

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D. Metaxas. Physics-Based Deformable Models : Applications to Computer Vision, Graphics, and Medical Imaging. Kluwer Academic Publishers, 1996.

....Today, there is a growing need for physics based image analysis of deformations in image sequences (e.g. real time MRI of the heart, image sequences showing brain deformation during neurosurgery, etc. The subject has recently lead to considerable interest in the medical image analysis community [1 8]. Medical image analysis has in the past relied heavily upon qualitative description. Today, modern applications can be enabled by providing to the clinician quantitative data derived from these images. For example, rather than simply observing erratic heart beat with real time MRI, clinicians ....

.... Shape and surface based image analysis is being increasingly used in the biomedical image analysis community, e.g. for pathological analysis [9] and for tracking deformations [10] Shape based models are also being used for image segmentation [11 13] to constrain active surface models [1, 14]. Such active surface models do not allow any physical interpretation of the deformation the surfaces undergo. Also, no volumetric deformation field is available. In an attempt to overcome these problems, several authors have proposed to use a physics based model to infer a volumetric deformation ....

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D.M. Metaxas. Physics-Based Deformable Models: Applications to Computer Vision, Graphics and Medical Imaging. Kluwer Academic Publishers, 1997.

....of mass elements in the body relative to a body frame OE is given by q(u; t) r(u; t) e(u; t) 2.1) Elastic deformations are represented by an energy ffl(e) which depends on the position of the body frame OE where ffl(x) can be represented by K(x) x. Figure 2. 4: Displacement Model Metaxas [Metaxas and Koh, 1996] [Metaxas, 1996] focused on utilizing the displacement model and implementing the FEM methodology for calculating the deformation component. The work in [Astley and Hayward, 1998] simulated the dynamics of deformable visco elastic 3 D bodies for haptic interaction. The dynamics were based on a ....

....body relative to a body frame OE is given by q(u; t) r(u; t) e(u; t) 2.1) Elastic deformations are represented by an energy ffl(e) which depends on the position of the body frame OE where ffl(x) can be represented by K(x) x. Figure 2. 4: Displacement Model Metaxas [Metaxas and Koh, 1996] [Metaxas, 1996] focused on utilizing the displacement model and implementing the FEM methodology for calculating the deformation component. The work in [Astley and Hayward, 1998] simulated the dynamics of deformable visco elastic 3 D bodies for haptic interaction. The dynamics were based on a multilayer FEM ....

Metaxas, D., editor (1996). Physics-Based Deformable Models: Applications to Computer Vision, Graphics, and Medical Imaging. Kluwer Academic Publishers, Boston.

....was developed for the numerically robust integration of nonlinear holonomic constraints within a deformable model framework, using Lagrange multipliers and a Baumgarte stabilization approach. We show that any type of illumination constraint can be incorporated in a physics based modeling framework [2], provided that the illumination law is a differentiable function of the normal or tangents to the surface. This encompasses practically all the illumination models used in computer vision, from the simple Lambertian model to more complex highly nonlinear models such as [3] Instead of extracting ....

D. Metaxas, Physics-Based Deformable Models: Applications to Computer Vision, Graphics and Medical Imaging, Kluwer-Academic Publishers, November 1996.

....techniques of pixel affinity [45] and clustering. A deformable model is then fitted to the estimated boundary data to fill in the missing boundary data and to override the spurious boundary data due to image noise. This is achieved by generalizing the formulation of the deformable models we use [30] to incorporate simple domain specific knowledge. In our particular application, we use knowledge of the fact that the detected organ boundaries are non intersecting closed curves [19] and the number of detected pixels on these boundaries will be significantly larger than the number of pixels ....

....image is shown for comparison but not directly used in the affinity based boundary estimation. a) b) c) Figure 3.2: a) MR slice of LV, b) gradient magnitude, and (c) estimated boundaries from pixel affinity 3. 2 Deformable Model We summarize the physics based deformable model framework [30] that we use and its integration with the estimated boundary data produced by the affinity based method described in Section 3.1. Our model is a superellipsoid with local deformations. The global parameters of the model determine its natural shape, and the local deformations determine the ....

D. Metaxas. Physics-Based Deformable Models: Applications to Computer Vision, Graphics and Medical Imaging. Kluwer-Academic Publishers, 1996.

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Metaxas, D.: Physics-based Deformable Models: Applications to Computer Vision, Graphics and Medical Imaging. Kluwer Academic Publishers (1996)

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D. Metaxas. Physics-based Deformable Models: Applications to Computer Vision, Graphics and Medical Imaging. Kluwer Academic Publishers, 1996.

....the point x = x, y, z) in the world coordinate system and the point x c = x c , y c , z c ) T in the camera coordinate system ensure the following equation. x = R c x c T c , 3) where, T c and R c are translation and rotation matrices. In the deformable model formulation presented in [8], by taking the time derivatives of the perspective projection equation, with an image point xp they get x p = H x c = H(R 1 c x) with H = f z c 0 x 0 f z c y (4) The focal length f is obtained by pre calibration of the camera. According to deformable model theory these 3D ....

D.N. Metaxas, Physics-Based Deformable Models -- Applications to Computer Vision, Graphics and Medical Imaging, Kluwer Academic Publishers, 1997.

....the method can be used with either orthographic or perspective projection assumptions. We also demonstrate how singular point information and images obtained under perspective projection can be handled in this framework. We use deformable models or grids with both global and local deformations [26, 25]. During shape estimation, we first fit the model s global parameters given the illumination constraints and then we refine its shape, based on the model s local deformations, using a coarse to fine grid. Use of a deformable model based approach offers shape flexibility and the additional ....

....suffers on surfaces that deviate significantly from this assumption. 21] derives accurate light source information from surfaces reconstructed using stereo data. 2.3. Deformable Models: Geometry, Kinematics, Dynamics In this section we review briefly the general formulation of deformable models [26, 25]. Geometrically, the models used in this paper are parameterized surfaces in space whose intrinsic parameters are u = u# v) defined on a domain Omega The positions x(u#t) of points on the model relative to an inertial frame of reference Phi in space are given by x = c Rp, where c(t) is the ....

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D. Metaxas. Physics-Based Deformable Models: Applications to Computer Vision,Graphics and Medical Imaging. Kluwer-Academic Publishers, November 1996.

.... models to appear in the literature of computer vision [13] This theory was expanded to allow statistical representation of the shape of the models and its points, as well as an increase the number of applications [5, 3] In our tracking example we use a general 3D deformable model framework [14] that has also been used for the estimation of shape from shading [19] for the combination of optical ow and edges in face tracking [7] and for the modeling of the human heart [15] There are several studies on how to represent the static shape of family of objects, like a pca decomposition ....

D. Metaxas. Physics-based Deformable Models: Applications to Computer Vision, Graphics and Medical Imaging. Kluwer Academic Publishers, 1996.

....of American Sign Language (ASL) using 3D tracking data, ASL phonology and modifications to the traditional use of Hidden Markov Models. We demonstrate the usefulness of this framework in computer vision and medical image analysis applications. 1 Introduction Physics based modeling [11] offers the methodology and techniques to address in a unified way difficult problems in computer vision. One of the advantages of using a deformable model in vision problems is that such models can be used to estimate the shapes and motions of objects (rigid and or nonrigid) with unknown initial ....

....recognition of ASL by taking into account the phonological aspects of ASL and by modifying the traditional use of Hidden Markov Models. In the following sections we elaborate more on the above techniques and we present our results. 2 Deformable Models: Geometry and Dynamics We have developed [18, 11] a physics based framework which provides deformable models with broad geometric coverage along with robust techniques for inferring shape and motion from noise corrupted data. In this framework, the positions of points on the model relative to an inertial frame of reference Phi in space are ....

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D. Metaxas. "Physics-Based Deformable Models: Applications to Computer Vision, Graphics and Medical Imaging", Kluwer-Academic Publishers, November 1996.

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Metaxas, D., #Physics-Based Deformable Models: Applications to Computer Vision, Graphics and Medical Imaging", KluwerAcademic Publishers, 1996.

....unlike most previous statistical approaches to computer vision, and it scales well with the number of parameters used in the deformable model description. 2. Deformable Model Tracking Fundamentally, a deformable model framework is a Lagrangian dynamics system parameterized by a vector q [18]: q = F(q) 1) As the tracking process evolves, we integrate q with the Euler integration method. We obtain the coordinates of each point on a deformable model through a series of linear and non linear operations applied over its parameters q. We convert contributions from a 2D visual cue i ....

D. Metaxas. Physics-based Deformable Models: Applications to Computer Vision, Graphics and Medical Imaging. Kluwer Academic Publishers, 1996.

....physics based sensor fusion method combining range and intensity data was presented in [51] Using a Kalman filter [2, 26] or Bayesian methods [12] for fusion combines solutions in a similar way. Aside from this, Kalman filtering has become a standard tool for estimation in dealing with noisy data [3, 19, 30, 32, 37]. Face tracking: There is a vast body of work on tracking the human face, with applications ranging from motion capture to human computer interaction. Among them, there are a number which bare similarity in some respect to the work presented in this paper. Several 2D face models based on splines ....

....the use of a Kalman filter. This section describes how the computation from Section 4.2 is reformulated using an iterated extended Kalman filter. Kalman filtering [3, 19, 30] has become a popular tool in computer vision, and the formulation here is, on the whole, similar to other applications [2, 7, 26, 32, 37]: there is a measurement equation which models the noise inherent in the data gathering process, and there is a process model, which predicts the behavior of the system based on the current state. The initialization and tuning of the filter is accomplished using standard techniques. The ....

D. Metaxas. Physics-Based Deformable Models : Applications to Computer Vision, Graphics, and Medical Imaging. Kluwer Academic Publishers, 1996.

....techniques of fuzzy affinity [14] and clustering. A deformable surface model is then fitted to the extracted boundary data to fill in the missing boundary data and to override the spurious boundary data due to image noise. This is achieved by generalizing the formulation of our deformable models [11] to incorporate simple domain specific knowledge. In our particular application, we use knowledge of the fact that the detected organ boundaries are closed curves [6] and the number of detected voxels on these boundaries will be significantly larger than the number of voxels which lie on false ....

....with its gradient magnitude and boundary pixels estimated from the affinity data. a) b) c) Fig. 2. a) MRI slice of left ventricle, b) its gradient magnitude, c) its estimated boundaries 3 Deformable Models We summarize our recently developed physics based framework for deformable models [11] and describe the integration of affinity data into the framework. Our model is a 3D superellipsoid with local deformations. The finite element method is used to compute the local displacements by dividing the model into small regions called elements. Between the nodal points within the model, ....

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D. Metaxas. Physics-Based Deformable Models: Applications to Computer Vision, Graphics and Medical Imaging. Kluwer-Academic Publishers, 1996.

....model with other computer graphics techniques so that dynamic objects can interact with a gas. There is some discussion about how an iterative relaxation step like that described in Sec. 3. 3 can be used to incorporate moving objects into animations of liquids in Foster and Metaxas [6] and Metaxas [9]. The methods used there are also applicable to the algorithm described in this paper, although that has not been explored in any detail. 6 Concluding Remarks Numerous techniques exist for animating hot gases for computer graphics. Nearly all of them concentrate on achieving a visual ....

Metaxas, D., "Physics-Based Deformable Models: Applications to Computer Vision, Graphics and Medical Imaging", Kluwer-Academic Publishers, 1996.

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D. Metaxas. Physics-based Deformable Models: Applications to Computer Vision, Graphics and Medical Imaging. Kluwer Academic Publishers, 1996.

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D. Metaxas, "Physics-based Deformable Models: Applications to Computer Vision, Graphics and Medical Imaging", Kluwer Academic Press, 1997.

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D. Metaxas, "Physics-based Deformable Models: Applications to Computer Vision, Graphics and Medical Imaging", Kluwer Academic Press, 1997.

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