D. Terzopoulos, A. Witkin, and M. Kass. Symmetry-seeking models and 3D object reconstruction. International Journal of Computer Vision, 1:211--221, 1987.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....adequate segmentation cannot be obtained without expert knowledge, requiring tedious manual interaction by a human specialist. Elastically deformable contour models (snakes) 2] have been proposed as tools for supporting manual object delineation. While such procedures can be extended to 3D [3, 4], their initialization becomes difficult. Most often, the initial guess must be very close to the sought contour to guarantee a successful result [5] While a careful and time consuming analysis is acceptable for outlining complex pathological objects, no real justification for such a procedure ....

D. Terzopoulos, A. Witkin and M. Kass, Symmetry-Seeking Models and 3D Object Reconstruction, Int. J. Comp. Vision 1(3) pp. 211-221, 1987

....known propagation speed and numper of iterations permit a determination of the surface of the cell nucleus by an ellipsoidal approximation. This ellipsoid is then used for the initialization of the elastic matching process. 4 Segmentation of the cell nucleus Elastically deformable surface models [7, 8] have been proven to be efficient tools for the segmentation of 3D images if a reasonable initialization can be provided. Parametric techniques as flexible Fourier surface models proposed by Staib and Duncan [9, 10] offer a convenient way for the elastic deformation of the ellipsoid resulting from ....

Terzopoulos, D., Witkin, A. and Kass, M.: Symmetry-Seeking Models and 3D Object Reconstruction. Int. J. Comp. Vision 1, 3, 211--221 (1988)

....tures. The ventricular modes of variation are exam ined qualitatively in Section 5, while Section 6 presents our more quantitative experimental results. Section 7 discusses the unresolved issues pertaining to this work. Section 8 summarizes the work done. 2 Related work Terzopoulos el al. [1] used a physical model with a very large number of degrees of freedom to perform dynamic shape fitting. Pentland and Sclaroff [2] em ployed a much smaller number of degrees of freedom, representing shape in terms of an object s physical deformation modes. Instead of using the modes of a ....

D. Terzopoulos, A. Witkin, and M. Kass. Symmetry-seeking models and 3D object reconstruction. Int. J. Cornput. lision, 1:211 221, 1987.

....recover depth, but we also have to merge (register and composite) multiple depth maps, and represent objects given no a priori knowledge about their rough shape or topology. For simple topologies and shapes, deformable physically based models can do a good job of recovering the unknown geometry [Terzopoulos et al. 1987; Pentland and Sclaroff, 1991] For general topologies, the problem is more difficult. Since many current shape recovery techniques produce incomplete or sparse geometric descriptions, a general 3 D surface interpolation technique may be required to generate a smooth continuous surface [Hoppe et ....

D. Terzopoulos, A. Witkin, and M. Kass. Symmetry-seeking models and 3D object reconstruction. International Journal of Computer Vision, 1(3):211--221, October 1987.

....The deformations that result produce a shape that agrees with the data. The use of physics also makes available additional mathematical tools. For example, smooth surfaces that interpolate a set of sparse data can be determined by associating an energy with the surface (which is minimized) TWK87] and produces a method of regularization useful as a data fitting technique. Constraint techniques from physics have been used to form articulated rigid models [MT93] and will be used in Chapter 5 to incorporate optical flow information. The next section describes how a model is specified and ....

D. Terzopoulos, A. Witkin, and M. Kass. Symmetry-seeking models and 3D object reconstruction. International Journal of Computer Vision, 1(3):211--221, 1987.

....that the prior probabilities in the Bayesian models are poor approximations of the true priors. 7.2 Segmentation Both physical and probabilistic methods have also been used for medical image segmentation. The primary way in which physical models have been used has been through the use of snakes [38] and their variants. Cohen [39] augmented the original snake formulation with a balloon force to help it avoid local minima. Staib and Duncan [40] used Fourier snakes , based on a Fourier decomposition of an object s shape. Instead of relying on the elastic constraints of a physical model, they ....

D. Terzopoulos, A. Witkin, and M. Kass. Symmetry-seeking models and 3D object reconstruction. Int. J. Comput. Vision, 1:211--221, 1987.

....real aerial images to simultaneously model terrain, roads, and ridgelines under consistency constraints. Keywords : Snakes, Deformable models, Constrained optimization, Consistency. 1 1 Introduction We propose an approach to imposing generic hard constraints on snake like deformable models [Terzopoulos et al. 1987, Kass et al. 1988] while both preserving the good convergence properties of snakes and avoiding having to solve large and ill conditioned linear systems of equations. The ability to apply such constraints is essential for the accurate modeling of complex objects that obey known geometric and ....

D. Terzopoulos, A. Witkin, and M. Kass. Symmetry-seeking Models and 3D Object Reconstruction. International Journal of Computer Vision, 1:211--221, 1987. 24

....and the need to increase efficiency motivates the development of computer assisted, automated procedures. Elastically deformable contour and surface models, socalled snakes [8] have been proposed as tools for supporting manual object delineation. While such procedures can be extended to 3 D [24, 3], their initialization is a critical issue. Most often, the initial guess must be very close to the sought contour to guarantee a satisfying result [14] An excellent overview of elastically deformable models can be found in [11] The primary reason for the need of a precise snake initialization ....

D. Terzopoulos, A. Witkin, and M. Kass. SymmetrySeeking Models and 3D Object Reconstruction. Int. J. Comp. Vision, 1(3):211--221, 1988.

.... and volume rendering [15, 17, 16, 6] The second approach transforms the data into something that is more readily displayed, such as a surface [9, 12, 7, 13, 5] Another technique is to generate models of the scanned objects using the volume data as a measure of the object s current configuration [10, 20, 14] . The major motivation for this technique is the ability of current technology to display geometric models rather than three dimensional scalar fields. The model can then be used for pattern recognition, visualization, or subject to a series of geometric measurements and operations. Object ....

....Other Solutions The proposed solution for controlling the deformation of a model to fit an object is based upon Breen s work on goal oriented motion for computer animation [2, 3] see Section 2.1. 1) and reflects a simpler approach to the problems presented by Kass et al. 10] Terzopoulos et al. [19, 20], and Bajcsy et al. 1] These other approaches involve modelling the elastic nature of a curve or surface in order to control the model s deformation. Such models are based on the differential equations of elastic properties. These algorithms are generally applicable because the model will deform ....

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D. Terzopoulos, A. Witkin, and M. Kass. Symmetry-seeking models and 3d object reconstruction. Int'l J. Computer Vision, 1(3):211--221, October 1987.

....to model interesting objects, yet simple enough to permit recognition or construction from images or other sensor data. A variety of surface based models have been proposed, including generalized cylinders [Brooks et al. 1979] superquadrics [Pentland, 1986] and deformable finite element models [Terzopoulos et al. 1987]. Volumetric models such as octrees [Jackins and Tanimoto, 1980; Meagher, 1982] have also been used. One popular approach to constructing such volumes has been to intersect multiple silhouettes of the 4 1 Introduction object seen from different views (see [Chen and Huang, 1988; Szeliski, 1990] ....

D. Terzopoulos, A. Witkin, and M. Kass. Symmetry-seeking models and 3D object reconstruction. International Journal of Computer Vision, 1(3):211--221, October 1987.

....28 B Computation of internal forces : ii Contents 1 Introduction 1 1 Introduction The modeling of free form surfaces is one of the central issues of computer graphics. Spline models [Bartels et al. 1987; Farin, 1990] and deformable surface models [Terzopoulos et al. 1987b; Terzopoulos and Fleischer, 1988a] have been very successful in creating and animating such surfaces. However, these methods either require the discretization of the surface into patches (for spline surfaces) or the specification of local connectivity (for springmass systems) These steps can ....

....are the control vertices, and B i (u 1 ; u 2 ) are the piecewise polynomial basis functions. The surface shape can then be adjusted by interactively positioning the control vertices or by directly manipulating points on the surface [Bartels and Beatty, 1989] Elastically deformable surface models [Terzopoulos et al. 1987b; Terzopoulos and Fleischer, 1988a] also start with a parametric representation for the surface s(u 1 ; u 2 ) To define the dynamics of the surface, Terzopoulos et al. 1987b] use the metric tensor or first fundamental form G whose components are given by G ij (s(u 1 ; u 2 ) s u i Delta ....

[Article contains additional citation context not shown here]

D. Terzopoulos, A. Witkin, and M. Kass. Symmetry-seeking models and 3D object reconstruction. International Journal of Computer Vision, 1(3):211--221, October 1987.

....to recover depth, but we also have to merge (register and composite) multiple depth maps, and represent objects given no a priori knowledge about their rough shape or topology. For simple topologies and shapes, deformable physically based models can do a good job of recovering the unknown geometry [Terzopoulos et al. 1987; Pentland and Sclaroff, 1991] For general topologies, the problem is more difficult. Since many current shape recovery techniques produce incomplete or sparse geometric descriptions, a general 3 D surface interpolation technique may be required to generate a smooth continuous surface [Hoppe et ....

D. Terzopoulos, A. Witkin, and M. Kass. Symmetry-seeking models and 3D object reconstruction. International Journal of Computer Vision, 1(3):211--221, October 1987.

....distributing curvature evenly across the patch, causing it to seek a fairer shape. From the user s point of view these forces reparameterize the model in terms of a higherlevel surface characteristic (fairness) Other possibilities for optimization forces include the shape attractors discussed in[TWK87] and [WFB87] In optimizing such function outputs, the modeler continuously adjusts numerous surface parameters in nontrivial ways in response to simple manipulation by the user. 2.5. Other Controls and Representations With Differential Manipulation, we can use the same manipulation techniques for ....

Demetri Terzopoulos, Andrew Witkin, and Michael Kass. Symmetry seeking models and 3d object reconstruction. International Journal Computer Vision, 1(3), 1987.

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D. Terzopoulos, A. Witkin, and M. Kass. Symmetry-seeking models and 3D object reconstruction. International Journal of Computer Vision, 1:211--221, 1987.

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D. Terzopoulos, A. Witkin, and M. Kass. Symmetry-seeking models and 3D object reconstruction. International Journal of Computer Vision, 1:211--221, 1987.

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D. Terzopoulos, A. Witkin, and M. Kass. Symmetry-seeking models and 3D object reconstruction. Int. J. Computer Vision, 1:211--221, 1987. 23

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Demetri Terzopoulos, Andrew Witkin, and Michael Kass. Symmetry-seeking models and 3d object reconstruction. Intl Journal of Computer Vision, 1(3):211-- 221, 1987.

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#181# D. Terzopoulos, A. Witkin, and M. Kass. Symmetry-seeking models and 3D object reconstruction. International Journal of Computer Vision, 1:211#221,

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