B. C. Vemuri and A. Radisavljevic, "Multiresolution stochastic hybrid shape models with fractal priors," ACM Trans. Graph., vol. 13, pp. 177--207, 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....within the normal anatomic variation of organs, such local minima could be eventually avoided. Inclusion of prior knowledge in the image interpretation process can be achieved e.g. by incorporation prior distributions on the variables to be estimated, as proposed by Vemuri and Radisavljevic [6]. Cootes et.al. 7] use an alternative way which parallelly reduces the dimensionality of the object descriptor space. They use active shape models, which strictly restrict their possible deformations according to the statistics of training samples. Object shapes are described by the point ....

....the 3D Fourier snake segmentation procedure. One has to realize, that the Fourier parametrization is just one possibility for the parametric description of contours. Alternative methods, as e.g. deformable superquadrics constructed in ortonormal wavelet bases has also proposed in the literature [6], and can be used for the implementation of elastically deformable parametric models. 4.2 Elastically deformable Fourier surface models Using the parametric surface description presented previously, the parametrized Fourier snake concept can be generalized from 2D to 3D. The concept is is ....

B.C. Vemuri and A. Radisavljevic, Multiresolution Stochastic Hybrid Shape Models with Fractal Priors, ACM Trans. Graphics, 13(2) pp. 177-207, 1994

....description is superquadrics, as introduced by Barr [3] As superquadrics alone are not able to describe complex shapes, they have been extended to deformable superquadrics by Terzopoulos [16] who takes a superquadric as a reference shape and combines it with a displacement function. Vemuri [17] later constructed this displacement function in a wavelet basis. Bardinet [2] on the other hand deforms superquadrics by applying free form deformations. With the extended approaches it is possible to describe complex shapes, which is necessary for example in medical image analysis. However, as ....

B. C. Vemuri and A. Radisavljevic. Multiresolution stochastic hybrid shape models with fractal priors. ACM Transactions on Graphics, 13(2):177-207, Apr. 1994.

....(curvature extrema) of tips and saddle structures. Examples of these types of landmarks of the human head are the tips of the ventricular horns or the saddle points at the zygomatic bones (see Fig. 1) To represent such structures, we utilize 3D surface models (e.g. 14] 12] 3] 13] 7] 15] [18], 1] Note that in comparison to previous work on deformable models, we are here interested in the accurate localization of salient surface loci. Central to an ecient solution of this speci c problem is that the model surface exhibits a unique point whose position can be directly computed from ....

....by black dots. Model tting is formulated as an optimization problem. As tting measure, we here use an edge based measure that incorporates the strength as well as the directions of the intensity variations (Sec. 3) Usually, only the strength of the intensity variations is incorporated (e.g. [18], 13] To determine initial values for the model parameters, we have developed a semi automatic di erential approach, which is described in Sec. 4. Experimental results for 3D tomographic data are presented in Sec. 5. In particular, we compare the localization accuracy of our new approach with ....

B.C. Vemuri and A. Radisavljevic. Multiresolution Stochastic Hybrid Shape Models with Fractal Priors. ACM Trans. on Graphics, 13(2):177-207, 1994.

....3D point landmarks of the human head are the tips of the ventricular horns or the saddle points at the zygomatic bones (see Fig. 1) To represent such structures, we utilize 3D surface models. In the literature, a variety of 3D surface models has been used (e.g. 15] 13] 3] 14] 7] 16] [19], 1] Note that in comparison to earlier work on deformable models, we are here interested in the accurate localization of salient surface loci. Central to an ecient solution of this speci c problem is that the model surface exhibits a unique point whose position can be directly computed from the ....

....edgebased tting measure that incorporates the strength as well as the direction of the intensity variations. This measure, which is described in Sect. 3, is a 3D generalization of a 2D tting measure suggested in [20] Usually, only the strength of the intensity variations is incorporated (e.g. [19], 14] To determine initial values for the model parameters, we have developed a semi automatic di erential approach (Sect. 4) Experimental results of applying our new approach to 3D tomographic images of the human head are presented in Sect. 5. In particular, we analyze the localization ....

B.C. Vemuri and A. Radisavljevic. Multiresolution Stochastic Hybrid Shape Models with Fractal Priors. ACM Trans. on Graphics, 13(2):177-207, 1994.

....tasks, as is described in [75] For this reason, a popular application of models based on superquadrics has been in cardiac imaging [74] where the simple shape of the heart can be readily modeled by a superellipsoid. The deformable superquadric model has been extended by Vemuri and Radisavljevic [76], who employed a wavelet parameterization of the local deformation process. The multiresolution nature of the wavelet decomposition allows for a smooth transition between the global superquadric and the local descriptors. They also present a method utilizing training data for obtaining a prior ....

B. C. Vemuri and A. Radisavljevic, "Multiresolution stochastic hybrid shape models with fractal priors," ACM Trans. Graph., vol. 13, pp. 177--207, 1994.

....models offer a straightforward way for the inclusion of prior knowledge in the image segmentation process. This is done by incor porating prior statistics to constrain the variation of the parameters of the elastic model. Such procedures have been developed by Vemuri and Radisavljevic [26] using a hybrid primitive called deformable superquadrics constructed in a multi resolution wavelet base, or by Staib and Duncan [18] for deformable Fourier models. For complex shapes described by a large number of often highly correlated parameters, the use of such priors may become tedious. The ....

B. Vemuri and A. Radisavljevic. Multiresolution Stochastic Hybrid Shape Models with Fractal Priors. ACM Trans. Graphics, 13(2):177--200, 1994.

....overcomes these difficulties. Subdivision surfaces allow the modeling of surfaces with arbitrary topological type. Wavelets provide a natural means for efficiently and uniquely decomposing a complex shape into a concise representation. 7.1.4 Vemuri and Radisavljevic. Vemuri and Radisavljevic [Vemuri Radisavljevic 94] develop a wavelet based technique for representing shapes built from deformable superquadrics [Terzopoulos Metaxas 91] Their method is capable of modeling topological cylinders at various resolutions, and they also describe a technique for fitting shapes to sampled medical data. Wavelets give ....

B. C. Vemuri and A. Radisavljevic. Multiresolution stochastic hybrid shape models with fractal priors. ACM Transactions on Graphics, 13(2):177--207, April 1994.

....Milan Sonka is with the Department of Electrical and Computer Engineering, The University of Iowa 2 [1 4] statistical tests to differentiate healthy subjects from normals were designed [7] and anatomical atlases were built. The numerous shape models were based on Fourier [1, 3] or wavelet [5] models, description of an object contour eigen shape models [2,7] or based on medial axis [4] However, regardless of the model used, the training data consist of a set of point coordinates along the contour of the object of interest from several images. It is usually desirable for a model to ....

B. C. Vemuri and A. Radisavljevic, "Multiresolution stochastic hybrid shape models with fractal priors," ACM Trans. Graphics, vol. 13(2), pp. 177--207, 1994.

....domain into two separate bands in each stage. Therefore, each subspace W j has its own frequency band, which means that all the wavelet basis functions in any particular level are fully contained in the frequency band associated with that level. This behavior of dividing the frequency domain [20, 29] exhibited by a wavelet decomposition is illustrated in figure 2. Notice that the closer the QMF filters are to the ideal low pass and high pass filters, the better it is for achieving a good frequency domain division, i.e. the overlap between the frequency bands associated with each level is ....

B. C. Vemuri and A. Radisavljevic. "Multiresolution stochastic hybrid shape models with fractal priors". ACM Trans. on Graphics, 13(2):177--207, April 1994.

....other by distributed models) Superimposing the free form deformation (FFD) on a core superquadric allows representation of a variety of global shapes with local detail as was reported in [1, 6, 7, 8] This modeling scheme requires only a few parameters to represent global shape deformations. In [9], Vemuri and Radisavljevic developed a multiresolution, hybrid modeling scheme which represents the displacement function of a deformable superquadric model in a wavelet basis. Pentland and Williams [4] reported a novel shape modeling scheme which is based on modal analysis. The number of ....

....models, a large number of parameters are required to describe the recovered shape. Model tting to desired features in the image data can be posed as a nonlinear minimization problem and solved numerically. In the process of numerically tting the model to the data, Vemuri and Radisavljevic [9] used a multiresolution gradient descent (GD) method, while Terzopoulos and Metaxas [5] used a rst order Euler scheme to t their dynamically deformable superquadric model to the data. Both of these methods are slow since only a small time step can be taken in each iteration in order to get a ....

B.C. Vemuri and A. Radisavljevic, \Multiresolution stochastic hybrid shape models with fractal priors," ACM Trans. on Graphics, pp. 177-207, 1994.

....which recovers the shape accurately with few degrees of freedom without being restricted to parameterized mesh initialization is a good candidate for the solution. The existing deformable models used to solve this problem can be classified into two categories namely, 1) fixed grid size models [3, 7] using few degrees of freedom for representation at the cost of accuracy of the recovered shape and (2) adaptive grid size models [2, 4, 6] involving large degrees of freedom and computationally expensive ad hoc schemes for accurate shape representation. The hierarchical shape representation using ....

B. C. Vemuri and A. Radisavljevic. Multiresolution stochastic hybrid shape models with fractal priors. ACM TOG, 13(2):177 -- 207, 1994.

....everything in real world physics. Free form deformable models were rst introduced to computer graphics and visualization in Terzopoulos et al. 23] and further developed by Terzopoulos and Fleischer [24] Pentland and Williams [25] Metaxas and Terzopoulos [26] and Vemuri and Radisavljevic [27]. Celniker and Gossard [28] developed a system for interactive free form design based on the nite element optimization of energy functionals proposed in [24] Bloor and Wilson [29] 30] Celniker and Welch [31] and Welch and Witkin [32] proposed deformable B spline curves and surfaces which can ....

....globally parameterize shapes of arbitrary topology over a rectangular domain. A physics based model satisfying the aforementioned criteria is a good candidate for a solution to the shape recovery problem. Physics based deformable models used to solve shape recovery problem involve either xed size [27], 36] 37] 38] 39] or adaptive size [40] 41] 42] 43] 44] 45] grids. The models with xed grid size generally use fewer degrees of freedom for representation, but the accuracy of the recovered shape is lacking in many cases. On the other hand, the number of degrees of freedom used ....

B.C. Vemuri and A. Radisavljevic, \Multiresolution stochastic hybrid shape models with fractal priors," ACM Transactions on Graphics, vol. 13, no. 2, pp. 177 - 207, April 1994.

....constraints relevant to shape design. Free form deformable models were first introduced to computer graphics and visualization in Terzopoulos et al. 15] and further developed by Terzopoulos and Fleischer [16] Pentland and Williams [17] Metaxas and Terzopoulos [18] and Vemuri and Radisavljevic [19]. Celniker and Gossard [20] developed a system for interactive free form design based on the finite element optimization of energy functionals proposed in [16] Bloor and Wilson [21] 22] Celniker and Welch [23] and Welch and Witkin [24] proposed deformable B spline curves and surfaces which can ....

....meshes since it is infeasible to parameterize shapes of arbitrary topology. A physics based model satisfying the aforementioned criteria is a good candidate for a solution to the shape recovery problem. Physics based deformable models used to solve shape recovery problem involve either fixed size [19], 28] 29] 30] 31] or adaptive size [32] 33] 34] 35] 36] 37] grids. The models with fixed grid size generally use less number of degrees of freedom for representation, but the accuracy of the recovered shape is lacking in many cases. On the other hand, the number of degrees of ....

B. C. Vemuri and A. Radisavljevic, "Multiresolution stochastic hybrid shape models with fractal priors," ACM Transactions on Graphics, vol. 13, no. 2, pp. 177 -- 207, April 1994.

....principle was presented in [1] This scheme involved superposing a core superquadric with a global volumetric deformation called the free form deformation (FFD) 18] This modeling scheme requires relatively fewer parameters to describe global deformations. In Vemuri and Radisavljevic [24], a multiresolution hybrid modeling scheme was developed which involved representing the membrane displacement function of a deformable superquadric model in a wavelet basis. In [15] Pentland et al. introduced a novel shape modeling technique based on modal representations. This scheme permits ....

B.C. Vemuri and A. Radisavljevic. Multiresolution stochastic hybrid shape models with fractal priors. ACM Trans. on Graphics, pages 177-207, 1994.

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B. C. Vemuri and A. Radisavljevic, "Multiresolution stochastic hybrid shape models with fractal priors," ACM Trans. Graph., vol. 13, pp. 177--207, 1994.

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B. Vemuri and A. Radisavljevic. Multiresolution stochastic hybrid shape models with fractal priors. ACM Transactions on Graphics, 13(2):177--207, April 1994. Special Issue on Interactive Sculpting. 312

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B.C. Vemuri and A. Radisavljevic, "Multiresolution Stochastic Hybrid Shape Models With Fractal Priors", ACM Transactions on Graphics, Vol. 13, No. 2, pp. 177--207, April 1994.

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