Art Matheny and Dmitry B. Goldgof. The use of three and four-dimensional surface harmonics for rigid and nonrigid shape recover y and representation. IEEE Trans. on Pattern Analysis and Machine Intelligence, 17(10):967--981, 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Euclidean space. With advent of fast algorithms in the last ten years through work of [19] and others, computing the SFT has become feasible. As a result, researchers have used the SFT in a wide variety of applications ranging from compression of human head models [7] and nonrigid shape recovery [17] to surface representations [5] It is fairly easy to describe the SFT, for it is a projection of functions in ) onto the set of spherical harmonics. One can invert the transform as a consequence of theorem 3.1 which states that spherical harmonics are an orthonormal basis for L ) Let ....

A. Matheny and D.B. Goldgof. The use of three and four-dimensional surface harmonics for rigid and nonrigid shapre recovery and representation. IEEE. Transactions on Pattern Analysis and Machine Intelligence, 18:959-971, October 1996.

....horizontal axis the number of profile. The total horizontal length corresponds to one whole round in both images. The value of the LAD was assumed to be 5. TREE SHAPE MODELLING An appealing way to describe the trees is the use of surface harmonics (Legendre functions and sinusoidal components) [4, 5, 6], because they are complete, orthogonal and ordered in spatial frequency. Moreover they are solutions of Laplace equations, which enables relatively simple analytic expressions for the scalar electrostatic potential. The surfaces are represented as linear combinations of spherical harmonics up to ....

A. Matheny and D.B. Goldgof, "The use of three- and four-dimensional surface harmonics for rigid and nonrigid shape recovery and representation", IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 17, No. 10, pp. 967- 981, 1995.

....initialization corresponds to a sphere. We set the constraints and T t ; the latter avoids degenerate shapes. Harmonic contours We consider the following generalization of superquadrics. Surface harmonics are star shaped surfaces defined on the unit sphere of IR (see [16, 17] for their use in image segmentation) Using notations of figure 1, we define the general parameterization: t 3 ] t f F f t F ( 13) We now use the following property [16] Any function ] t of finite energy and differentiable on the unit sphere of IR can be decomposed ....

....superquadrics. Surface harmonics are star shaped surfaces defined on the unit sphere of IR (see [16, 17] for their use in image segmentation) Using notations of figure 1, we define the general parameterization: t 3 ] t f F f t F ( 13) We now use the following property [16]. Any function ] t of finite energy and differentiable on the unit sphere of IR can be decomposed as a linear combination of spherical harmonics: t l r l X (14) where spherical harmonics are linked to Legendre polynomials [16] Introducing a cut off , we consider the ....

[Article contains additional citation context not shown here]

A. Matheny and D. B. Goldgof, "The use of three and four-dimensional surface harmonics for rigid and nonrigid shape recovery and representation," IEEE Trans. Pattern Anal. Mach. Intell., 17, pp. 967--981, October 1995.

....and represents a sphere in 3D space, analogous to Fourier series it is referred to as the DC harmonic. Spherical harmonic shape representation has been used for molecular surface visualisation [3] object recognition [4] object orientation calculations [5] visualisation of human internal organs [6] and reconstruction of shape deformation [7] 3D human head models are commonly used in computer graphics applications, mainly in the animation of humans for image sequences [8] and model based video coding [9] Furthermore injury analysis in medical applications [10] as well as design and ....

A. Matheny and D.B. Goldgof: `The use of three- and four- dimensional surface harmonics for rigid and nonrigid shape recovery and representation', 1995, IEEE Trans. on Patt. Anal. and Mach. Int., Vol.17, pp 967-981.

....As contrasted to non parametric shape estimation, parametric approaches to shape extraction are model based. Examples of parametric methods include: Fourier descriptors [31] 36] piecewise poynomials such as Bezier curves, B splines or Beta splines [3] 37] and spherical harmonic expansions [23], 5] These parametric methods require the object to be star shaped, i.e. its boundary is uniquely specified by some radial function in polar (2D shapes) or spherical (3D shapes) coordinates with origin located at a center of description inside the object. It is for such models that the CR ....

A. Matheny, "The use of three and four dimensional surface harmonics for rigid and non-rigid shape recovery and representation," IEEE Trans. on Pattern Anal. and Machine Intell., vol. PAMI-17, no. 10, pp. 967--981, Oct 1995.

....initialization corresponds to a sphere. We set the constraints 0 a b c and 0:2 ; 3; the latter avoids degenerate shapes. Harmonic contours We consider the following generalization of superquadrics. Surface harmonics are star shaped surfaces defined on the unit sphere of IR 3 (see [16, 17] for their use in image segmentation) Using notations of figure 1, we define the general parameterization: GM( sin cos ;sin sin ;cos ] t : 13) We now use the following property [16] Any function ( of finite energy and differentiable on the unit sphere of IR 3 can be ....

.... Surface harmonics are star shaped surfaces defined on the unit sphere of IR 3 (see [16, 17] for their use in image segmentation) Using notations of figure 1, we define the general parameterization: GM( sin cos ;sin sin ;cos ] t : 13) We now use the following property [16]. Any function ( of finite energy and differentiable on the unit sphere of IR 3 can be decomposed as a linear combination of spherical harmonics: 1 X l=0 X jmj l a m l m l ( 14) where spherical harmonics m l are linked to Legendre polynomials [16] ....

[Article contains additional citation context not shown here]

A. Matheny and D. B. Goldgof, "The use of three and four-dimensional surface harmonics for rigid and nonrigid shape recovery and representation," IEEE Trans. Pattern Anal. Mach. Intell., 17, pp. 967--981, October 1995.

....data produced caused a revolution of the heart dynamic study these last few years. 5.2.1 Segmentation and contour tracking The heart left ventricle tracking in 2D or 3D image sequences and the segmentation of cardiac images have been the motivation for many research papers. Matheny and Goldgof [51] and Schudy and Ballard [84] use surface harmonics to model the shape and motion of the heart left ventricle. Many works [41, 37, 94] are dedicated to the heart left ventricle tracking in 2D ultrasound sequences. Jacob et al. [41] use a predictive algorithm of the displacements between two ....

A. Matheny and D. Goldgof. The use of three- and four-dimensional surface harmonics for rigid and non-rigid shape recovery and representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 17(10):967978, Oct. 1995.

....because the correspondence is defined between two successive images, regularity and periodicity in time is not guaranteed. Only a few studies impose temporal continuity or periodicity in their model: these studies deal with segmentation of 2D (O Donnell et al. 1994) or 3D images (de Murcia, 1996; Matheny and Goldgof, 1995; Schudy and Ballard, 1979) Some other rare methods in 2D (Todd Constable et al. 1994; McEachen et al. 1994) or in 3D (Thirion, 1995; Nastar, 1994) perform a posteriori time filtering. Moreover, all these tracking techniques ( Park et al. 1996; Park et al. 1994) excepted) do not provide ....

Matheny, A. and Goldgof, D. (1995). The use of three- and fourdimensional surface harmonics for rigid and nonrigid shape recovery and representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 17(10), 967--978.

....in a deformable heart model. Cohen [16] used a deformable surface model inspired by the work of Terzopoulos active contour, or snake model [46,89] to first detect and then track deforming cardiac surfaces. Parametric surface models based on superquadrics [8,13,88,92] spherical harmonics [56], polar transforma 14 tions [25] or probabilistic models [84] have all been used to assist in the segmentation and tracking of the cardiac surface. Finite element models of varying detail have also been used to describe the motion of the heart [71] Some go as far as mapping the cardiac muscle ....

....the algorithm needed to be run successfully using only the spatial continuity constraints. Alternate approaches have been proposed that would incorporate four dimensional continuity constraints more naturally and do not suffer from the initialization problem as does the prediction field method [25, 56,58]. Approaches like these warrant further investigation. A detailed study of the effects of noise is also needed. Most of the results obtained in this dissertation were obtained using noise free data. For those datasets, it was advantageous in a motion estimation algorithm to accurately model the ....

A Matheny and D B Goldgof. "The use of three- and four-dimensional surface harmonics for rigid and nonrigid shape recovery and representation." IEEE Trans Patt Anal Machine Intell, 17(10):967--981, 1995.

....clearer in Table 1. Although we used orthography as an image projection model, the results of error evaluation were regarded to be acceptable for the results of the viewpoint varying sequences. 5 Discussion For the representation of LV shape, spherical harmonics has been considered to be suitable [12, 13]. However, a recent work has shown that fitting high order degree harmonics is unstable in the blank regions where no data is present because the linear system is nearly underdetermined [13] Also in our experiments, it was shown that 3D recovery was unstable for small weight of the smoothness ....

.... Discussion For the representation of LV shape, spherical harmonics has been considered to be suitable [12, 13] However, a recent work has shown that fitting high order degree harmonics is unstable in the blank regions where no data is present because the linear system is nearly underdetermined [13]. Also in our experiments, it was shown that 3D recovery was unstable for small weight of the smoothness constraint as shown in Fig.5(b) As an alternative representation which stabilizes the recovery results, basis functions with small support regions such as B splines can be used by combining ....

A Matheny and D.B.Goldgof: "The use of three- and four-dimensional surface harmonics for rigid and nonrigid shape recovery and representation", IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol.17, No.10, pp.967-981 (1995).

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Art Matheny and Dmitry B. Goldgof. The use of three and four-dimensional surface harmonics for rigid and nonrigid shape recover y and representation. IEEE Trans. on Pattern Analysis and Machine Intelligence, 17(10):967--981, 1995.

No context found.

A. Matheny and D. B. Goldgof, "The use of three and four dimensional surface harmonics for rigid and nonrigid shape recovery and representation," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 17, no. 10, pp. 967--981, Oct. 1995.

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