Simchony, T., Chellappa, R., Shao, M.: Direct analytical methods for solving poisson equations in computer vision problems. IEEE Trans. Pattern Anal. Machine Intell. 12 (1990) 435--446  Home/Search   Document Not in Database   Summary   Related Articles   Check

....FDM. These SM approaches take advantage of symmetries by transforming the equation into the spectral domain. They only require O#N ### N# operations for a 2D problem on a N # N grid. It was Simchony who first applied SM to solve Poisson equations on 2D rectangles for computer vision problems [30]. Although similar methods for solving PDE s over the unit sphere have been used in numerical weather prediction and the study of ocean dynamics [9] 38] to the best of our knowledge, we are the first to propose applying them to 3D computer vision problems. When the PDE (21) is expressed in ....

T. Simchony, R. Chellappa, and M. Shao, "Direct analytical methods for solving Poisson equations in computer vision problems," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 12, no. 5, pp. 435--446, May 1990.

....D## #Dwhere# is the domain of definition of the entire image. Equation (8) defines a 2 dimensional harmonic function on the region to be removed, and thus we call this method harmonic cut . The Laplace equation is a special case of Poisson equation, which has been studied extensively [13]. In the actual implementation, a small scale is selected and elliptic features are detected. These features correspond to either noise or tiny substructures (approximately 20 pixels) on the nuclei. The corresponding regions are subsequently interpolated with a harmonic function. Figure 5(b) shows ....

T. Simchony, R. Chellappa, and M. Shao, "Direct analytical methods for solving poisson equations in computer vision problems," PAM I , vol. 12, no. 5, pp. 435--446, May 1990.

....contours [3] These problems can be formulated in the framework of variational principles and lead to solving Euler Lagrange equations of elliptic type as the necessary condition for a minimum. Although there exist direct analytical methods for solving these equations on 2D rectangular domain [4], current approaches that we are aware of solve these equations defined over closed 3D surface by iterative techniques [3] In this paper, we apply spectral methods [5, 6] to solve elliptic equations over the unit sphere and apply this to the problems of surface reconstruction and 3D active ....

....and FDM methods. These methods usually take advantage of symmetries by transforming the equation into spectral domain and only require O(N 2 log N) operations for a 2D problem on N N grid. It was Simchony who first applied spectral method to solve Poisson equations in computer vision problems [4]. Although similar methods for solving PDE over unit sphere have been used in numerical weather prediction and the study of ocean dynamics [5, 6] to the best of our knowledge, they have not been used in computer vision. In the subsequent sections, we discuss the application of spectral methods to ....

T. Simchony, R. Chellappa, and M. Shao, "Direct analytical methods for solving Poisson equations in computer vision problems," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 12, no. 5, pp. 435--446, May 1990.

....data problems with nonuniform weighting on the data constraints, such as the optical flow problem, since the size of the associated ( dense ) capacitance matrix is too large. Although this problem may be circumvented by incorporating the capacitance matrix technique as part of an iterative scheme [21], however it was pointed out in [6] that this semi direct numerical scheme only converges when the regularization parameter is very large. In this paper, we will introduce a physically based adaptive preconditioning technique which when used in conjunction with the conjugate gradient algorithm, ....

....on a novel preconditioning technique, in a subsequent section. Numerous solution methods using variational principle formulations of the SFS problem have been proposed. For a comprehensive set of papers on this topic, we refer the reader to the book edited by Horn and Brooks [12] and the work in [24, 21, 11, 23]. In this problem, it is required to recover the shape of surfaces from image irradiance which depends on surface geometry and reflectance, scene illuminance and imaging geometry. The sum of the smoothness constraint and the penalty terms in this problem are, E(Z; p; q) 2 Z Z Omega (p 2 ....

T. Simchony, R. Chellappa, and M. Shao. "Direct analytical methods for solving Poisson equations in computer vision problems". IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(5), May 1990.

....wherever the brightness gradient is non zero, or when it is greater than a threshold in the presence of noise, thus avoiding an ill posed formulation of the reconstruction problem. Issues concerning the fusion of shading cues with parallax cues have been discussed in several works, including [1, 29, 17, 32, 19, 7, 3, 28]. To our knowledge, the merging of multi view geometry with shading in a variational framework is novel. Also, the re visitation of the correspondence problem and the de nition of correspondence sets is novel, and so is the fast level set implementation of the stereoscopic shading algorithm that ....

T. Simchony, R. Chellappa, and M. Shao. Direct analytical methods for solving Poisson equations in computer vision problems. IEEE Trans. Pattern Anal. Mach. Intell., 12(5):435-446, 1990.

....channel. We instead remove intensity gradients from the logarithm of the luminance image by thresholding whenever the chromaticity changes abruptly. Both the luminance and the chromaticity combine information from all three color channels. Many examples of lightness computation in the literature [13, 14, 1, 8, 4] use only synthetic images. A notable exception is in Horn [7] in which he discusses the problem of thresholding and the need for appropriate sensor spacing. He conducts experiments on a few very simple real images. Choosing an appropriate threshold is notoriously difficult and the current problem ....

....context of shape from shading, Frankot and Chellappa [3] enforce integrability of the gradient image (p; q) by projecting in the Fourier domain onto an integrable set. This turns out to be equivalent to taking another derivative of (p; q) and assuming the resulting sum equals the Laplacian of z [13]. For the lightness problem, then, integrating by forming the Laplacian and inverting is a method of enforcing integrability of TrI . The most efficient method for inverting the Laplacian is integration in the Fourier domain, as set forward in [13] While these methods of projecting TrI onto an ....

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T. Simchony, R. Chellappa, and M. Shao. Direct analytical methods for solving Poisson equations in computer vision problems. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12:435--445, 1990.

....of the digital ellipse. b) Corners detected. Only two convex corners are detected. Results compare favorable with results given in [21] Figure 20 in [21] a) b) Figure 21: Comparison with related work. A digital object consisting of a large semi circle and 3 small semi circles digitized from [25]. a) the scale space corner map of the object. b) Corners detected are marked and superimposed on the object s boundary. The figure shows 13 convex corners and 2 concave corners are detected. Results compare favorably with results given in [21] Figure 22in [21] distribution. The interior ....

....equation to model and accommodate for the time variation of the potential distribution. The most critical step in the proposed approach in terms of the running time performance is the generation of the potential distribution. Non iterative direct analytical methods for solving the Poisson equation [25] deserve further investigation. The experience in this work suggests that interesting features exhibited by the EFTbased approach of corner detection and skeletonization promote the investigation of more physics motivated models in solving computer vision problems. Finally, it is believed that ....

T. Simchony, R. Chellappa, and M. Shao, Direct analytical methods for solving Poisson equations in computer vision problems, IEEE Trans. Patt. Anal. Machine Intell., vol. 12, no. 5, pp. 435-446, 1990.

....equipotential contour. The potential distribution of an object is obtained by solving the Poisson equation inside the object. The Poisson equation has been used before to model and solve computer vision problems such as the lightness problem, shape from shading, and the computation of optical flow [29]. The proposed potential surface approach can represent the object s shape at different levels of smoothing or scale and can capture important shape information such as curvature. Furthermore, equipotential contours are smoother than equidistance contours which are employed in the ridge following ....

....for the Laplace equation was employed in [1] for the detection of corners. It can be easily verified that the solution is unique. Many methods for the solution of the interior Dirichlet boundary value problem have been reported in the literature. Both iterative [11] and direct analytical [29] solutions have been used to solve vision problems such as the lightness problem, the shape from shading problem, and the computation of optical flow. In this paper, the Jacobi relaxation method [31] is adopted because of its simplicity. In a digital grid, the Laplacian operator is approximated by ....

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T. Simchony, R. Chellappa, and M. Shao, Direct analytical methods for solving Poisson equations in computer vision problems, IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-12, no. 5, pp. 435-446, 1990.

.... the discretized Poisson equation (for irregular regions) are based on a theorem called the capacitance matrix theorem which was stated and proved in Buzbee et al. 6] The direct solutions using the capacitance matrix theorem employ the Fourier Toeplitz method in combination with LU decomposition [19], the Cholesky decomposition [6] or the conjugate gradient [18] technique. The Fourier Toeplitz method requires O(N log N) time and the LU decomposition, Cholesky factorization or the conjugate gradient require O(n 3 ) O(N p N ) Thus, making the overall complexity O(N p N ) In this ....

....section 6. 2 Low level Vision Problems and Previous Work There are many problems in low level vision which when formulated as variational principles lead to solving one or more discretized Poisson equations. Some of these problems are: the surface reconstruction [3, 23, 26, 4] shape from shading [12, 19], lightness [11] and optical flow [13, 19] In this paper, we will very briefly discuss the formulation of the first two of these problems as variational principles and without dwelling much on them, will point out the structure of the matrices that appear in the linear system which needs to be ....

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T. Simchony, R. Chellappa, and M. Shao. "Direct analytical methods for solving Poisson equations in computer vision problems,". IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(5), May 1990.

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Simchony, T., Chellappa, R., Shao, M.: Direct analytical methods for solving poisson equations in computer vision problems. IEEE Trans. Pattern Anal. Machine Intell. 12 (1990) 435--446

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T. Simchony, R. Chellappa, and M. Shao. Direct analytical methods for solving Poisson equations in computer vision problems. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12:435--445, 1990.

No context found.

T. Simchony, R. Chellappa, and M. Shao. Direct analytical methods for solving Poisson equations in computer vision problems. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12:435--445, 1990.

No context found.

T. Symchony, R. Chellappa, and M. Shao, "Direct Analytical Methods for Solving Poisson Equations in Computer Vision Problems," IEEE Trans. on PAMI 12, pp. 435--446, May 1990.

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T. Simchony, R. Chellappa, and M. Shao, Direct analytical methods for solving Poisson equations in computer vision problems, IEEE Transactions Pattern Analysis and Machine Intelligence, Vol. 12, No. 5, pp. 435-446, 1990.

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