S. Acton. Multigrid anisotropic diffusion. IEEE IP, 7(3):280--291, Mar. 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....thereby propagating information between coarse and fine scales. Multigrid methods have been primarily used for solving partial differential equations [21] but more recently they have been applied to a variety of imaging problems such as image analysis [22] 23] and anisotropic diffusion [24]. Perhaps surprisingly, multigrid algorithms have not been widely applied in tomography problems. In earlier work, Bouman and Sauer [25] used multigrid algorithms to solve the nonquadratic optimization problems resulting from projection tomography applications such as computed tomography (CT) ....

S. T. Acton, "Multigrid anisotropic diffusion," IEEE Trans. Image Processing, vol. 7, pp. 280--291, Mar. 1998.

.... in various image processing problems, for example, lightness computation [31] shape from shading [31] optical flow estimation [31] 32] 33] 34] adaptive smoothing of signals [35] multispectral MRI image analysis [36] image matching [37] image restoration [38] and anisotropic diffusion [39]. More recently, multigrid algorithms have been used to solve image reconstruction problems. Bouman and Sauer showed that nonlinear multigrid algorithms could be applied to inversion of Bayesian tomography problems [40] This work used nonlinear multigrid techniques to compute maximum a ....

S. T. Acton, "Multigrid anisotropic diffusion," IEEE Trans. on Image Processing, vol. 7, no. 3, pp. 280--291, March 1998.

....linear solver in each timestep uses on the fly matrix multiplication based on efficient grid traversals. Let us mention that this approach benefits from general and efficient multilevel data post processing methodology [16, 19] and is related to the multilevel methods discussed in [1, 25]. Finally, as a to our knowledge new area of application we will present a scale space method in vector field visualization. Flow visualization is an important task in scientific visualization. Simply drawing vector plots at nodes of some overlayed regular grid in general produces visual ....

S. T. Acton. Multigrid anisotropic diffusion. IEEE Trans. Image Proc., 7:280--291, 1998.

....popular example of a partial differential equation used in image processing is given by an anisotropic diffusion equation that we shall discuss in greater detail. Numerous 2 applications of the anisotropic diffusion equation have recently been reported, such as in image filtering and restoration [2, 3, 4]. The majority of considerations related to anisotropic diffusion equations can be traced back to a seminal contribution to the solution of such equations given in [5] Other PDEs, such as heat equations and wave equations have also been studied in the context of image processing. In our work we ....

....lens area are assigned value of 0. We begin with initialisation of the gradient vector and the diffusion tensors: Initialisation of gradient and anisotropy vector g = zeros(R,C,2) h = g ; Initialisation of diffusion tensor, each Lij = V V = eye(2) L = permute(V( ones(1,R) ones(1,C) [3 4 1 2]) memory allocation for the force tensor F 6 F = zeros(R,C,2,2) Next, we set three important parameters, the sampling time, t s , the time scale, t s , responsible for the speed of iterations, and the stiffness threshold, s (image gradient threshold parameter) sampling time and ....

[Article contains additional citation context not shown here]

S. T. Acton, "Multigrid anisotropic diffusion," IEEE Transactions on Image Processing, vol. 7, pp. 280--291, March 1998.

....of the combined segmentation process by applying it to several examples. The paper is concluded with a summary in Section 6. Related work. The work presented here has been influenced by several related approaches. Closest in terms of efficient PDE based regularization methods is the work of Acton [3] on multigrid versions for nonlinear diffusion filtering. They are, however not based on AOS schemes and they do not use methods with a reaction term. It is common to supplement watershed segmentations with tools for reducing the oversegmentation problem. An algorithm by Orphanoudakis et al. 4] ....

S.T. Acton, Multigrid anisotropic diffusion, IEEE Trans. Image Proc., Vol. 7, 280-- 291, 1998.

....due to the shape of the structuring element. For example, morphological filtering of a rectangular object with a circular structuring element leads to corner rounding. Scale spaces based on anisotropic diffusion [16] cannot guarantee the position nor causality of edges in the image. As shown in [1], anisotropic diffusion can produce false edges at increased scales, such as staircase artifacts. C. Scale Space Classification Given a scale space , with intensity at position and scale , we wish to track through scale. For fixed defines a one dimensional signal with independent variable , ....

S. T. Acton, "Multigrid anisotropic diffusion," IEEE Trans. Image Processing, vol. 7, pp. 280--291, Mar. 1998.

....process is invariant to translation and rotation. Also, the edge maps are causal new (false) edges are nol produced as scale is increased. At the conch, sion of the paper, comparative examples are given that demonstrate the salieut properties o[ the area operator based edge detectors. 1. INTRODUCTION We propose an approach Io edge detection based on arert operators. Area operators, such as area open and area cloxe, modily tin image by removing connected components within the image level sots that do not meet a prescribed miuimum area. Although arca open and a, ea close are ....

....area (scale) parameter and do not depend on structuring element shape. In this manner, the area operators avoid the associated problems of tinposing the structuring clement shape on a processed image. With standard morphology, the structuring clement shape can produce artifacts and leads to edge 1ocalizafion errors. Area opcralors have been utilized in general filtering for image enhancement and image rcconsn uction [61, 71. The fihcrs have the desirable property of connected invariancc connected components in lhe image level sets (that may correspond to image objccls) are ncvcr 2. ....

[Article contains additional citation context not shown here]

S.T. Acton, "Multigrid anisotropic diffusion," IEEE Trans. hnage Processirlg, vol. 7, pp, 280-291, 1998.

No context found.

S. Acton. Multigrid anisotropic diffusion. IEEE IP, 7(3):280--291, Mar. 1998.

No context found.

S Acton. Multigrid anisotropic diffusion. IEEE Trans. Im.Proc., 7:280--291, 1998.

No context found.

S. Acton, Multigrid anisotropic diffusion, IEEE Trans. Image Proc., Vol. 7, 280--291, 1998.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC