V. Caselles, J. M. Morel, G. Sapiro, and A. Tannenbaum, Editors, "Special Issue on Partial Differential Equations and Geometry-Driven Diffusion in Image Processing and Analysis," IEEE Trans. Image Processing 7, March 1998.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....highly desirable. The scaling of the image is represented by a solution of a nonlinear PDE for which the processed image gives an initial condition. In the last decade such models have been suggested and studied, and in general they are based on degenerate diffusion equations, see for instance [2, 8 11, 15 17, 19]. The multiscale approach has been axiomatized, i.e. derived from first principles , in [1] There, it was proved in a rigorous way that the majority of image processing operations can be viewed as solutions of second order degenerate parabolic partial differential equation. In some sense, it ....

Caselles, V., Morel, J.-M., Sapiro, G., Tannenbaum, A. (eds.): Special issue on partial differential equations and geometry-driven diffusion in image processing and analysis. IEEE Transactions on Image Processing 7(3) (1998)

....minutes to a few hours, depending on the pattern and parameters chosen. All the volumes used contain roughly 64 3 voxels. 4.1. Diffusion of images on surfaces The use of partial differential equations for image enhancement has become one of the most active research areas in image processing [12]. In particular, diffusion VARIATIONAL PROBLEMS AND PDE S ON IMPLICIT SURFACES 11 equations are commonly used for image regularization, denoising, and multiscale representations (representing the image simultaneously at several scales or levels of resolution) This started with the works in [34, ....

V. Caselles, J. M. Morel, G. Sapiro, and A. Tannenbaum, Editors, "Special Issue on Partial Differential Equations and Geometry-Driven Diffusion in Image Processing and Analysis," IEEE Trans. Image Processing 7, March 1998.

....approach. As a result, variational modeling has contributed much to the fields of image processing and computer vision during the last years. Parallel to this development, the application of partial differential equations (PDE s) to image processing has been a very active field of research [18, 39, 9]. Research problems that motivated corresponding work include nonlinear extensions to the linear scale space paradigm [1] invariant scale spaces [31, 32] active contours and surfaces [25, 8] and sound mathematical models for image enhancement through local backward diffusion. For a review, we ....

V. Caselles, J.M. Morel, G. Sapiro, and A. Tannenbaum, editors. IEEE Trans. Image Proc.: Special Issue on Partial Differential Equations and Geometry--Driven Diffusion in Image Processing, 7(3), 1998.

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V. Caselles, J. M. Morel, G. Sapiro, and A. Tannenbaum, Editors, "Special Issue on Partial Differential Equations and Geometry-Driven Diffusion in Image Processing and Analysis," IEEE Trans. Image Processing 7, March 1998.

....use of straightforward Cartesian numerics reduces the overall algorithmic complexity, improving accuracy and simplifying the implementation. 4.3. 1 Diffusion of scalar images on surfaces The use of PDE s for image enhancement has become one of the most active research areas in image processing [17]. In particular, diffusion equations are commonly used for image regularization, denoising, and multiscale representations (representing the image simultaneously at several scales or levels of resolution) This started with the works in [51, 102] where the authors suggested the use of the linear ....

V. Caselles, J. M. Morel, G. Sapiro, and A. Tannenbaum, Editors, "Special Issue on Partial Differential Equations and Geometry-Driven Diffusion in Image Processing and Analysis," IEEE Trans. Image Processing 7, March 1998.

....integral, which is associated with the linear heat equation (x, t) ot Extensive research is also being done on the direct derivation of evolution equations which are not necessarily obtained from the energy approaches. The attributes of PDE s in image processing are discussed for example in [22, 161]. In the pioneering paper [2] the authors prove that a few basic image processing principles naturally lead to PDE s. Note that when considering PDE s for image processing and numerical implementations, we are dealing with derivatives of non smooth signals, and the right framework must be ....

.... [104] Weickert s book on anisotropic diffusion in image processing [189] Kimmel s lecture notes [97] Sapiro s recent book [161] Toga s book on brain warping that includes a number of PDE s based algorithms [179] and the special March 1998 issue of the IEEE Transactions on Image Processing [22]. The interested reader will find in these publications some fascinating contributions in the area of PDE s in image processing and computer vision, much beyond the few introductory examples provided below. 4.1 The Total Variation Model for Image Denoising As mentioned above, the use of PDE s ....

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Caselies, V., Morel, J.M., Sapiro, G. and Tannenbaum, A., Editors, Special Issue on Partial Differential Equations and Geometry-Driven Diffusion in Image Processing and Analysis, IEEE Trans. Image Processing 7, March 1998.

.... is selected as the vector that minimizes the sum of angles between every pair in U ) When considering u(x) IR 2 # IR as an image defined in the continuous plane, there is a close relationship between median filtering, inf sup morphological operations, and partial differential equations [2, 4], see Section 2. The goal of this paper is to extend these theoretical results to the vectorial case, u(x) IR 2 #IR N This is presented in Section 3 . Other PDE s approaches for vector valued images can be found for example in [7, 11, 17] 2. Scalar Case The background material in this ....

V. Caselles, J.M. Morel, G. Sapiro, and A. Tannenbaum (Eds.), "Special issue on partial differential equations and geometrydriven diffusion in image processing and analysis," IEEE Trans. Image Processing, Vol. 7, pp. 269--273, 1998.

....reduces the overall algorithmic complexity, improving accuracy and simplifying the implementation. Solving PDE s on Implicit Surfaces 62 4.3. 1 Diffusion of scalar images on surfaces The use of PDE s for image enhancement has become one of the most active research areas in image processing [17]. In particular, diffusion equations are commonly used for image regularization, denoising, and multiscale representations (representing the image simultaneously at several scales or levels of resolution) This started with the works in [51, 102] where the authors suggested the use of the linear ....

V. Caselles, J. M. Morel, G. Sapiro, and A. Tannenbaum, Editors, "Special Issue on Partial Differential Equations and Geometry-Driven Diffusion in Image Processing and Analysis," IEEE Trans. Image Processing 7, March 1998.

....the use of straightforward Cartesian numerics reduces the overall algorithmic complexity, improving accuracy and simplifying the implementation. 3. 1 Diffusion of scalar images on surfaces The use of PDE s for image enhancement has become one of the most active research areas in image processing [6]. In particular, diffusion equations are commonly used for image regularization, 4 denoising, and multiscale representations (representing the image simultaneously at several scales or levels of resolution) This started with the works in [19, 39] where the authors suggested the use of the ....

V. Caselles, J. M. Morel, G. Sapiro, and A. Tannenbaum, Editors, "Special Issue on Partial Differential Equations and Geometry-Driven Diffusion in Image Processing and Analysis, " IEEE Trans. Image Processing 7, March 1998.

.... median is selected as the vector that minimizes the sum of angles between every pair in U ) When considering u(x) IR 2 IR as an image defined in the continuous plane, there is a close relationship between median filtering, inf sup morphological operations, and partial differential equations [2, 4], see Section 2. The goal of this paper is to extend these theoretical results to the vectorial case, u(x) IR 2 IR N . This is presented in Section 3. Other PDE s approaches for vector valued images can be found for example in [7, 11, 17] 2 Scalar case The background material in this ....

V. Caselles, J. M. Morel, G. Sapiro, and A. Tannenbaum, Editors, "Special Issue on Partial Differential Equations and Geometry-Driven Diffusion in Image Processing and Analysis," IEEE Trans. Image Processing 7, March 1998.

.... (the median is selected as the vector that minimizes the sum of angles between every pair in U) When considering u(x) IR 2 IR as an image defined in the continuous plane, there is a close relationship between median filtering, morphological operations, and partial differential equations [2, 5], see Section 2. The goal of this paper is to extend these results to the vectorial case, u(x) IR 2 IR N . This is presented in Section 3. 2. SCALAR CASE The background material in this section is adapted from [5] We refer the interested reader to these notes and references therein for ....

V. Caselles, J. M. Morel, G. Sapiro, and A. Tannenbaum, Editors, "Special Issue on Partial Differential Equations and Geometry-Driven Diffusion in Image Processing and Analysis," IEEE Trans. Image Processing 7, March 1998.

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