H.E. Knutsson, R. Wilson, and G.H. Granlund, "Anisotropic nonstationary image estimation and its applications part I: Restoration of noisy images," Trans. Comm., vol. 31, pp. 388--397, 1983.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....systems for image processing and analysis. 11 Chapter 2 Tools for Image Analysis Steerable Filters 2. 1 Introduction Oriented filters are used in many vision and image processing tasks, such as texture analysis, edge detection, image data compression, motion analysis, and image enhancement [70, 27, 20, 43, 89, 33, 45, 4, 38, 57, 60]. In many of these tasks, it is necessary to apply filters of arbitrary orientation under adaptivecontrol, and to examine the filter output as a function of both orientation and phase. We will discuss techniques that allow the synthesis of a filter at arbitrary orientation and phase, and develop ....

....consider the 2 dimensional, circularly symmetric Gaussian function, G, written in Cartesian coordinates, x and y: G(x# y) e ; x 2 y 2 ) # (2:1) where scaling and normalization constants have been set to 1 for convenience. The directional derivative operator is steerable as is well known [25, 31, 43, 54, 60, 61, 62, 63, 73, 85]. Let us write the nth derivative of a Gaussian in the x direction as G n . Let ( represent the rotation operator, such that, for any function f(x# y) f (x# y)isf(x# y) rotated through an angle about the origin. The first x derivative of a Gaussian, G 0 ffi 1 ,is G 0 ffi 1 = ....

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H. Knutsson, R. Wilson, and G. H. Granlund. Anisotropic nonstationary image estimation and its applications: Part 1 -- Restoration of noisy images. IEEE Trans. Comm., 31(3):388--397, 1983.

....of the separation ability of the vector used. Segmentation is a special case of classification in which the classes are natural objects. The features are used in enhancement applications as feedback information to remove noise, while in coding applications they are used as control information [9]. Now to the question of how to extract features connected with special shapes. The answers given are many. Many of the methods are based upon template matchings of the picture using target patterns. However, there are also methods projecting the local neighbourhood onto basis functions connected ....

H.E. Knutsson, R. Wilson and G.H. Granlund: "Anisotropic Nonstationary Image Estimation and It's Applications: Part I--Restoration of Noisy Images." IEEE Transactions on Communications, Vol. Com--31, No.3, March 1983.

....image into a set of coefficients that allow discrimination between image information and noise. These coefficients can be modified according to the likelihood that they represent signal rather than noise. The cleaned image can then be constructed by inverting the transform. see, for example, [37, 23, 6]) Natural images tend to contain locally oriented structures such as lines, edges, and textures, while noise tends to be isotropic (i.e. without preferred orientation) Therefore an image decomposition based on oriented filters should help one to determine whether a given image structure is due ....

.... edges, and textures, while noise tends to be isotropic (i.e. without preferred orientation) Therefore an image decomposition based on oriented filters should help one to determine whether a given image structure is due to image or noise, and should allow one to enhance the image quality (cf. [23]) For these reasons, the steerable pyramid representation described in the previous section is well suited for image enhancement. Shiftability in orientation and space allow all orientations and positions to be treated uniformly. The multi scale nature of the representation allows the processing ....

H. Knutsson, R. Wilson, and G. H. Granlund. Anisotropic nonstationary image estimation and its applications: Part 1 -- Restoration of noisy images. IEEE Trans. Comm., 31(3):388--397, 1983.

....the 2 dimensional, circularly symmetric Gaussian function, G, written in Cartesian coordinates, x and y: G(x; y) e Gamma(x 2 y 2 ) 1) where scaling and normalization constants have been set to 1 for convenience. The directional derivative operator is steerable as is well known [8, 12, 16, 18, 21, 22, 23, 24, 27, 34]. Let us write the nth derivative of a Gaussian in the x direction as G n . Let ( represent the rotation operator, such that, for any function f(x; y) f (x; y) is f(x; y) rotated through an angle about the origin. The first x derivative of a Gaussian, G 0 ffi 1 , is G 0 ffi ....

....because each one is a polynomial (the Hermite polynomials [32] times a radially symmetric window function. Fig. 3 shows a general architecture for using steerable filters. cf. Koenderink and van Doorn [22, 23, 24] who used such an architecture with derivatives of Gaussians, and Knutsson et al. [21] who used it with related filters. The front end consists of a bank of permanent, dedicated basis filters, which always convolve the image as it comes in; their outputs are multiplied by a set of gain masks, which apply the appropriate interpolation functions at each position and time. The final ....

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H. Knutsson, R. Wilson, and G. H. Granlund. Anisotropic nonstationary image estimation and its applications: Part 1 -- Restoration of noisy images. IEEE Trans. Comm., 31(3):388--397, 1983.

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Knutsson H, Wilson R, Granlund GH. Anisotropic non-stationary image estimation and its applications---part I: restoration of noisy images. IEEE Trans Comm 1983;31:388--397.

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H.E. Knutsson, R. Wilson, and G.H. Granlund, "Anisotropic nonstationary image estimation and its applications part I: Restoration of noisy images," Trans. Comm., vol. 31, pp. 388--397, 1983.

No context found.

H. Knutsson, R. Wilson, and G.H. Granlund. Anisotropic non-stationary image estimation and its applications --- Part I: Restoration of noisy images. IEEE Transactions on Communications, 31(3):388--397, March 1983.

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