R H Bamberger and M J T Smith, "A filter bank for the directional decomposition of images: theory and design", IEEE Trans. Signal Proc., 40(4), pp 882-893, April 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....from the one dimensional case (e.g. regularity of the basis functions) The drawbacks are a partial treatment of the complexity inherent in two dimensional images, which goes well beyond horizontal and vertical directions. Non separable approaches [4] in particular using directional filter banks [1, 5], have been investigated, showing the potential of truly non separable methods. Such methods come at a price in terms of design and computational complexity. Some separable approaches have been made in [9] but not on discrete space. In the present paper, we wish to retain the simplicity of ....

R. H. Bamberger and M. J. T. Smith. A filter bank for the directional decomposition of images: Theory and design. IEEE Signal Proc., pages 882--893, April 1992.

....(1 D) wavelets along the horizontal and vertical direction. For this reason, this separable transform is good at isolating horizontal and vertical edges, but it is not adequate at treating more complex discontinuities. Non separable approaches [2] in particular using directional filter banks [3, 4], have been investigated, showing the potential of truly non separable methods. Such methods come at a price in terms of design and computational complexity. Some separable approached have been made in [5] but not on discrete spaces. In our work, we wish to retain the simplicity of the separable ....

R.H. Bamberger and M.J.T. Smith, "A filter bank for the directional decomposition of images: Theory and design," IEEE Trans. Signal Processing, pp. 882--893, April 1992.

....compromises the optimality of the DWT representation of nat ural images. Non separable multi dimensional filter banks have been used to obtain excellent directionality because they can partition the frequency domain optimally. Notable examples are Bamberger and Smith s directional filter bank [29] and the curvelet transforms of Donoho and Cands [30] 31] and Do and Vetterli [32] However, to avoid complicated, non separable filter design, Watson [5] and Burns [6] showed that filter banks with separable, analytic filters can also provide transforms with improved directionality. The DTWT of ....

R. H. Bamberger and M. J. T. Smith, "A filter bank for the directional decomposition of images: Theory and design," IEEE Transactions on Signal Processing, vol. 40, no. 4, pp. 882-893, Apr. 1992.

....and they have been used for image compression [1] However the tensor product of two real valued wavelet packets is always associated with four symmetric peaks in the frequency plane. It is therefore not possible to selectively localize a unique frequency. Directionally oriented filter banks [2] have been used for image compression and image analysis. However they do not allow an arbitrary partitioning of the Fourier plane. Steerable filters with arbitrary orientation have been designed in [3] However, these filters are significantly overcomplete: the number of coefficients is increased ....

....l] see Fig. 11) b(t) 0l,0] 0, l] 27) We choose r such that b O , the Fourier transform of b, is positive. An example of such b is the cubic spline C(x) x [01 2,1 2] x [01 2,1 2] x [01 2,1 2] x [01 2,1 2] 28) where x [01 2,1 2] is the characteristic function of [0 2 , 2 ]. C is compactly supported on [02, 2] as shown in Fig. 11. Since the Fourier transform of x [01 2,1 2] is sin(pj) pj, the Fourier transform of C is C O (j) S sin(pj) pj D 4 . The tail of C is rapidly decreasing to zero. Another choice for b is the Gaussian. In theory, b is not compactly ....

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R. H. Bamberger and M. J. T. Smith, A filter bank for the directional decomposition of images: theory and design, IEEE Trans. Signal Process. (Apr 1992), 882 -- 893.

....of one dimensional wavelets will be good at isolating the discontinuity across the edge, but will not see the smoothness along the edge. This disappointing behavior indicates that more powerful bases are needed in higher dimensions. In the filter bank literature, Bamberger and Smith [1] had proposed an effective filter bank for the directional decomposition of images. This directional filter bank (DFB) has the important property that it can be critically sampled while achieving perfect reconstruction. In order to obtain sparse image representations, where maximum information is ....

....between PDFB and the curvelet transform. Finally, Section 5 illustrates some numerical experiments on real images. 2. DIRECTIONAL FILTER BANKS The DFB realizes a division of 2 D spectrum into 2 wedgeshaped slices as shown in Fig. 1 using an n levels iterated treestructured filter banks [1]. The method is to use appropriately the quincunx filter bank (QFB) 3] together with modulations and rotations. Rotations in DFB are achieved by resampling matrices Ri (that is, matrices with determinant equal to 4 1, so they represent a rearrangement of the input samples) 4, 2 ( Fig. 1. ....

R.H. Barnberger and M. J. T. Smith, "A filter bank for the directional decomposition of images: Theory and design," IEEE Trans. Signal Proc., vol. 40, no. 4, pp. 88893, April 1992.

....by Simoncelli, et al. for the steerable pyramid decomposition and reconstruction [1] An outgrowth of the Laplacian pyramid [3] it decomposes an image into oriented, bandpass filtered components at different (binary) scales. It has useful shiftability properties in both translation and rotation [4]. 3 H 0 L 0 B 2 L 1 H 0 L 0 B 2 L 1 B 1 B 1 1 2 4 Preprocessing Postprocessing Decomposition Reconstruction Figure 1. Block diagram of the steerable pyramid transform for k=2. The decomposition reconstruction filter bank is iterated at node 4. The down and uparrows indicate binary ....

R.H. Bamberger and M. J. T. Smith, "A Filter Bank for the Directional Decomposition of Images: Theory and Design," IEEE Trans. SP-40(4):882-893, 1992.

.... wavelet transform [6] While most of these developments concentrated on one dimensional signals, and the multidimensional case was handled via the tensor product, some of the more recent efforts concentrated on the true multidimensional case, both from the filter bank and the wavelet aspects [7] [17] By true we mean that both nonseparable sampling and filtering are allowed. Although the true multidimensional approach suffers from some drawbacks such as higher computational complexity, it offers a few important advantages. For example, using nonseparable filters leads to more degrees of ....

R. Bamberger and M. Smith, "A filter bank for the directional decomposition of images: Theory and design," IEEE Trans. Signal Proc., vol. 40, pp. 882--893, April 1992.

....problems (enhancement, denoising) may also be approached successfully using elementary descriptors such as edges and textures. Image compression schemes using sub bands coders, oriented along the preferred texture orientation in the image, proved advantageous in terms of visual rendition [1, 2, 3, 4, 5, 6]. Velocity may be interpreted as orientation in spatio temporal domain, and motion compensated spatio temporal filters may be used succesfully for prediction, interpolation and smoothing [7] as well as for coding [8] Regardless of the specific descriptor of interest, most techniques start ....

R.H. Bamberger and M. Smith. A filter bank for the directional decomposition of images: Theory and design. IEEE Trans. Signal Processing, 40(4):882--893, April 1992.

....it should be possible to decompose s(nx ; nr ) into a set of subaperture images s ff (nx ; nr ) with non overlapping subapertures without having to increase the overall amount of data. Such a decomposition can be achieved with a perfect reconstructing, maximally decimated directional filterbank [4]. Figure 2a shows the geometry of the subbands. The 2 Theta 2 frequency cell is divided into a vertical and a horizontal hourglass shaped area. Each of these two areas can be further decomposed into an arbitrary number of wedge shaped directional subbands. The frequency support of s(nx ; nr ) ....

....the mapped window b( Delta) in (11) the wedge shaped area between the two dotted straight lines in Fig. 2a) We consider here only directional filterbanks with a power of 2 directional subbands in each hourglass shaped area. They can be realized either as a binary tree of two channel filterbanks [4] or in a parallel form [5] The computation of an arbitrary subband in the parallel form is shown in 2b) The 2 D directional filters H ff (kx ; kr ) have to be designed such that the overall structure is invertible [4] Using [4] the H ff (kx ; kr ) can be designed such that the de x r k k ....

[Article contains additional citation context not shown here]

R. H. Bamberger and M. J. T. Smith, "A Filter Bank for the Directional Decomposition of Images: Theory and Design ", IEEE Transactions on Signal Processing, vol.40, no.4, pp.882-893, April 1992

....and they have been used for image compression [1] However the tensor product of two real valued wavelet packets is always associated with four symmetric peaks in the frequency plane. It is therefore not possible to selectively localize a unique frequency. Directionally oriented filter banks [2] have been used for image compression and image analysis. They do not allow however an arbitrary partitioning of the Fourier plane. In order to obtain a better angular resolution than the standard wavelet packets we expand the Fourier plane into windowed Fourier bases [3] The method results in an ....

R.H. Bamberger and M.J.T. Smith. A filter bank for the directional decomposition of images: theory and design. IEEE Trans. on Signal Processing, pages 882--893, April 1992.

....and they have been used for image compression [1] However the tensor product of two real valued wavelet packets is always associated with four symmetric peaks in the frequency plane. It is therefore not possible to selectively localize a unique frequency. Directionally oriented filter banks [2] have been used for image compression and image analysis. However they do not allow an arbitrary partitioning of the Fourier plane. Steerable filters with arbitrary orientation have been designed in [3] However, these filters are significantly overcomplete: the number of coefficients is increased ....

....are always associated with a real wavelet. As a result a wavelet packet expansion will require many more coefficients to describe a pattern with an arbitrary orientation; whereas the same pattern can be coded with a single brushlet coefficient. Directionally oriented filter banks (e.g. 11] [2]) have been used for image compression and image analysis. They do not allow however an arbitrary partitioning of the Fourier plane. Furthermore in our method the tiling can be adapted to the image content, as explained in the next section. D. Adaptive tiling of the Fourier plane As explained in ....

R.H. Bamberger and M.J.T. Smith. A filter bank for the directional decomposition of images: theory and design. IEEE Trans. on Signal Processing, pages 882--893, April 1992.

....x M r x r a x r a x r H (k ,k ) s (n ,n ) s(n ,n ) b) Figure 2: a) Directional subbands and frequency support of SAR data. b) One channel of directional filter bank in parallel form. Such a decomposition can be achieved with a perfect reconstructing, maximally decimated directional filter bank [4]. Figure 2a shows the geometry of the subbands. The 2 Theta 2 frequency cell is divided into a vertical and a horizontal hourglass shaped area. Each of these two areas can be further decomposed into an arbitrary number of wedge shaped directional subbands. The frequency support of s(n x ; n r ....

....the mapped window w( Delta) in (12) the wedge shaped area between the two dotted straight lines in Fig. 2a. We consider here only directional filter banks with a power of 2 directional subbands in each hourglass shaped area. They can be realized either as a binary tree of two channel filter banks [4] or in a parallel form [5] The computation of an arbitrary subband in the parallel form is shown in Fig. 2b. The 2 D directional filters H ff (k x ; k r ) have to be designed such that the overall structure is invertible [4] Using [4] the H ff (k x ; k r ) can be designed such that the ....

[Article contains additional citation context not shown here]

R. H. Bamberger and M. J. T. Smith, "A Filter Bank for the Directional Decomposition of Images: Theory and Design", IEEE Transactions on Signal Processing, vol.40, no.4, pp.882-893, April 1992

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R H Bamberger and M J T Smith, "A filter bank for the directional decomposition of images: theory and design", IEEE Trans. Signal Proc., 40(4), pp 882-893, April 1992.

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R.H. Bamberger and M.J.T. Smith. A filter bank for the directional decomposition of images: Theory and design. IEEE Trans. Signal Processing, pages 882--893, April 1992.

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R. H. Bamberger and M. J. T. Smith, "A filter bank for the directional decomposition of images: Theory and design," IEEE Trans. Signal Processing, pp. 882--893, Apr. 1992.

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R. H. Bamberger and M. J. T. Smith. A filter bank for the directional decomposition of images: Theory and design. IEEE Signal Proc., pages 882--893, April 1992.

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R. H. Bamberger and M. J. T. Smith. A filter bank for the directional decomposition of images: Theory and design. IEEE Signal Proc., pages 882--893, April 1992.

No context found.

R.H. Bamberger and M.J.T. Smith, "A filter bank for the directional decomposition of images: Theory and design," IEEE Trans. Signal Processing, vol. 40., pp. 882-893, Apr. 1992.

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R. H. Bamberger and M. J. T. Smith, "A filter bank for the directionaldecomposition of images: Theory and design," IEEE Trans. Signal Processing, vol. 40, pp. 882--893, Apr. 1992.

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R.H. Bamberger and M. Smith. A filter bank for the directional decomposition of images: Theory and design. IEEE Trans. Signal Processing, 40(4):882--893, April 1992.

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R. H. Bamberger and M. J. T. Smith, "A filter bank for the directional decomposition of images: Theory and design," IEEE Transactions on Signal Processing, vol. 40, no. 4, pp. 882-- 893, Apr. 1992.

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