G. J. Yang T. S. Huang and G. Y. Tang. Fast two-dimensional median filtering algorithm. IEEE Transactions on Acoustics, Speech, and Signal Processing, 1979.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... to improve the consistency of the divergence estimates, we apply temporal and spatial median filters to the individual divergence values (process 3 in Figure 1) 5 Simple Robust Filters Median filtering performed on dense two dimensional data can use fast running histogram methods such as in [19] if the dynamic range of the data and desired quantization resolution of the median value can be specified. The algorithm described in [19] was intended for finding the true median and reduces an O(nm) complexity algorithm to approximately O(n) per pixel for an filtering window, where . It can, ....

....(process 3 in Figure 1) 5 Simple Robust Filters Median filtering performed on dense two dimensional data can use fast running histogram methods such as in [19] if the dynamic range of the data and desired quantization resolution of the median value can be specified. The algorithm described in [19] was intended for finding the true median and reduces an O(nm) complexity algorithm to approximately O(n) per pixel for an filtering window, where . It can, however, be generalized to the separable median [26] which approximates a two dimensional true median filter by the successive application ....

T. Huang, G. Yang, G. Tang, A Fast Two-dimensional Median Filtering Algorithm", IEEE Transactions on Acoustics, Speech, and Signal Processing, 1:13-18, Feb 1979.

....or have iterative behavior is still difficult. These types of filters have not been implemented on the graphics hardware yet, but there are already various software implementations available. We focus on three specific types of non linear filters. The first is the Median operator. Huang et al. [11] presents one of the fastest Median filtering algorithms. It is based on storing and updating the gray level histogram of pixels within the operator mask. From one filtered pixel to the next, the mn operator mask moves only one column. It means, only n values have to be removed and n added to the ....

....within the operator mask. There has been a lot of research involved in efficient median filter implementation. We have already discussed software implementations in section 2. Due to graphics hardware limitations our implementation is not based on the histogram based approach by Huang et al. [11]. Our method is based on traversing all voxels within the operator mask, comparing the estimated pivot value to all voxel values within the operator mask. For the 555 filter size, the number of contributing voxels N is equal to 125. Because of 12 bit precision we operate on a range of [0. 4095] ....

T. Huang, G. Yang, and G. Tang. A fast two-dimensional median filtering algorithm. IEEE Transactions on Acoustics, Speech, and Signal Processing, 27:13--18, 1979.

....type of response in many cases, and preserves edges while reducing impulse noise. Finally, the pseudomedian filter can be implemented by an algorithm that is theoretically of lower order than most algorithms for the median filter. The fast median filtering algorithm developed by Huang, et al. [5] is a very fast implementation of the median filter, however, and a similar implementation of the pseudomedian filter would not be as efficient. Other algorithms for the median filter are either similar in speed or noticeably slower than most implementations of the pseudomedian filter. Overview ....

....four filters studied, but it was initially developed as a more efficient substitute for the median filter. The theoretical order of the algorithm for computing the pseudomedian is indeed 77 lower than that of most algorithms for computing the median, but the fast median algorithm of Huang, et al. [5] appears to be faster than any pseudomedian implementation. Since a thorough study of the filter algorithms has not been performed, no specific conclusions can be drawn about the relative speeds of the filters. However, the differences in computation time for the various filters in this study may ....

Huang, T. S., G. J. Yang, and G. Y. Yang. "A fast two-dimensional median filtering algorithm." IEEE Trans Acoust Speech Signal Process, v. ASSP-27 n. 1 (1979), pp. 13-18.

....] nbhd (a, i, w, N) and nbhd (b, j, w, N) where nbhd (p, q, r, s) false otherwise true (p q) mod s r or (q p) mod s r A straightforward serial computation of MEDIAN2D takes O (N ) time. This is easily reduced to O (N WlogW) by using balanced search trees. Huang, Yang, and Tang [HUAN79] have developed an O (N W) algorithm for the case when the image values are in the range 0 through K 1 (i.e. there are K gray levels) Narendra [NARE81] has introduced a related filtering operation, separable median filter, that can be computed in O (N logW) serial time (The algorithm ....

T. S. Huang, G.Y. Yang, and G. Y. Tang, "A Fast Two dimensional Median Filtering Algorithm", IEEE Transaction on ASSP, Vol. ASSP-27, No. 1, February 1979, pp. 13-18.

.... robust estimatots employed in the MRBF learning algorithm gave lesser expected bias than classical estimators when a certain overlap occurred among different Gaussian components of the mixture [5] 3 Fast implementation of the learning algorithm A histogram based median implementation algorithm [8] was adapted in order to be applied for MRBF learning. The first data sample assigned to a unit becomes the starting point in finding the median. In the updating stage we take into consideration pairs of two data samples Xi and Xi i assigned to the same hidden unit. We build up the marginal ....

T. S. Huang, G. J. Yang, G. Y. Tang, "A fast two-dimensional median filtering algorithm," IEEE Trans. on Acoust., Speech and Sig. Proc., vol. ASSP-27, no. 1, pp. 13-18, 1979.

....needed for MMLVQ. MMLVQ needs the calculation of the median of data sets of ever increasing size, as can be seen from (5) This may pose severe computational problems for relatively large n. However, for integer valued data, a modification of the running median algorithm proposed by Huang et el. [15] can be devised to facilitate median calculations by exploiting the fact that the marginal median of the already assigned samples Xi(n) is known. Another definition of the multichannel median (based on R ordering principles) is the so called vector median. The vector median is the observation ....

HUANG T.S., YANG G.J. and TANG G.Y., "A fast two-dimensional median filtering algorithm," IEEE Trans. on Acoustics, Speech and Signal Processing 27, 13-18 (1979).

....assumptions, seven operations are expended for each LOMO diffusion iteration per pixel. Implementing the median filter in the standard sorting scheme, comparison operations are used for a width filter on one pixel. We have not accounted for more expeditious median filter schemes, as in [2] and [7]. Although the assumptions used in the complexity analysis may be argued, the difference between the costs is stark. For LOMO degrees above 10, the difference in the number of operations needed exceeds an order of magnitude. Clearly, it is advantageous computationally to use LOMO diffusion when ....

T. S. Huang, G. J. Yang, and G. Y. Tang, "A fast two-dimensional median filtering algorithm," IEEE Trans. Acoust., Speech, Signal Processing, vol. 27, pp. 13--18, Jan. 1981.

....d is o to oueffo line filtering alternatives m the presen ofhea tailed noise. In ft, it e sho t the mxim likelood ( estimate of a eonst iersed m ind endent Laplaci noise is obtned by the me of e av]able mples. Moreover, hat algodts exist for median filtering ofony or two dimemional sifls [5]. O estimator for Sin] which relies on the medi filter e h ex pressed as follows: where the me operator orders the samples withn e bracket, and selects the middle vflue, N = 2M 1 is the wind lh of the ning medi filter, d 1.5920 is a coection te tt satisfies f fz(x) dx = f fn(z) dz = 0.5, ....

T. S. Huang, G. J. Yang, and G. Y. Tang, "A fast two-dimensional median filtering algorithm," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-27, pp. 13-18, Jan. 1979.

....been written as , This formulation offers the small advantage that only two different types of dilation are needed instead of three. A completely different approach to the implementation of openings was provided by CHAUDHURI [1] who extended the work of HUANG et al. [3]. Both authors based their algorithms on a local histogram computed in a sliding window. Contrary to other methods the computation time of histogram based algorithms does not depend on the size of the structuring element, but it depends on the image content. In [11] VAN HERCK proposed a 1 D ....

T. Huang, G. Yang, and G. Tang. A fast two-dimensional median filtering algorithm. IEEE Transactions on Acoustics, Speech and Signal Processing, 27(1):13--18, February 1979.

....complex structures such as streaks, corners, etc. In this section, a simple but more effective directional filtering scheme is proposed to deal with the more complex structure. Within a small analysis window of an image, the local structure can often be characterized by a bimodal distribution [16, 17]. In their work of doubling the sample density of an image in both the horizontal and vertical directions, Algazi et al. 17] used a 3 Theta 3 analysis window to analyze the spatial structure of interest which is characterized by a bimodal distribution. They obtained good perceived quality of ....

T.S. Huang and G.Y. Tang, "A fast two dimensional median filtering algorithm," IEEE Trans. ASSP., 27:13-18, 1979.

....small portion of current cameras is equipped with a cooling system to reduce the amount of dark current noise. Given no additional information about the properties of this noise, the only possibility to remove it is to apply general noise detection and removal techniques such as median filtering [4]. However these techniques only detect that a pixel is noisy and try to infer the true pixel value from the values of neighboring pixels. As each sensor element on a CCD chip generates a characteristic amount of dark current [7] it is possible to capture this information in a separate ....

T. Huang, G. Yang, and G. Tang. A fast twodimensional median filtering algorithm. IEEE Transactions on Acoustics, Speech, and Signal Processing, 27(1):13--18, February 1979.

....nearby pixels are mutually less correlated than the signal values, so noise is averaged away while signal is preserved. The assumption of slow spatial variations fails at edges, which are consequently blurred by low pass filtering. Many efforts have been devoted to reducing this undesired effect [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 17]. How can Supported by NSF grant IRI 9506064 and DoD grants DAAH0494 G 0284 and DAAH04 96 1 0007, and by a gift from the Charles Lee Powell foundation. we prevent averaging across edges, while still averaging within smooth regions Anisotropic diffusion [12, 14] is a popular answer: local image ....

....of our method, in which a pixel is either counted or it is not. Neighbors in [1] are strictly adjacent pixels, so iteration is necessary. A common technique for preserving edges during smoothing is to compute the median in the filter s support, rather than the mean. Examples of this approach are [6, 9], and an important variation [3] that uses K means instead of medians to achieve greater robustness. More related to our approach are weighting schemes that essentially average values within a sliding window, but change the weights according to local differential [4, 15] or statistical [10, 7] ....

T. S. Huang, G. J. Yang, and G. Y. Tang. A fast two-dimensional median filtering algorithm. IEEE Trans., ASSP-27(1):13--18, 1979.

....is replaced by the mean of a neighborhood. This does remove noise, but also blurs details. Another important and well studied algorithm, is median filtering. In median filtering the current pixel value is replaced with the median value of a local neighborhood, see [ Tukey 1976, Narendra 1981, Huang et al. 1979, Gallagher and Wise 1981 ] This is noticeably better with respect to preserving detail, when the detail is larger than the median window. It still, however, blurs fine detail, e.g. corners, thin lines, rapidly varying texture. To make these statistical algorithms more robust and still ....

T.S. Huang, G.J. Yang and G.Y. Tang. A fast two-dimensional median filtering algorithm. IEEE Trans. on Acoustics, Speech and Signal Processing, ASSP-27(1):13--18, February 1979.

.... For example, in morphological signal processing, dilation and erosion operations involve running maximum and minimum calculations, respectively [1] The problem of running max min calculation is a subset of the general task of determining the ranked order of a sequence across a sliding data window [2, 3, 4, 5]. It should be recognized, however, that running max min calculation is potentially much simpler than the general ranked order task because i) only one output needs to be calculated per sample time and ii) the maximum or minimum value appears at either end of a running sorted list. Existing ....

T.S. Huang, G.J. Yang, and G.Y. Tang, "A fast two-dimensional median filtering algorithm," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-27, no. 1, pp. 13-18, February 1979.

....training in Median RBF based on data sample histograms When the data samples are distributed in a discrete range of values we can find solutions for a fast MRBF training stage. A fast implementation for the median algorithm based on histogram updating, used in image filtering, was proposed in [34]. The first data sample assigned to a unit becomes the starting point in finding the median. In the updating stage we take into consideration pairs of data samples X i and X i 1 , assigned to the same unit according to either (10) or (14) We build up the marginal histogram associated with each ....

T. S. Huang, G. J. Yang, G. Y. Tang, "A fast two-dimensional median filtering algorithm, " IEEE Trans. on Acoustics, Speech and Signal Processing, vol. 27, no. 1, pp 13-18, 1979.

.... algorithm requires calculating the running maximum of the absolute value of the input signal to selectively update one filter coefficient at each time instant [2] Running max min calculation is a subset of the general task of determining the ranked order of a sequence across a sliding data window [3, 4, 5, 6, 7, 8]. It should be recognized, however, that running max min calculation is potentially much simpler than the general ranked order task because i) only one output needs to be calculated per sample time, and ii) the maximum or minimum value appears at either end of a running sorted list. Existing ....

T.S. Huang, G.J. Yang, and G.Y. Tang, "A fast two-dimensional median filtering algorithm," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-27, no. 1, pp. 13-18, February 1979.

.... of support [Cheung and Zeng, 1995] Zeng and Venetsanopoulos use the median filter with local image features for their interpolation [Zeng and Venetsanopoulos, 1992] The median filter is known to remove outliers in the local distribution of pixels and to preserve certain types of image structure [Huang and Tang, 1979]. They attempt to exploit this property of the median filter to 41 produce more accurate interpolation results in edge regions. Fathima and Yegnanarayana have used a maximum entropy approach to interpolation. They specifically address the problem of recovery of the missing samples of a signal ....

Huang, T.S. and Tang, G.Y. (1979), "A Fast Two Dimensional Median Filtering Algorithm," IEEE Trans. Acoustics, Speech, Sig. Process., Vol. 27, pp. 13-18.

....computed in sequence by columns (or rows) starting from 1 In the rest of this summary we omit the mod operation which affects only processors with index n Gamma 1. the first pixel and updating the values for consecutive pixels according to the pixels that come out and enter into the window [4]. Processing can be straight parallelized with a maximum efficiency whenever the pixels of the windows can be directly accessed. This is true for the case of pixels I [ 0; i Theta ] to I [ N; i 1) Theta Gamma w] for all processors P i (0 i n) when ( w Gamma 1) and the architecture ....

T. S. Huang, G. Y. Yang, and G. Y. Tang. A fast two-dimensional median filtering algorithm. IEEE Transactions on Acoustic, Speech, and Signal Processing, 27(1):13--18, February 1979.

.... true by virtue of the fact that, given n numbers, their median is the constant that minimizes the sum of absolute errors between itself and all n given numbers (e.g. cf. 9] Again, computational savings may be realized by using an efficient running median algorithm, e.g. the one of Huang et al. [38] based on histogram updates, for computing all required constant sub regressions under a least absolute error measure in between level switches. Other types of locally constrained (e.g. piecewise convex) regression problems can be handled in the June 9, 1997 DRAFT 21 same spirit. VII. ....

T.S. Huang, G.J. Yang, and G.Y. Tang, "A fast two-dimensional median filtering algorithm", IEEE Trans. ASSP, vol. ASSP-27, no. 1, pp. 13--18, 1979.

....of the neighborhood to the center pixel. This is repeated for all pixels in the image, with the effect being a reduction in the number of outliers while preserving edges and non noisy portions of the image (Figure 7) An especially fast version of the median filtering algorithm can be found in [32]. The function FM for median filtering can be described as: FM (X m;n ) Median(Nm;n ) 15) B. Applicability of Image Processing Production of tactually perceivable tactile images bears some similarity to the challenges of the field of computer vision. The aim of computer vision is ....

T.S. Huang, G.J. Yang, and G.Y. Tang. A fast two dimensional median filtering algorithm. Proceedings of the IEEE Conference on Pattern Recognition and Image Processing, 1978.

....first with low level algorithms. For such algorithms it is the synchronous mode that is usually used. But the performances can be improved, even for low level algorithms, through the use of the MIMD operating mode. A very good example is Huang s algorithm for the computation of the median filter [10]. The advantages of MIMD operating mode are much more obvious for high level algorithms, where the data to be processed, which represent some image features extracted by the low level algorithms, have an irregular nature, and are thus badly suited to be processed in SIMD mode. Nevertheless, ....

T.S. Huang, G.J. Yang, G.Y. Tang, "A fast two-dimensional median filtering algorithm," IEEE trans. Acoust., Speech and Signal Process., Vol. ASSP-27, N° 1, 1979, pp. 13-18.

....for MMLVQ. MMLVQ requires the calculation of the median of data sets of ever increasing size, as can be seen from (4) This may pose severe computational problems for relatively large n. However, for integer valued data, a modification of the running median algorithm proposed by Huang et al. [13] can be devised to facilitate greatly median calculations by exploiting the fact that the marginal median of the already assigned samples X i (n) is known. This algorithm leads to very large computational savings. It must be noted that, although MMLVQ employs the entire past data set for the ....

....does not influence the performance of the algorithm which always converges in a similar way. That is, the MSE achieved at the end of the learning phase or the number of the training sessions is not significantly affected. Furthermore, in cases where the running algorithm proposed by Huang et al. [13] is applicable (e.g. in image processing) each training session of the MMLVQ requires less computation time than the one of LBG LVQ because the learning procedure of MMLVQ does not involve any floating point arithmetic. This is not the case with LBG and linear LVQ that require floating point ....

T.S. Huang, G.J. Yang, and G.Y. Tang, "A fast two-dimensional median filtering algorithm," IEEE Trans. on Acoustics, Speech and Signal Processing, vol. ASSP-27, no. 1, pp. 13--18, 1979.

....takes O(n 2 K log K) time, since each pixel needs O(K log K) time for sorting and O(K) time for computing the weighted sum or weighted maximum. Many researchers have proposed fast algorithms for a very special case, the median filter, which needs only one specific value in the neighborhood [24, 25, 26, 27, 28]. Even combining the moving window technique and a balanced search tree data structure, we can only reduce the time to O(n 2 K) since we still have to take the weighted sum or maximum of K elements for every pixel. On an n Theta n mesh connected computer with a pixel per PE, we are able to ....

T. S. Huang, G. T. Yang, and G. Y. Tang. A fast two-dimensional median filtering algorithm. IEEE Transactions on Acoustics, Speech, and Signal Processing, 27:13--18, February 1979.

....The median filtering algorithm replaces each pixel by the median value of a window (w Theta w) containing neighbor pixels. The median values can be computed in sequence by columns (or rows) The values for consecutive pixels are updated according to the pixels that come in and out of the window [4]. Processing can be straight parallelized with a maximum efficiency whenever the pixels of the windows can be directly accessed. This is true for the case of pixels I[0; i Theta ] to I [N; i 1) Theta Gamma w] for all processors P i (0 i n) when ( w Gamma 1) and the architecture ....

T. S. Huang, G. Y. Yang, and G. Y. Tang. A fast twodimensional median filtering algorithm. IEEE Transactions on Acoustic, Speech, and Signal Processing, 27(1):13--18, February 1979.

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G. J. Yang T. S. Huang and G. Y. Tang. Fast two-dimensional median filtering algorithm. IEEE Transactions on Acoustics, Speech, and Signal Processing, 1979.

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T. S. Huang, G. J. Yang, and G. Y. Tang, "Fast two-dimensional median filtering algorithm", IEEE Transactions on Acoustics, Speech, and Signal Processing, 1 (1979), pp. 13-201318.

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G. J. Y. T. S. Huang and G. Y. Tang, "Fast two-dimensional median filtering algorithm," IEEE Transactions on Acoustics, Speech, and Signal Processing, 1979.

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T.S. Huang, G.J. Yang, and G.Y. Tang, "A Fast Two-Dimensional Median Filtering Algoritm," IEEE Trans. Acoustics Speech Signal Proc., vol. ASSP-27, pp. 13-18, Feb. 1979.

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T. Huang, G. Yang, and G. Tang. A fast two-dimensional median filtering algorithm. IEEE Transactions on Acoustics, Speech and Signal Processing, 27(1):13--18, February 1979.

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T.S.Huang, G. J. Yang, and G. Y. Tang. A fast two-dimensional median filtering algorithm. IEEE transactions on acoustics, speech and signal processing, 27(1), February 1979.

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T. Huang, G. Yang, and G. Tang. A fast two-dimensional median filtering algorithm. IEEE Transactions on Acoustics, Speech, and Signal Processing, 1:13--18, February 1979.

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T.S.Huang, G. J. Yang, and G. Y. Tang. A fast two-dimensional median filtering algorithm. IEEE transactions on acoustics, speech and signal processing, 27(1), February 1979.

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T. Huang, G. Yang, and G. Tang. A fast two-dimensional median filtering algorithm. IEEE Transactions on Acoustics, Speech, and Signal Processing, 27(1):13--18, 1979.

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T. S. Huang, G. T. Yang, Q. Y. Tang. A Fast TwoDimensional Median Filtering Algorithm, in IEEE Trans. Acoustics, Speech, and Signal Processing, ASSP-27(1), 1318, 1979.

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T.S.Huang, G. J. Yang, and G. Y. Tang. A fast two-dimensional median filtering algorithm. IEEE transactions on acoustics, speech and signal processing, 27(1), February 1979.

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Huang, T.S., G.J. Yang, and G.Y. Tang, A Fast Two-Dimensional Median Filtering Algorithm. IEEE Transactions on Acoustics, Speech, and Signal Processing, 1979. ASSP-27: p. 13-18.

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T.S. Huang, G.J. Yang and G.Y. Tang. A fast two-dimensional median filtering algorithm. IEEE Trans. on Acoustics, Speech and Signal Processing, ASSP-27(1):13-18, February 1979.

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T. S. Huang, G. J. Yang, and G. Y. Tang, "A fast two-dimensional median filtering algorithm," IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. ASSP-27, no. 1, pp. 13--18, 1979.

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