Showing papers on "Median filter published in 1987"

Morphological filters--Part II: Their relations to median, order-statistic, and stack filters

Abstract: This paper extends the theory of median, order-statistic (OS), and stack filters by using mathematical morphology to analyze them and by relating them to those morphological erosions, dilations, openings, closings, and open-closings that commute with thresholding. The max-min representation of OS filters is introduced by showing that any median or other OS filter is equal to a maximum of erosions (moving local minima) and also to a minimum of dilations (moving local maxima). Thus, OS filters can be computed by a closed formula that involves a max-min on prespecified sets of numbers and no sorting. Stack filters are established as the class of filters that are composed exactly of a finite number of max-min operations. The kernels of median, OS, and stack filters are collections of input signals that uniquely represent these filters due to their translation-invariance. The max-min functional definitions of these nonlinear iliters is shown to be equivalent to a maximum of erosions by minimal (with respect to a signal ordering) kernel elements, and also to a minimum of dilations by minimal kernel elements of dual filters. The representation of stack filters based on their minimal kernel elements is proven to be equivalent to their representation based on irreducible sum-of-products expressions of Boolean functions. It is also shown that median filtering (and its iterations) of any signal by convex 1-D windows is bounded below by openings and above by closings; a signal is a root (fixed point) of the median iff it is a root of both an opening and a closing; the open-closing and clos-opening yield median roots in one pass, suppress impulse noise similarly to the median, can discriminate between positive and negative noise impulses, and are computationally less complex than the median. Some similar results are obtained for 2-D median filtering.

A New Class of Detail-Preserving Filters for Image Processing

Abstract: A new class of median type filters for image processing is proposed. In the filters, linear FIR substructures are used in conjunction with the median operation. The root signals and noise attenuation properties of the FIR-median hybrid filters are analyzed and compared to representative edge preserving filtering operations. The concept of multilevel median operation is introduced to improve the detail preserving property of conventional median and the FIR-median hybrid filters. In the multilevel filters there exists a tradeoff between noise attenuation and detail preservation. The analysis and examples indicate that FIR-median hybrid filters preserve details better and are computationally much more efficient than the conventional median and the K-nearest neighbor averaging filters.

The Effect of Median Filtering on Edge Estimation and Detection

Abstract: In this paper we consider the effect of median prefiltering on the subsequent estimation and detection of edges in digital images. Where possible, a quantitative statistical comparison is made for a number of filters defined with two-dimensional geometries; in some cases one-dimensional analyses are required to illustrate certain points. Noise images prefiltered by median filters defined with a variety of windowing geometries are used to support the analysis, and it is found that median prefiltering improves the performance of both thresholding and zero-crossing based edge detectors.

Theoretical analysis of the max/Median filter

Abstract: Median filtering has been used successfully for extracting features from noisy one-dimensional signals; however, the extension of the one-dimensional case to higher dimensions has not always yielded satisfactory results. Although noise suppression is obtained, too much signal distortion is introduced and many features of interest are lost. In this paper, we introduce a multidimensional filter based on a combination of one-dimensional median estimates. It is shown that threshold decomposition holds for this class of filters, making the deterministic analysis simpler. Invariant signals to the filter, called root signals, consist of very low resolution features making this filter much more attractive than conventional median filters.

Adaptive nonlinear filters for simultaneous removal of different kinds of noise in images

Abstract: A novel adaptive median filter is proposed. It allows the simultaneous removal of a combination of signal-dependent and additive random noise in addition to mixed impulse noise in images, processed in a single filtering pass. The adaptation algorithm is based on the local signal-to-noise ratio. An extension of the class of nonlinear mean filters to adaptive filters is considered. The performance of the adaptive median filter is compared to the commonly used median filter and the nonlinear mean filter.

Streaking in median filtered images

Abstract: This paper presents a probabilistic analysis of the streaking or blotching effect commonly observed in median filtered signals in both one and two dimensions. The effcts are identified as runs of equal or nearly equal values which create visual impressions that have no visual correlate. For one-dimensional discrete iid random signals with continuous input probability densities, the probability of a streak of length L occurring is computed and shown to be independent of the input probability distribution. Expressions for the first and second moments of the streak length are also derived, and certain asymptotic results are given. As the analysis and definition of the analogous effect in two dimensions is less tractable, the probability that medians taken from distinct overlapping windows will take the same value is derived for various filter geometries. The analytic results are supported by examples using both one- and two-dimensional signals.

A spectral autocorrelation method for measurement of the fundamental frequency of noise-corrupted speech

Abstract: A method for measurement of the fundamental frequency of a voiced speech signal corrupted by high levels of additive white Gaussian noise is described. The method is based on flattening the spectrum of the signal by a bank of bandpass lifters and extracting the pitch frequency from autocorrelation functions calculated at the output of the lifters. A smoothing modified median filter is applied to the calculated pitch frequency contour to result in an improvement in the accuracy of the method. A byproduct of the pitch tracker is a voiced/ unvoiced classifier. The maximum and the variance of the autocorrelation function maxima, over the bank of lifters, serve as the basis for voiced/unvoiced classification by making use of a two-dimensional, nearest-neighbor pattern recognition approach. Results are presented for fundamental frequency measurement and voiced/unvoiced classification for several signal-to-noise ratios.

An edge gradient enhancing adaptive order statistic filter

Abstract: We consider an adaptive order statistic (OS) filter that can enhance gradients of edges while suppressing impulsive and some nonimpulsive noise components. In particular, comparison and selection (CS) filters are introduced, in which the output is determined by comparing the sample mean and median values inside each window. It is shown theoretically that CS filters can enhance gradients of a variety of edges including noisy blurred ones. Some root properties of CS filters are also shown. Finally, experimental results are presented to illustrate the performance characteristics of these filters.

A fast algorithm for two dimensional median filtering

Abstract: The median of a set of numbers is a number which partitions the given set, excluding that number, into two subsets with an equal number of elements such that the number is greater than or equal to the elements in one subset and less than or equal to in the other In image processing, in order to compute the running median, the window is moved from one neighborhood to the next In this paper, a fast two-dimensional median filtering algorithm is proposed The algorithm is designed in such a way that in order to find the median of a window, the results obtained during the partitioning of the previous window are used Test results obtained by running the algorithm on VAX 11/780 are presented and its performance is compared with the Huang's histogram algorithm for median filtering It is shown that the proposed algorithm's execution time is faster and is independent of the number of bits used to represent the data values The novel features in the algorithm design that contribute to fast execution are also presented

On root structures of median and median-type filters

Abstract: In this correspondence, we analyze the root structures of the standard median (SM) filters, the recursive median (RM) filters, and the FIR median hybrid (FMH) filters. It is shown that these filters have many oscillatory infinitely long root signals. When a section of an oscillatory root is present in a signal, the filter's noise attenuation of the filter is not as good as predicted by statistical measures. We also suggest methods to prevent the possible harmful effect caused by the existence of these roots.

Deterministic properties of the recursive separable median filter

Abstract: The recursive separable median filter has been successfully used to extract features from noisy two-dimensional signals. In many applications, it gives better noise suppression and edge preservation than the standard separable median filter. In this paper we use a new approach for studying the deterministic properties of separable median filters. In particular, using threshold decomposition, we derive the root structure of the recursive separable median filter, where a root is a signal invariant to further filtering. It is shown that these root structures differ from those of their nonrecursive counterparts. We also show that any two-dimensional signal will converge to a root after repeated passes of the recursive separable median filter.

Generalized homomorphic and adaptive order statistic filters for the removal of impulsive and signal-dependent noise

Abstract: In this paper, we propose two new nonlinear filters for filtering signal-dependent noise, additive noise, and impulsive noise in image processing. The first filter proposed is an order statistic filter based on a generalized homomorphic transformation. The second is an adaptive order statistic filter with a variable threshold, which changes according to the noise level. Both of these filters perform well for the different kinds of noise encountered in image processing. They suppress signal-dependent noise, additive noise, and impulsive noise better than median filters, \alpha -trimmed mean filters, general nonlinear mean filters, modified trimmed mean filters, and double-window modified trimmed mean filters. They also preserve the edges of an image better than median filters and are simple to implement.

Optical median filtering using threshold decomposition

Abstract: A hybrid optical/electronic system performs median filtering and related ranked-order operations using threshold decomposition to encode the image. Threshold decomposition transforms the nonlinear neighborhood ranking operation into a linear space-invariant filtering step followed by a point-to-point threshold comparison step. Spatial multiplexing allows parallel processing of all the threshold components as well as recombination by a second linear space-invariant filtering step. An incoherent optical correlation system performs the linear filtering, using a magnetooptic spatial light modulator as the input device and a computergenerated hologram in the filter plane. Thresholding is done electronically. By adjusting the value of the threshold, the same architecture is used to perform median, minimum, and maximum filtering of images.

Edge detection in tactile images

Abstract: Some of the edge detection methods well known in robotic vision systems have been applied to detect edges in tactile images. Two dimensional median filtering with a 3 × 3 window size has been employed for the removal of noise present in the tactile images with excellent results. The LTS-200 tactile sensor system developed by the LORD Corporation has been used to obtain the tactile images analyzed in this research. The study has been carried out to obtain the contours of objects smaller in size than the LTS-200 sensor (with an active area of 1.131 in. × 0.707 in.) with a single probing operation. For larger objects, a straight line extraction method has been employed by which one can obtain the polygonal approximation of the shape of the object by sequential touching and integrating the straight lines so extracted.

Optical ranked-order filtering using threshold decomposition

Abstract: A hybrid optical/electronic system performs median filtering and related ranked-order operations using threshold decomposition to encode the image. Threshold decomposition transforms the nonlinear neighborhood ranking operation into a linear space-invariant filtering step followed by a point-to-point threshold comparison step. Spatial multiplexing allows parallel processing of all the threshold components as well as recombination by a second linear, space-invariant filtering step. An incoherent optical correlation system performs the linear filtering, using a magneto-optic spatial light modulator as the input device and a computer-generated hologram in the filter plane. Thresholding is done electronically. By adjusting the value of the threshold, the same architecture is used to perform median, minimum, and maximum filtering of images. A totally optical system is also disclosed.

On the synthesis of median filter systems

Abstract: In this paper, we address the problem of median filtering synthesis, that is, the design of a median filter system realization that will satisfy a given set of specifications. In particular, we address the problem of a cascade median filter realization, where the performance of a median filter is achieved through the cascade of several median filters of smaller window size. Because of the nonlinear nature of these filters, a statistical performance criterion is chosen for the system specifications. In order to evaluate the output of the cascade filter, a method is developed which finds the statistics of the roots of median filters, where roots are signals obtained after several median filter passes. Finally, a VLSI implementation for a cascade median filter system is presented.

Quantitative phase analysis in electron holographic interferometry.

Abstract: Holographic interferometry in an electron microscope and its phase analysis technique are described. The fringe scanning method is used to gain high sensitivity in phase detection. An example of measuring a magnetic field of a fine particle is presented. The measurement accuracy for median filtering is about 1/70 fringe corresponding to the magnetic flux sensitivity of 6 × 10−17 Wb. Noise reduction techniques are also discussed.

Adaptive Median Filtering for Impulse Noise Elimination in Real-Time TV Signals

Abstract: A two-dimensional (3 × 3) median filter with controlled turn-on is employed in an adaptive fashion for selective removal of impulse noise interference in real-time television signals. Various filters and threshold conditions are selected from programmed PROM's as a function of impulse noise detected and counted during a vertical interval window period. The adaptive median filter is used in conjunction with a satellite FM communication downlink system and can effectively improve the onset of threshold performance by about 3 dB carrier-to-noise ratio. The particular FM system discussed employs a multiplexed analog component, MAC, formatted TV signal. Use of the filter for standard NTSC composite signals is indicated.

Detection of unknown-frequency sinusoids in noise: Spectral versus correlation domain

Abstract: The purpose here is 1) to put into perspective the notions of spectral-versus correlation-domain detection algorithms, 2) to couple such decision rules with certain linear and nonlinear predetection-processing possibilities, and 3) to illustrate by simulation results the potential of a family of autoregressive (AR) detection statistics.

Increased noise immunity in large vocabulary speech recognition with the aid of spectral subtraction

Abstract: This paper presents several ways of making the signal processing in the IBM speech recognition system more robust with respect to variations in the background noise level. The underlying problem is that the speech recognition system trains on the specific noise circumstances of the training session. A simple solution lays in the controlled addition of noise. The level of noise that has to be added in to effectively mask all background noise is rather high and causes a significant reduction in accuracy. Spectral subtraction does a better job in a limited number of cases, but the thresholding in spectral subtraction often leads to training problems in the hidden Markov model based recognition system. The best results were obtained by reintroducing a semi-natural background by adding noise after applying spectral subtraction.

Algorithms and hardware for efficient image smoothing

Abstract: This work develops some algorithms for efficient implementation of mean and separable median filters for image noise smoothing. The procedures suggested use one-dimensional algorithms repeatedly to obtain two-dimensional mean and separable median in ≤4 and 4[log 2 ( n +1)]-2 operations, respectively, for an n × n square neighborhood (nbhd). A simple generalization of the algorithms to k dimensions shows that at most 2 k and k (2[log 2 ( n +1)]−1) operations are required for obtaining the mean and separable median of an n k nbhd. However, parallel processing can be easily applied to these algorithms. given only five parallel processors, less than one operation is required to obtain the sum of an n × n nbhd in two dimensions, and for n ≤31 the maximum number of comparisons required to obtain the two-dimensional separable median filter of an n × n nbhd is reduced to less than four. Experimentally we demonstrate that the separable median filter performs better than the median filter for certain classes of images. A simple hardware implementation of the above algorithm is also outlined. It is seen that the complexity of this implementation increases linearly depending on the number of inputs, unlike sort-based implementations whose complexity increases exponentially.

Speckle noise reduction of 1-look SAR imagery

Abstract: Speckle noise is inherent to synthetic aperture radar (SAR) imagery. Since the degradation of the image due to this noise results in uncertainties in the interpretation of the scene and in a loss of apparent resolution, it is desirable to filter the image to reduce this noise. In this paper, an adaptive algorithm based on the calculation of the local statistics around a pixel is applied to 1-look SAR imagery. The filter adapts to the nonstationarity of the image statistics since the size of the blocks is very small compared to that of the image. The performance of the filter is measured in terms of the equivalent number of looks (ENL) of the filtered image and the resulting resolution degradation. The results are compared to those obtained from different techniques applied to similar data. The local adaptive filter (LAF) significantly increases the ENL of the final image. The associated loss of resolution is also lower than that for other commonly used speckle reduction techniques.

Noise removal for SPOT HRV imagery

Abstract: SPOT HRV imagery acquired in ‘double’ mode displays near vertical striping occurring every seven or eight pixels in the down-track scan direction. Six digital image restoration procedures have been examined for suppressing or removing this noise. Image restoration by filtering in the spatial frequency domain was found to be the most effective procedure. However, although less effective at noise removal, a simple median filtering procedure could be used with greatly reduced computational cost.

Median type filters with linear predictive substructures

Abstract: In this paper, we introduce a new class of FIR Median Hybrid (FMH) filters which contain linear FIR substructures to estimate the current signal value using forward and backward prediction The output of the overall filter is the median of the predicted values and the actual signal value in the middle of the filter window Predictors maximizing the signal to noise ratio on signal sections described by an 1th order polynomial are derived The ramp enhancement filters are shown to attenuate the noise on a ramp signal better than the Standard Median (SM) filters The new predictive FMH filters are shown to have root signals which do not exist for the SM filters, eg triangular waves By combining the level and the ramp enhancement FMH filters, we obtain a filter which attenuates noise on constant and ramp signals

Noise reducer using magnitude of noise and non-linear signal processing

Abstract: A level difference detecting circuit 9 and an integrating circuit 10 receive a digital image signal inputted from an image signal input terminal 1 and detect a magnitude during a constant level period in every field. A determining circuit 12 determines the magnitude of the detected noise and selects the kind of a non-linear parameters to be used in a digital filter 8. Therefore, the digital filter 8 always performs processing for reducing noise by the most suitable non-linear parameter in accordance with the magnitude of noise.

Directed graph representation for root-signal set of median filters

Abstract: Median filtering is a simple digital technique for smoothing signals A root signal is defined as an invariant signal to the median filtering We describe directed graph representation for the root-signal set of median filters The directed graph representation allows us to obtain a set of roots and the number of roots in a straightforward manner

Compound Median Filtering Applied to Sonic Logs

Abstract: LOW pass filtering of sonic logs is often desired to remove high frequency measurement errors, to allow a valid comparison with a particular inversion scheme, and simply to make interpretation easier. However, because abrupt changes in velocity require high frequencies for their represenation, conventional low pass filtering tends to smear the important features of the signal. This has lead to non linear techniques such as median filtering, which however, can also degrade edges producing ‘edge artifacts’, especially for longer filter lengths. Recently the signal conditions necessary for the production of edge artifacts have been established (Leaney and Clrych 1987) and an extension to median filtering, compound median filtering, has been shown to preserve signal edges. In addition, compound median filtering has lead to a signal decomposition which allows greater flexibiltiy in the filtering operation. In this paper compound median filtering and decomposition are discussed and two applications of the decomposition, significant event reconstruction and time varying compound median filtering, are demonstrated as applied to sonic well log data.