Yrjö Neuvo

Analysis of the properties of median and weighted median filters using threshold logic and stack filter representation

The deterministic properties of weighted median (WM) filters are analyzed. Threshold decomposition and the stacking property together establish a unique relationship between integer and binary domain filtering. The authors present a method to find the weighted median filter which is equivalent to a stack filter defined by a positive Boolean function. Because the cascade of WM filters can always be expressed as a single stack filter this allows expression of the cascade of WM filters as a single WM filter. A direct application is the computation of the output distribution of a cascade of WM filters. The same method is used to find a nonrecursive expansion of a recursive WM filter. As applications of theoretical results, several interesting deterministic and statistical properties of WM filters are derived. >

The maximum sampling rate of digital filters under hardware speed constraints

This paper presents a framework for Fiding efficient multiprocessor realizations of digital filters. Based on simple graph-theoretic concepts, a method is derived for determining the minimal sampling period of a given digital filter structure when the speed of arithmetic operations is given but the number of processing units Is unlimited. It Is shown how realistic hardware implementations can be found and evaluated by using the timing diagram of this maximal rate realization as a starting point. The minimal sampling periods of several common digital filter structures are given in terms of addition and multiplication times.

FIR-median hybrid filters with predictive FIR substructures

A class of finite-impulse response (FIR) median hybrid (FMH) filters that contain linear FIR substructures to estimate the current signal value using forward and backward prediction is introduced. 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 lth-order polynominal 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, e.g. triangular waves. By combining the level and the ramp enhancement FMH filters, a filter is obtained which attenuates noise on constant and ramp signals. The noise attenuation on ramp signals is better than with the SM filter, and the predictive FMH filter has novel and meaningful root structures. The number of arithmetic operations needed to implement the predictive FMH filter grows linearly with the length of the filter. >

Three-dimensional median-related filters for color image sequence filtering

Most current algorithms developed for image sequence filtering require motion information in order to obtain good results both in the still and moving parts of an image sequence. In the present paper, filters which completely preserve stationary regions in image sequences are introduced. In moving regions, the 3D filters inherently reduce to spatial filters and perform well in these areas without any motion-compensation or motion-detection. A new multivariate filtering operation called the alpha-trimmed vector median is proposed. Guidelines for the determination of optimal 3D median-related structures for color and gray-level image sequence filtering are given. Algorithms based on vector median, extended vector median, alpha-trimmed vector median, and componentwise median operations are developed. Properties of the human visual system are taken into account in the design of filters. Noise attenuation and detail preservation capability of the filters is examined. In particular, the impulsive noise attenuation capability of the filters is analyzed theoretically. Simulation results based on real image sequences are given. >

Nonlinear multivariate image filtering techniques

In this paper, nonlinear multivariate image filtering techniques are proposed to handle color images corrupted by noise. First, we briefly review the principle of reduced ordering (R-ordering) and then define three R-orderings by selecting different central locations. Considering noise attenuation, edge preservation, and detail retention, R-ordering based multivariate filters are designed by combining the R-ordering schemes. To implement color image filtering more effectively, we develop them into a locally adaptive version. The output of the adaptive filter is the closest sample to a central location that is a weighted linear combination of the mean, the marginal median, and the center sample. As a result, we study an adaptive hybrid multivariate (AHM) filter consisting of the mean filter, the marginal median filter, and the identity filter. The performance of the two adaptive filtering techniques is compared with that of some nonadaptive ones. The examples of color image filtering show that the adaptive multivariate image filtering gives a rather good performance improvement.

On properties and design of nonuniformly spaced linear arrays (antennas)

The properties of nonuniformly spaced linear arrays (and nonrecursive filters with nonequidistant taps) are studied. It is shown that in many cases the element spacings of the optimal solution are integer multiples of a suitably chosen basic spacing. This significantly simplifies the design procedure since the arrays can be designed as thinned uniformly spaced arrays, thus avoiding complicated nonlinear optimizations. A simple thinning procedure is used. Another design procedure based on Nth-band FIR (finite-impulse response) filter concepts is introduced, making possible the use of standard FIR filter design methods for nonuniformly spaced arrays; illustrative examples are included. The results compare favorably to published results for nonuniformly spaced designs that did not exploit the special properties of uniform or discrete nonuniform arrays. >

On root structures of median and median-type filters

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 filters 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.

FIR-median hybrid filters with excellent transient response in noisy conditions

Two classes of FIR-median hybrid (FMH) filters are introduced, which are called in-place growing FIR-median hybrid (IPG-FMH) and recursive in-place growing FIR-median hybrid (RIPG-FMH) filters. This new extended family of filters exhibits a very small bias error in the vicinity of an edge, an yet provides good noise attenuation. It is shown that the IPG-FMH filters can be expressed as weighted FMH (WFMH) filters. >

Multichannel edge enhancement in color image processing

In the paper, a multichannel edge enhancing filter (MEEF) based on the vector median is introduced for enhancing degraded edges in color images. An input multichannel signal is filtered with three subfilters, and the final output is determined by comparing the outputs of the subfilters and their vector median. Root signal and edge enhancement properties of the MEEF are examined in detail. In addition, the authors discuss line preservation and edge jitter resistance of the MEEF in noisy conditions. Finally, the MEEF is tested with: i) blurred edges caused by unfocusing or fast movement of camera, ii) serrated edges caused by interlaced scan, iii) false color edges caused by channel dispersion. The results show that the MEEF outperforms channelwise edge enhancing filtering in enhancing these degraded edges. >

Comments on "Theoretical analysis of the max/median filter" by G.R. Arce and M. P. McLaughlin

In the original paper (ibid., vol.ASSP-35, no.1, p.60-9, Jan. 1987), an approach (the max/median filter) to remove noise from images without distorting geometrical information was introduced. The proposed filter structure, due to its asymmetrical nature, is able to preserve only the subtle signal structures that are larger in intensity than the local background level. The commenters suggest another filter structure that has the ability to preserve both positive and negative geometrical information with respect to the background level. >