Median filter

About: Median filter is a research topic. Over the lifetime, 12479 publications have been published within this topic receiving 178253 citations.

A new efficient approach for the removal of impulse noise from highly corrupted images

Abstract: A new framework for removing impulse noise from images is presented in which the nature of the filtering operation is conditioned on a state variable defined as the output of a classifier that operates on the differences between the input pixel and the remaining rank-ordered pixels in a sliding window. As part of this framework, several algorithms are examined, each of which is applicable to fixed and random-valued impulse noise models. First, a simple two-state approach is described in which the algorithm switches between the output of an identity filter and a rank-ordered mean (ROM) filter. The technique achieves an excellent tradeoff between noise suppression and detail preservation with little increase in computational complexity over the simple median filter. For a small additional cost in memory, this simple strategy is easily generalized into a multistate approach using weighted combinations of the identity and ROM filter in which the weighting coefficients can be optimized using image training data. Extensive simulations indicate that these methods perform significantly better in terms of noise suppression and detail preservation than a number of existing nonlinear techniques with as much as 40% impulse noise corruption. Moreover, the method can effectively restore images corrupted with Gaussian noise and mixed Gaussian and impulse noise. Finally, the method is shown to be extremely robust with respect to the training data and the percentage of impulse noise.

Tri-state median filter for image denoising

Abstract: A novel nonlinear filter, called tri-state median (TSM) filter, is proposed for preserving image details while effectively suppressing impulse noise. We incorporate the standard median (SM) filter and the center weighted median (CWM) filter into a noise detection framework to determine whether a pixel is corrupted, before applying filtering unconditionally. Extensive simulation results demonstrate that the proposed filter consistently outperforms other median filters by balancing the tradeoff between noise reduction and detail preservation.

Weighted median filters: a tutorial

Abstract: Weighted Median (WM) filters have the robustness and edge preserving capability of the classical median filter and resemble linear FIR filters in certain properties. Furthermore, WM filters belong to the broad class of nonlinear filters called stack filters. This enables the use of the tools developed for the latter class in characterizing and analyzing the behavior and properties of WM filters, e.g. noise attenuation capability. The fact that WM filters are threshold functions allows the use of neural network training methods to obtain adaptive WM filters. In this tutorial paper we trace the development of the theory of WM filtering from its beginnings in the median filter to the recently developed theory of optimal weighted median filtering. Applications discussed include: idempotent weighted median filters for speech processing, adaptive weighted median and optimal weighted median filters for image and image sequence restoration, weighted medians as robust predictors in DPCM coding and Quincunx coding, and weighted median filters in scan rate conversion in normal TV and HDTV systems.

A Quantitative Analysis of Current Practices in Optical Flow Estimation and the Principles Behind Them

Abstract: The accuracy of optical flow estimation algorithms has been improving steadily as evidenced by results on the Middlebury optical flow benchmark. The typical formulation, however, has changed little since the work of Horn and Schunck. We attempt to uncover what has made recent advances possible through a thorough analysis of how the objective function, the optimization method, and modern implementation practices influence accuracy. We discover that "classical" flow formulations perform surprisingly well when combined with modern optimization and implementation techniques. One key implementation detail is the median filtering of intermediate flow fields during optimization. While this improves the robustness of classical methods it actually leads to higher energy solutions, meaning that these methods are not optimizing the original objective function. To understand the principles behind this phenomenon, we derive a new objective function that formalizes the median filtering heuristic. This objective function includes a non-local smoothness term that robustly integrates flow estimates over large spatial neighborhoods. By modifying this new term to include information about flow and image boundaries we develop a method that can better preserve motion details. To take advantage of the trend towards video in wide-screen format, we further introduce an asymmetric pyramid downsampling scheme that enables the estimation of longer range horizontal motions. The methods are evaluated on the Middlebury, MPI Sintel, and KITTI datasets using the same parameter settings.

Stack filters

Abstract: The median and other rank-order operators possess two properties called the threshold decomposition and the stacking properties. The first is a limited superposition property which leads to a new architecture for these filters; the second is an ordering property which allows an efficient VLSI implementation of the threshold decomposition architecture. Motivated by the success of rank-order filters in a wide variety of applications and by the ease with which they can now be implemented, we consider in this paper a new class of filters called stack filters. They share the threshold decomposition and stacking properties of rank-order filters but are otherwise unconstrained. They are shown to form a very large class of easily implemented nonlinear filters which includes the rank-order operators as well as all compositions of morphological operators. The convergence properties of these filters are investigated using techniques similar to those used to determine root signal behavior of median filters. The results obtained include necessary conditions for a stack filter to preserve monotone regions or edges in signals. The output distribution for these filters is also found. All the stack filters of window width 3 are determined along with their convergence properties. Among these filters are found two which we have named asymmetric median filters. They share all the properties of median filters except that they remove impulses of one sign only; that is, one removes only positive going edges, the other removes only negative going edges, while the median filter removes impulses of both signs. This investigation of the properties of stack filters thus produces several new, useful, and easily implemented filters.