Median filter

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

Max-mean and max-median filters for detection of small targets

Abstract: This paper deals with the problem of detection and tracking of low observable small-targets from a sequence of IR images against structural background and non-stationary clutter. There are many algorithms reported in the open literature for detection and tracking of targets of significant size in the image plane with good results. However, the difficulties of detecting small-targets arise from the fact that they are not easily discernable from clutter. The focus of research in this area is to reduce the false alarm rate to an acceptable level. Triple Temporal Filter reported by Jerry Silverman et. al., is one of the promising algorithms in this are. In this paper, we investigate the usefulness of Max-Mean and Max-Median filters in preserving the edges of clouds and structural backgrounds, which helps in detecting small-targets. Subsequently, anti-mean and anti-median operations result in good performance of detecting targets against moving clutter. The raw image is first filtered by max-mean/max-median filter. Then the filtered output is subtracted from the original image to enhance the potential targets. A thresholding step is incorporated in order to limit the number of potential target pixels. The threshold is obtained by using the statistics of the image. Finally, the thresholded images are accumulated so that the moving target forms a continuous trajectory and can be detected by using the post-processing algorithm. It is assumed that most of the targets occupy a couple of pixels. Head-on moving and maneuvering targets are not considered. These filters have ben tested successfully with the available database and the result are presented.

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.

Removal of High Density Salt and Pepper Noise Through Modified Decision Based Unsymmetric Trimmed Median Filter

Abstract: A modified decision based unsymmetrical trimmed median filter algorithm for the restoration of gray scale, and color images that are highly corrupted by salt and pepper noise is proposed in this paper. The proposed algorithm replaces the noisy pixel by trimmed median value when other pixel values, 0's and 255's are present in the selected window and when all the pixel values are 0's and 255's then the noise pixel is replaced by mean value of all the elements present in the selected window. This proposed algorithm shows better results than the Standard Median Filter (MF), Decision Based Algorithm (DBA), Modified Decision Based Algorithm (MDBA), and Progressive Switched Median Filter (PSMF). The proposed algorithm is tested against different grayscale and color images and it gives better Peak Signal-to-Noise Ratio (PSNR) and Image Enhancement Factor (IEF).

Nonlocal Means-Based Speckle Filtering for Ultrasound Images

Abstract: In image processing, restoration is expected to improve the qualitative inspection of the image and the performance of quantitative image analysis techniques. In this paper, an adaptation of the nonlocal (NL)-means filter is proposed for speckle reduction in ultrasound (US) images. Originally developed for additive white Gaussian noise, we propose to use a Bayesian framework to derive a NL-means filter adapted to a relevant ultrasound noise model. Quantitative results on synthetic data show the performances of the proposed method compared to well-established and state-of-the-art methods. Results on real images demonstrate that the proposed method is able to preserve accurately edges and structural details of the image.

A versatile wavelet domain noise filtration technique for medical imaging

Abstract: We propose a robust wavelet domain method for noise filtering in medical images. The proposed method adapts itself to various types of image noise as well as to the preference of the medical expert; a single parameter can be used to balance the preservation of (expert-dependent) relevant details against the degree of noise reduction. The algorithm exploits generally valid knowledge about the correlation of significant image features across the resolution scales to perform a preliminary coefficient classification. This preliminary coefficient classification is used to empirically estimate the statistical distributions of the coefficients that represent useful image features on the one hand and mainly noise on the other. The adaptation to the spatial context in the image is achieved by using a wavelet domain indicator of the local spatial activity. The proposed method is of low complexity, both in its implementation and execution time. The results demonstrate its usefulness for noise suppression in medical ultrasound and magnetic resonance imaging. In these applications, the proposed method clearly outperforms single-resolution spatially adaptive algorithms, in terms of quantitative performance measures as well as in terms of visual quality of the images.