Anastasios N. Venetsanopoulos

Nonlinear Digital Filters

1. Introduction.- 2. Statistical preliminaries.- 3. Image formation.- 4. Median filters.- 5. Digital filters based on order statistics.- 6. Morphological image and signal processing.- 7. Homomorphie filters.- 8. Polynomial filters.- 9. Adaptive nonlinear filters.- 10. Generalizations and new trends.- 11. Algorithms and architectures.

Order statistics in digital image processing

A family of nonlinear filters based on order statistics is presented. A mathematical tool derived through robust estimation theory, order statistics has allowed engineers to develop nonlinear filters with excellent robustness properties. These filters are well suited to digital image processing because they preserve the edges and the fine details of an image much better than conventional linear filters. The probabilistic and deterministic properties of the best known and most widely used filter in this family, the median filter, are discussed. In addition, the authors consider filters that, while not based on order statistics, are related to them through robust estimation theory. A table that ranks nonlinear filters under a variety of performance criteria is included. Most of the topics treated are very active research areas, and the applications are varied, including HDTV, multichannel signal processing of geophysical and ECG/EEG data, and a variety of telecommunications applications. >

Kernel-Based Positioning in Wireless Local Area Networks

The recent proliferation of location-based services (LBSs) has necessitated the development of effective indoor positioning solutions. In such a context, wireless local area network (WLAN) positioning is a particularly viable solution in terms of hardware and installation costs due to the ubiquity of WLAN infrastructures. This paper examines three aspects of the problem of indoor WLAN positioning using received signal strength (RSS). First, we show that, due to the variability of RSS features over space, a spatially localized positioning method leads to improved positioning results. Second, we explore the problem of access point (AP) selection for positioning and demonstrate the need for further research in this area. Third, we present a kernelized distance calculation algorithm for comparing RSS observations to RSS training records. Experimental results indicate that the proposed system leads to a 17 percent (0.56 m) improvement over the widely used K-nearest neighbor and histogram-based methods

Vector directional filters-a new class of multichannel image processing filters

Vector directional filters (VDF) for multichannel image processing are introduced and studied. These filters separate the processing of vector-valued signals into directional processing and magnitude processing. This provides a link between single-channel image processing where only magnitude processing is essentially performed, and multichannel image processing where both the direction and the magnitude of the image vectors play an important role in the resulting (processed) image. VDF find applications in satellite image data processing, color image processing, and multispectral biomedical image processing. Results are presented here for the case of color images, as an important example of multichannel image processing. It is shown that VDF can achieve very good filtering results for various noise source models.

Vector filtering for color imaging

Vector processing operations use essential spectral and spatial information to remove noise and localize microarray spots. The proposed fully automated vector technique can be easily implemented in either hardware or software; and incorporated in any existing microarray image analysis and gene expression tool.

Morphological shape decomposition

A technique for decomposing a binary shape into a union of simple binary shapes is presented. The decomposition is shown to be unique and invariant to translation, rotation, and scaling. The techniques used in the decomposition are based on mathematical morphology. The shape description produced can be used in object recognition and in binary image coding. >

Nonlinear mean filters in image processing

The use of nonlinear means in image processing is introduced. The properties of these means in the presence of different types of noise are investigated. It is shown that nonlinear filters based on these means behave well for both additive and impulse noise. Their performance in the presence of signal dependent noise is satisfactory. They preserve the edges better than linear filters, and they reject the noise better than median filters.

Adaptive fuzzy systems for multichannel signal processing

Processing multichannel signals using digital signal processing techniques has received increased attention lately due to its importance in applications such as multimedia technologies and telecommunications. The objective of this paper is twofold: 1) to introduce adaptive filtering techniques to the reader who is just beginning in this area and 2) to provide a review for the reader who may be well versed in signal processing. The perspective of the topic offered here is one that comes primarily from work done in the field of multichannel (color) image processing. Hence, many of the techniques and works cited here relate to image processing with the emphasis placed primarily on filtering algorithms based on fuzzy concepts, multidimensional scaling, and order statistics-based designs. It should be noted, however, that multichannel signal processing is a very broad field and thus contains many other approaches that have been developed from different perspectives, such as transform domain filtering, classical least-square approaches, neural networks, and stochastic methods, just to name a few. We present a general formulation based on fuzzy concepts, which allows the use of adaptive weights in the filtering structure, and we discuss different filter designs. The strong potential of fuzzy adaptive filters for multichannel signal applications, such as color image processing, is illustrated with several examples.

Color edge detection using vector order statistics

A method is proposed whereby a color image is treated as a vector field and the edge information carried directly by the vectors is exploited. A class of color edge detectors is defined as the minimum over the magnitudes of linear combinations of the sorted vector samples. From this class, a specific edge detector is obtained and its performance characteristics studied. Results of a quantitative evaluation and comparison to other color edge detectors, using Pratts (1991) figure of merit and an artificially generated test image, are presented. Edge detection results obtained for real color images demonstrate the efficiency of the detector.

Location of mobile terminals using time measurements and survey points

Mobile terminal location has attracted much interest for its applications in emergency communications, location-sensitive browsing, and resource allocation. The paper introduces the use of nonparametric kernel-based estimators for location of mobile terminals using measurements of propagation delays. It is demonstrated that these estimators perform better than the previously used parametric maximum likelihood estimators for the case of a simulated microcell environment with line-of-sight (LOS) and non-line-of-sight (NLOS) radio propagation at several different levels of measurement noise. Their performance is not greatly degraded by NLOS effects. Methods for calculating good values for parameters of the kernel functions are demonstrated, as well as the robustness of the estimators when the values of the parameters vary from the optimal points. A lower bound on the mean square error of location estimation that considers the transition between LOS to NLOS propagation over short distances is presented. It is demonstrated the proposed location estimation method comes close to meeting this bound.