Alternate Filters Research Articles

Conservative correction procedures utilizing artificial dissipation operators

The conservative correction procedure of Abgrall [1] is studied from the perspective of filter-based artificial dissipation methods, which motivates the ability to tailor the behavior of the method in both physical and spectral space. Compared to the original formulation, employing diffusion operators biases the correction towards smaller scales and better controls discretization errors when seeking to enforce auxiliary conservation relations. Effective entropy-stable regularization of sharp gradients is furthermore shown to be attainable. Calculations of the Sod shock tube problem as governed by the one-dimensional Euler equations are used to highlight the utility of considering alternate filters within the original correction framework, where the notion of entropy conservation/stability is leveraged for improving non-linear scheme robustness.

COMPARISON OF FILTERS DEDICATED TO SPECKLE SUPPRESSION IN SAR IMAGES

Abstract. This paper presents the results of research on the effectiveness of different filtering methods dedicated to speckle suppression in SAR images. The tests were performed on RadarSat-2 images and on an artificial image treated with simulated speckle noise. The research analysed the performance of particular filters related to the effectiveness of speckle suppression and to the ability to preserve image details and edges. Speckle is a phenomenon inherent to radar images – a deterministic noise connected with land cover type, but also causing significant changes in digital numbers of pixels. As a result, it may affect interpretation, classification and other processes concerning radar images. Speckle, resembling “salt and pepper” noise, has the form of a set of relatively small groups of pixels of values markedly different from values of other pixels representing the same type of land cover. Suppression of this noise may also cause suppression of small image details, therefore the ability to preserve the important parts of an image, was analysed as well. In the present study, selected filters were tested, and methods dedicated particularly to speckle noise suppression: Frost, Gamma-MAP, Lee, Lee-Sigma, Local Region, general filtering methods which might be effective in this respect: Mean, Median, in addition to morphological filters (alternate sequential filters with multiple structuring element and by reconstruction). The analysis presented in this paper compared the effectiveness of different filtering methods. It proved that some of the dedicated radar filters are efficient tools for speckle suppression, but also demonstrated a significant efficiency of the morphological approach, especially its ability to preserve image details.

COMPARISON OF FILTERS DEDICATED TO SPECKLE SUPPRESSION IN SAR IMAGES

This paper presents the results of research on the effectiveness of different filtering methods dedicated to speckle suppression in SAR images. The tests were performed on RadarSat-2 images and on an artificial image treated with simulated speckle noise. The research analysed the performance of particular filters related to the effectiveness of speckle suppression and to the ability to preserve image details and edges. Speckle is a phenomenon inherent to radar images – a deterministic noise connected with land cover type, but also causing significant changes in digital numbers of pixels. As a result, it may affect interpretation, classification and other processes concerning radar images. Speckle, resembling “salt and pepper” noise, has the form of a set of relatively small groups of pixels of values markedly different from values of other pixels representing the same type of land cover. Suppression of this noise may also cause suppression of small image details, therefore the ability to preserve the important parts of an image, was analysed as well. In the present study, selected filters were tested, and methods dedicated particularly to speckle noise suppression: Frost, Gamma-MAP, Lee, Lee-Sigma, Local Region, general filtering methods which might be effective in this respect: Mean, Median, in addition to morphological filters (alternate sequential filters with multiple structuring element and by reconstruction). The analysis presented in this paper compared the effectiveness of different filtering methods. It proved that some of the dedicated radar filters are efficient tools for speckle suppression, but also demonstrated a significant efficiency of the morphological approach, especially its ability to preserve image details.

Morphological filtering on hypergraphs

In this work we study the framework of mathematical morphology on hypergraph spaces. Hypergraphs were introduced in the 60s as a natural generalization of graphs, where edges become hyperedges and can contain more than two vertices. Mathematical morphology is one of the most powerful frameworks for image processing, and is heavily used for many applications. However, morphological operators on hypergraph spaces is not a concept fully developed in the literature. We consider lattice structures on hypergraphs on which we build morphological operators. We propose several new openings, closings, granulometries and alternate sequential filters acting (i) on the subsets of the vertex and hyperedge set of a hypergraph and (ii) on the subhypergraphs of a hypergraph. We illustrate with applications in image processing for filtering objects defined on hypergraph spaces.

Mutagenicity of smoke condensates from Canadian cigarettes with different design features

There is currently limited knowledge regarding the impact of different cigarette designs on the toxicological properties of cigarette smoke condensate (CSC). This study used the Salmonella Mutagenicity Assay to examine the mutagenic activity of mainstream CSCs from 11 commercial Canadian cigarette brands with different design features or tobacco blend. The brands were selected to include design features that are common for cigarettes sold in the Canadian market, as well as cigarettes with alternate filters (charcoal or MicroBlue™), the super slim design, and cigarettes containing mixed blends of different tobacco types. CSCs were obtained using the International Organization for Standardization (ISO) and Health Canada Intense (HCI) smoking regimes, and mutagenic activity was assessed using Salmonella strains TA98, YG1041 and YG5185. Comparisons of the commercial brands to the Kentucky 3R4F, the Canadian Monitor 8 reference and a Canadian best seller revealed no significant reduction in CSC mutagenicity for cigarettes with alternate filters. However, the super slim design did afford some reduction in mutagenic potency. Nevertheless, since the study did not attempt to evaluate the impact of the cigarette designs on human health at the individual or population level, the super slim cigarettes cannot be considered 'reduced-harm' cigarettes.

Morphological filtering on graphs

We study some basic morphological operators acting on the lattice of all subgraphs of an arbitrary (unweighted) graph G. To this end, we consider two dual adjunctions between the edge set and the vertex set of G. This allows us (i) to recover the classical notion of a dilation/erosion of a subset of the vertices of G and (ii) to extend it to subgraphs of G. Afterward, we propose several new openings, closings, granulometries and alternate filters acting (i) on the subsets of the edge and vertex set of G and (ii) on the subgraphs of G. The proposed framework is then extended to functions that weight the vertices and edges of a graph. We illustrate with applications to binary and grayscale image denoising, for which, on the provided images, the proposed approach outperforms the usual one based on structuring elements.

A SIMPLE METHODOLOGY TO SEGMENT X-RAY TOMOGRAPHIC IMAGES OF A MULTIPHASIC BUILDING STONE

Assessment of the weathering of a particular limestone, the tuffeau, used in historical monuments requires an accurate description of its microstructure. An efficient tools to obtain such a description is X-ray microtomography. However the segmentation of the images of this multiphasic material is not trivial. As the identification of pertinent markers of the structural components to extract is difficult, a two steps filtering approach is chosen. Alternate sequential filters are shown to efficiently remove the noise but, as they destroy the structural components smaller than the structuring element used, they cannot be carried out far enough. Hence as a second step in the filtering process, a mosaic operator, relying on a pragmatic yet efficient marker determination, is implemented to simplify further the images.

Objective estimates of westward Rossby wave and eddy propagation from sea surface height analyses

An objective method to estimate westward propagation of sea surface height (SSH) anomalies is introduced and compared to a subjective technique. Both approaches use time series extracted from global SSH analyses, prepared by optimal interpolation of altimeter data, as described in detail. The cost function used in the objective method calculates the mean along‐slope standard deviation, where slope is the reciprocal of propagation speed and defines the angle of linear samples through the SSH time series along each transect. The along‐slope standard deviation can be computed as an extension of the Radon transform, as shown. The optimum speed estimate minimizes the cost function, and speeds with mean along‐slope standard deviation within 1% of the minimum define the range of uncertainty. The 1% criteria was chosen to give a seemingly reasonable uncertainty range over a variety of cases and does not imply a specific probability that the true minimum is bounded in the uncertainty range. Applied in the central Pacific, objective speed estimates increase from 1 cm s−1 or less at the highest latitudes to above 30 cm s−1 nearer the equator. Subjective speed estimates are similar to, but generally lower than, their objective counterparts, reflecting a bias in subjective interpretation that is likely to vary among different individuals. A more detailed examination of the along‐slope minimization over 160°E–95°W focuses on the higher low‐latitude speeds, returning estimates of 48 cm s−1 (45 cm s−1) at 5.5°N (5.5°S) over 1993–2006. The corresponding 42–55 cm s−1 (38–65 cm s−1) uncertainty ranges bound most of the predictions from sensitivity test cases with alternate preprocessing filters or different multiyear time windows, although variability is larger south of the equator. The findings are consistent with prior studies and suggest the methods may be useful for other applications over the global ocean.

A controlled phantom study of a noise equalization algorithm for detecting microcalcifications in digital mammograms.

We report on some extensions and further developments of a well-known microcalcification detection algorithm based on adaptive noise equalization. Tissue equivalent phantom images with and without labeled microcalcifications were subjected to this algorithm, and analyses of results revealed some shortcomings in the approach. Particularly, it was observed that the method of estimating the width of distributions in the feature space was based on assumptions which resulted in the loss of similarity preservation characteristics. A modification involving a change of estimator statistic was made, and the modified approach was tested on the same phantom images. Other modifications for improving detectability such as downsampling and use of alternate local contrast filters were also tested. The results indicate that these modifications yield improvements in detectability, while extending the generality of the approach. Extensions to real mammograms and further directions of research are discussed.

Improvement in birefringent filters 4: The alternate partial polarizer filter

A design for a birefringent filter is proposed in which alternate polarizers are partial polarizers. Calculated performance characteristics of alternate partial polarizer filters (APP) are compared with those of Lyot and contrast element Lyot filters. These calculations show that the APP design has significant advantages in both transmission and profile shape. Using pulse techniques, partial polarizer systems are shown to be a natural evolution from the standard Lyot and contrast element Lyot systems. The APP filter using achromatic waveplates discussed in earlier papers of this series has been used to construct a universal alternate partial polarizer filter. This filter has a measured full width at half-maximum (FWHM) of 0.09 A at 5500 A and a transmission in polarized light of 38%. It is tunable from 4500 A to 8500 A. The measured characteristics of the filter agree well with theoretical predictions.