Morphological Dilation Research Articles

Color image morphology using an adaptive saturation-based technique

An adaptive algorithm that implements a saturation-based ordering (for color image morphology) is introduced. The adaptation is achieved using a tradeoff parameter in the form of a nonlinear function of the local saturation. To evaluate the performance of the proposed algorithm, a deigned psychophysical experiment is used to derive a metric denoted as the average value for the psychophysical evaluation in percent (APE%). Results of implementing the proposed APE show that an APE=73 to 96% can be achieved for basic morphological operators, i.e., dilation, erosion, opening, and closing. APE value depends on the size and shape of the structuring element as well as on the image details. The proposed algorithm has also been extended to other morphological operators, such as image smoothing (noise suppression), top hat, gradient, and Laplacian operators. In the case of a smoothing operation, an average peak signal-to-noise ratio (PSNR)=31 to 37 dB is achieved at various structuring elements and applied noise variances, while good results are achieved with the proposed top-hat operators.

Resuming Shapes with Applications

Many image processing tasks need some kind of average of different shapes. Frequently, different shapes obtained from several images have to be summarized. If these shapes can be considered as different realizations of a given random compact set, then the natural summaries are the different mean sets proposed in the literature. In this paper, new mean sets are defined by using the basic transformations of Mathematical Morphology (dilation, erosion, opening and closing). These new definitions can be considered, under some additional assumptions, as particular cases of the distance average of Baddeley and Molchanov. The use of the former and new mean sets as summary descriptors of shapes is illustrated with two applications: the analysis of human corneal endothelium images and the segmentation of the fovea in a fundus image. The variation of the random compact sets is described by means of confidence sets for the mean and by using set intervals (a generalization of confidence intervals for random sets). Finally, a third application is proposed: a procedure for denoising a single image by using mean sets.

Automatic segmentation of liver region based on extracted blood vessels

AbstractWith the rapid progress of CT (Computed Tomography) scanners, four‐phase CT images with resolutions as high as 1 mm have started to be used for diagnosing liver diseases. The first‐, second‐, third‐, and fourth‐phase CT images correspond to before dye injection, the early stage, the full stage, and the wash‐out stage of the injected dye. Such CT data offer useful information for diagnosing hepatic cancer. This paper describes an automatic method for segmenting the liver region using the blood vessel stream in the first‐ and third‐phase CTs by tracing the portal vein and then the hepatic vein. First, the tracing of the veins is carried out by performing a 3D labeling operation in the region extracted with a threshold that separates blood vessels from liver soft tissue. The adjoining stomach and spleen regions are separated by applying erosion and dilation, which are 3D morphological operations. Then, an operation for determining the accurate liver region is carried out to derive an approximate liver region, by enlarging the liver blood vessel region by morphological dilation and then extracting the liver region with an optimal threshold. This method was applied to eight CT data. The resulting regions agree well with the manually detected regions. © 2004 Wiley Periodicals, Inc. Syst Comp Jpn, 35(5): 1–10, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/scj.10592

Phantom Studies Investigating Extravascular Density Imaging for Partial Volume Correction of 3-D PET<tex>$^18$</tex>FDG Studies

Limited scanner resolution and cardiac motion contribute to partial volume (PV) averaging of cardiac PET images. An extravascular (EV) density image, created from the subtraction of a blood pool scan from a transmission image, has been used to correct for PV averaging in H/sub 2//sup 15/O studies using 2-D imaging but not with 3-D imaging of other tracers such as /sup 18/FDG. A cardiac phantom emulating the left ventricle was used to characterize the method for use in 3-D PET studies. Measurement of the average myocardial activity showed PV losses of 32% below the true activity (p<0.001). Initial application of the EV density correction still yielded a myocardial activity 13% below the true value (p<0.001). This failure of the EV density image was due to the 1.66 mm thick plastic barrier separating the myocardial and ventricular chambers within the phantom. Upon removal of this artifact by morphological dilation of the blood pool, the corrected myocardial value was within 2% of the true value (p=ns). Spherical ROIs (diameter of 2 to 10 mm), evenly distributed about the myocardium, were also used to calculate the average activity. The EV density image was able to account for PV averaging throughout the range of diameters to within a 5% accuracy, however, a small bias was seen as the size of the ROIs increased. This indicated a slight mismatch between the emission and transmission image resolutions, a result of the difference in data acquisitions (i.e., span and ring difference) and default smoothing. These results show that the use of EV density image to correct for PV averaging is possible with 3-D PET. A method of correcting barrier effects in phantoms has been presented, as well as a process for evaluating resolution mismatch.

Automatic Extraction of Filaments in Hα Solar Images

This paper presents a new method which allows for the automatic extraction and tracking of the evolution of filaments in solar images. Series of Hα full-disk images are taken in regular time intervals to observe the changes of the solar disk features. In each picture, the solar chromosphere filaments are identified for further evolution examination. Two alternative preprocessing techniques converting grayscale images into black-and-white pictures with enhanced chromosphere granularity are examined: local thresholding based on median values and global thresholding with brightness and area normalization. The next step employs morphological closing operations with multi-directional linear structuring elements to extract elongated shapes in the image. After logical intersection of directional filtering results, remaining noise is removed from the final outcome using morphological dilation and erosion with a circular structuring element. Experimental results show that the developed technique can achieve excellent results in detecting large filaments and good detection rates for small filaments.

Increased brain white matter diffusivity in normal adult aging: relationship to anisotropy and partial voluming.

Diffusion tensor imaging (DTI) was used to examine 1) age-related changes in genu, splenium, and centrum semiovale white matter diffusivity in 64 healthy men and women (age 23-85 years); 2) the relationship between diffusivity (trace) and fractional anisotropy (FA) across and within individuals; and 3) the role of macrostructural and microstructural partial voluming effects on the DTI metrics. Regional differences were greater in FA (approximately 43%) than in trace (approximately 16%). Depending on the region of interest, trace increased with age (r = 0.24 to 0.58) and FA decreased with age (r = -0.29 to -0.79). FA was inversely correlated with trace, even when controlling for age. Histogram analysis of trace and FA following systematic expansion and dilation of the white matter regions demonstrated greater susceptibility of FA than trace to error arising from macrostructural partial voluming, i.e., erroneous inclusion of primarily nonwhite-matter voxels. Three-phase ellipsoid shape analysis revealed that after morphometric erosion the spherical component remained greater in older than younger subjects in the splenium and centrum, suggesting that age-related reduction in FA arises from intravoxel increased interstitial fluid. Reducing the size of the white matter samples to control for macrostructural partial voluming attenuated but did not negate effects, indicating that observed changes in white matter with aging can reflect real microstructural alterations rather than sampling artifact. Morphological dilation of white matter regions of interest resulting in purposeful inclusion of non-white matter pixels significantly reduced mean FA, suggesting that reports of FA values below 0.25 in healthy adults may reflect partial voluming rather than actual changes in white matter coherence.

Mathematical morphology operations with a comparator array processor

We present a demonstrator photonic system for mathematical morphology image processing. Optically interconnected arrays of differential pairs of optoelectronic transceivers realize morphological erosion and dilation in an 8x8 pixel size image.

Modal Logics Based on Mathematical Morphology for Qualitative Spatial Reasoning

We propose in this paper to construct modal logics based on mathematical morphology. The contribution of this paper is twofold. First we show that mathematical morphology can be used to define modal operators in the context of normal modal logics. We propose definitions of modal operators as algebraic dilations and erosions, based on the notion of adjunction. We detail the particular case of morphological dilations and erosions, and of there compositions, as opening and closing. An extension to the fuzzy case is also proposed. Then we show how this can be interpreted for spatial reasoning by using qualitative symbolic representations of spatial relationships (topological and metric ones) derived from mathematical morphology. This allows to establish some links between numerical and symbolic representations of spatial knowledge.

An unsupervised generalized Hough transform for natural shapes

The Hough transform was originally designed to recognize artifical objects in images. A Hough transform for natural shapes (HTNS) was subsequently proposed, but necessitates the supervised learning of the class of shapes. Here, we extend HTNS to unsupervised pattern recognition, the variability of the object class being coded with tools originating from mathematical morphology (erosion, dilation and distance functions).

Face localization based on the morphological multiscale fingerprints

Face localization is a previous step for face recognition systems. We propose morphological multiscale fingerprints (MMF) as a holistic feature extraction technique for face localization. The MMF is computed as the local maxima and minima preserved up to a certain scale in a multiscale analysis based on morphological erosion and dilation. We do not consider any geometrical model of the face features. As an initial validation of our approach, we have compared it with principal component analysis (PCA) over a small custom image database. Afterwards, we have tested it over the CMU image database, with good results. Finally, we present the receiving operator curve (ROC) results as well as some instances of face detection.

AN IMPROVED EMBEDDED ZEROTREE WAVELET IMAGE CODING METHOD BASED ON COEFFICIENT PARTITIONING USING MORPHOLOGICAL OPERATION

In recent years, wavelets have attracted great attention in both still image compression and video coding, and several novel wavelet-based image compression algorithms have been developed so far, one of which is Shapiro's embedded zerotree wavelet (EZW) image compression algorithm. However, there are still some deficiencies in this algorithm. In this paper, after the analysis of the deficiency in EZW, a new algorithm based on quantized coefficient partitioning using morphological operation is proposed. Instead of encoding the coefficients in each subband line-by-line, regions in which most of the quantized coefficients are significant are extracted by morphological dilation and encoded first. This is followed by using zerotrees to encode the remaining space which has mostly zeros. Experimental results show that the proposed algorithm is not only superior to the EZW, but also compares favorably with the most efficient wavelet-based image compression algorithms reported so far.

Image compression based on energy clustering and zero-quadtree representation

An efficient image compression algorithm based on energy clustering and zero-quadtree representation (ECZQR) in the wavelet transform domain is proposed. In embedded coding, zeros within each subband are encoded in the framework of quadtree representation instead of zerotree representation. To use large rectangular blocks to represent zeros, it first uses morphological dilation to extract the arbitrarily shaped clusters of significant coefficients within each subband. The proposed encoding method results in less distortion in the decoded image than the line-by-line encoding method. Experimental results show that the algorithm is among the most efficient wavelet image compression algorithms.

Automatic acquisition of hierarchical mathematical morphology procedures by genetic algorithms

This paper presents a method to obtain an image processing procedure by showing an original image and a goal image. There has been previous work concerning automatic acquisition of image processing procedures by combining subroutine packages. In our approach, we do not use any image processing subroutine packages, but use only hierarchical mathematical morphology procedures, i.e. erosion and dilation operators. We use genetic algorithms to search procedures, i.e. erosion and dilation operators. Utilizing a parallel searching function of genetic algorithms and introducing a concept of era, we construct hierarchical procedures of mathematical morphology.

Wavelet image coding based on significance extraction using morphological operations

An algorithm is proposed for improving Servetto et al.&apos;s method of morphological representation of wavelet data (MRWD), which is among the most efficient wavelet-based image compression algorithms. In MRWD, morphological dilation is used to capture and encode the arbitrarily shaped clusters of significant coefficients within each subband and high compression is achieved. But there are still several deficiencies for rectification in MRWD. An efficient image compression algorithm is proposed, in which, for each subband, morphological dilation is first used to extract and encode the clustered significant coefficients, and the remaining space is encoded in an efficient way. Instead of encoding the large number of zeros one by one, only the small number of remaining significant coefficients and their positional information are encoded. Experimental results show that this improvement is very effective, especially for images with large and relatively smooth regions.

Morphologic image processing operators: reduction of partial volume effects for improved 3D visualization of CT data

The quality of segmentation and three-dimensional reconstruction of anatomical structures in tomographic slices is often impaired by disturbances due to partial volume effects (PVE). The potential for artefact reduction by use of the morphological image processing operators (MO) erosion and dilation is investigated. The CT examinations of 31 patients with pathological alterations in lung or brain were segmented using automatic region growing and the MO were applied in a different number of iterations. The processed regions were 3D-reconstructed (shaded surface display, MIP, volume rendering) and the occurrence of PVE-related artefacts using the signal-to-background ratio (SBR) prior to and after MO application was compared. For all patients under review, the artefacts caused by PVE were significantly reduced by erosion (lung: mean SBRpre = 1.67, SBRpost = 4.83; brain: SBRpre = 1.06, SBRpost = 1.29) even with only a small number of iterations. Region dilation was applied to integrate further structures (e.g. at tumor borders) into a configurable neighbourhood for segmentation and quantitative analysis. The MO represent an efficient approach for the reduction of PVE artefacts in 3D-CT reconstructions and allow optimized visualization of individual objects.

Correction of surface roughness measurements in SPM imaging

In STM and AFM, when rough surfaces are concerned, image formation is essentially governed by the nonlinear geometrical interaction between the specimen surface and the tip surface. The shape and finite size of the tip are responsible for imperfections in images. Consequently the measured roughnesses are not exact. They are always smaller than the true roughness value because the surface is imperfectly probed. We propose a method to predict the true roughness value from the experimental image obtained. For this purpose a large variety of different 3D surfaces which mimic the experimental ones are computed and classified with respect to the shape and density of grains composing the surface. Then, by using the mathematical morphology dilation operation which describes the image formation in SPM, the corresponding dilated images are computed for different tip geometries. For each category of surfaces and given tip shapes the correction factors between the true r.m.s. roughness values and the experimental ones are obtained. This allows us to predict the true roughness value. Scanning probe microscopy (SPM) (mainly scanning tunneling microscopy (STM) and atomic force microscopy (AFM)), have provided the unique possibility of 3D investigation of surface topography and access to material properties on the nanometer scale. These instruments are now currently used as precision dimensional metrology tools for the study and manufacturing control process of technologically important surfaces, such as semiconductor nanolithography devices, Si patterned wafers, magnetic thin films, optical data storage media and numerous others [1–8]. The number of nano-roughness measurements using SPM is increasing, since roughness parameters have profound practical consequences in many fields of engineering and pure science (nano-tribology, semiconductor devices, biomechanics, electrochemical or sputtering deposition etc.). A number of workers have used directly acquired images and SPM imaging processing software developed by the manufacturers ∗ Corresponding author to draw some quantitative conclusions about roughness parameters. Unfortunately, the surface is not perfectly probed by the tip, since it is not infinitely sharp. Its shape and finite size are responsible for the imperfections of images and thus for roughness measurement errors. These errors are particularly important in the case of highly corrugated surfaces. In this case, the surface features can be comparable in size to the tip and the image is strongly distorted. These distortions are well known, having been analyzed by several authors [9– 15], but very little work has been done to date to correct the roughness measurements. It has been shown recently that SPM image formation and restoration can be described by two mathematical morphology operations (dilation and erosion, respectively [16–20]) or by the concept of an envelope function [21]. Erosion is the dual operation of dilation, not its inverse function. Consequently, the image cannot be perfectly restored. The topography of the surface can only be corrected in the zones probed (“seen”) by the tip. Therefore the correction is partial and depends on the tip size that defines the amount of lost information. In this paper we propose a method, based on appropriate simulations and on mathematical morphology, of predicting the true r.m.s. roughness value from the experimental image if the tip shape is known. For this purpose, we have computed and classified, with respect to the shape and density of grains composing the surface, a large variety of different 3D surfaces which mimic the real ones. For each category of surfaces and a given tip, the correction factor between the true r.m.s. roughness value and the experimental one is obtained. 1 Tip influence on roughness measurements In SPM, the image is formed by recording the height of the tip apex when the tip is scanned across the surface. Unfortunately, the proximal point, i.e. the point of the tip surface which interacts with the specimen surface and, therefore, gives the useful signal, is not necessarily located at the tip apex, is not unique, and does not remain the same during the tip motion [8, 17]. This situation is the main reason why image formation has been qualified as a non-linear process.

Probabilistic comparisons of morphological dilation and erosion with their equivalent linear shift-invariant systems in the case of a memoryless uniform source

This correspondence compares dilation and erosion with their spectrally equivalent affine-linear shift-invariant system in probabilistic characteristics in the case of a memoryless uniform source. The equivalent system, which is derived through spectral factorization, turns out to be of a finite-impulse-response filter and has a much smoother probability density than dilation.

Two Image-Template Operations for Binary Image Processing

This paper presents two new image algebra image-template operationsmatch and mismatch derived from the general image-template product. These image algebra operations extend the binary morphological erosion and dilation operations and can be used to express elegantly most of binary image processing algorithms in a more natural way than binary morphological operations from the image processing viewpoint. In addition, the match and mismatch operations are easy to implement efficiently on SIMD bit-serial parallel computers.

Optical intrinsically fuzzy mathematical morphology for gray-scale image processing

Intrinsically fuzzy morphological erosion and dilation are extended to a total of eight operations that have been formulated in terms of a single morphological operation-biased dilation. Based on the spatial coding of a fuzzy variable, a bidirectional projection concept is proposed. Thus, fuzzy logic operations, arithmetic operations, gray-scale dilation, and erosion for the extended intrinsically fuzzy morphological operations can be included in a unified algorithm with only biased dilation and fuzzy logic operations. To execute this image algebra approach we present a cellular two-layer processing architecture that consists of a biased dilation processor and a fuzzy logic processor.

Solid state integrated optical cellular two-layer logic image processor: design and demonstration

An all solid state integrated optical cellular two-layer logic image processor, which can be used for binary image processing, has been designed and fabricated. The first layer is an optical parallel self-programming logic processor, constructed with prism combinations. The second layer is an optical, morphological dilation processor assembled with birefringent plates. The complete system uses the direct cascade of these two processors. It is shown that the integrated system is compact in structure, insensitive to environmental influences, and efficient in performance.