Decomposition of geometric-shaped structuring elements using morphological transformations on binary images

The two fundamental operations in morphological image processing are dilation and erosion. These processes are defined via structuring elements. It is of practical interest to consider a variety of structuring element shapes. The realisation of dilation/erosion for convex structuring elements by use of partial differential equations (PDEs) allows for digital scalability and subpixel accuracy. However, numerical schemes suffer from blur by dissipative artifacts. In our paper we present a family of so-called flux-corrected transport (FCT) schemes that addresses this problem for arbitrary convex structuring elements. The main characteristics of the FCT-schemes are: (i) They keep edges very sharp during the morphological evolution process, and (ii) they feature a high degree of rotational invariance. We validate the FCT-scheme theoretically by proving consistency and stability. Numerical experiments with diamonds and ellipses as structuring elements show that FCT-schemes are superior to standard schemes in the field of PDE-based morphology.

SKIPSM (separated-kernel image processing using finite state machines) is a technique for implementing large-kernel binary- morphology operators and many other operations. While earlier papers on SKIPSM concentrated mainly on implementations using pipelined hardware, there is considerable scope for achieving major speed improvements in software systems. Using identical control software, one-pass binary erosion and dilation structuring elements (SEs) ranging from the trivial (3 by 3) to the gigantic (51 by 51, or even larger), are readily available. Processing speed is independent of the size of the SE, making the SKIPSM approach practical for work with very large SEs on ordinary desktop computers. PIP (prolog image processing) is an interactive machine vision prototyping environment developed at the University of Wales Cardiff. It consists of a large number of image processing operators embedded within the standard AI language Prolog. This paper describes the SKIPSM implementation of binary morphology operators within PIP. A large set of binary erosion and dilation operations (circles, squares, diamonds, octagons, etc.) is available to the user through a command-line driven dialogue, via pull-down menus, or incorporated into standard (Prolog) programs. Little has been done thus far to optimize speed on this first software implementation of SKIPSM. Nevertheless, the results are impressive. The paper describes sample applications and presents timing figures. Readers have the opportunity to try out these operations on demonstration software written by the University of Wales, or via their WWW home page at http://bruce.cs.cf.ac.uk/bruce/index.html .

In this paper, a novel image denoising method with a morphological opening is proposed. In many image recovery, the regularization has been introduced to prevent overfitting between a recovered image and a noisy observation. In the regularization of an image, the smoothness of the image is assumed. The cost function, which is minimized during the regularization, is defined as a sum of the approximation error term and the smoothness penalty of the image. In morphological image processing, an image is approximated as a union of structuring elements (SEs) by the morphological image opening. In the approximation with the opening, the SE represents the local intensity surface of the image. We hence impose the smoothness penalty on the SE, instead of the recovered image itself, and propose an image opening method with the regularization penalty for the SE. In denoising, the approximation error is minimized under the constraint of the penalty for the SE. In experiments, we show that the proposed filtering method has ability to remove impulsive noises from degraded texture images.

Mammography is the main exam used to perform early detection of breast cancer. Using digital mammographic images processing, it’s possible to improve visualization of structures and facilitate diagnosis, using noise-reduction filters, contrast enhancement and segmentation. Segmentation divides the image in regions of interest (lesions) and background. Watershed segmentation performs a topographic analysis of the image and object’s boundaries extraction. Watershed demands using markers, that limit the regions where processing will be applied, avoiding issues such as over-segmentation. The markers can be defined using morphological operators, which use structuring elements to identify interest pixels. Therefore, the aim of this work is to evaluate watershed segmentation of breast lesions, by changing the pre-processing and structuring elements. There were applied disk and diamond-shaped structuring elements, with 25, 50 and 100 pixels as size, in addition to noise-reduction Wiener filter and contrast enhancement with Wavelet transform and contrast limited adaptive histogram equalization (CLAHE). The results were evaluated by using accuracy, ROC curve and visual analysis of the images, allowing to more easily compare the efficiency of each processing. For the disk format obtained AUC equal to 0.891, while the diamond format has 0.909, it was possible to identify the relationship between size and pre-processing with the number of detected regions. Moreover, small structuring elements are more effective in watershed segmentation, requiring research with different denoising methods and marker definition algorithms. Finally, the results allowed us to establish how breast density and shape, size and type of lesion interfere in watershed segmentation results.

In a 6th-order section of the lowland River Spree, we analysed the retention of particulate organic matter (POM) by the following characteristic benthic structural elements: stable sands colonised by macrophytes or mussels, shallow sandy banks, and shifting sands. Our hypothesis was that the retention and storage of suspended particles and, therefore, the organic matter budget of a specific river reach is determined by the retentive properties of the various types of benthic structural elements in the channel. The relative storage capacity of each structural element for POM, chlorophyll-a, and protein was calculated. This storage capacity reflects the dynamics of processes that occur on the time scale of several months. Additionally, the relative trapping efficiencies of the structural elements were determined by means of tracer particles, which provide information about their retentive properties on shorter time scales. The investigated structural elements differed significantly with respect to the amount and composition of stored POM, and the time scale of retention. Biotic structures were the most effective retention features on longer time scales in the investigated lowland river. Macrophyte stands showed the highest relative storage capacity for organic matter, followed by stable sands that were colonised by mussels. On a shorter time scale during low discharge conditions, shallow sandy banks were similarly retentive. Shifting sands were least retentive, but the highest nutritional quality of the organic matter was found there. Those spatial patterns within a river reach are supposed to be an important factor controlling the microbial processing of POM in the benthic zone and the distribution of benthic invertebrates. Based on our results, it can be expected that changes in the size and composition of benthic structural elements within the channel (e.g. due to bank reinforcements, straightening measures, or impoundments) will influence the organic matter budget of a stream ecosystem considerably.

Existing methods and means for measurements and identification of the vegetable matter (VM) in wool fibre assemblies are time consuming, labour-intensive and therefore expensive. This paper presents the measurements of VM content, sorting and counting (identification) of VM particles using digital image processing and analysis. A measuring system has been constructed, and the compound light mode has been used for the measurements. A formula has been derived to translate the VM content by area into the VM content by mass. MATLAB and its image processing toolbox have been used in the image processing and analysis. The area, perimeter and shape factor of each VM particle were measured, and using the values of the boundary limits of the shape factor for each type of VM, sorting and counting of four types of VM in wool have been carried out.

Existing standardised methods and means are time consuming, labour-intensive and therefore expensive. This paper presents the measurements of trash contents and grades in cotton using digital image processing and analysis. A measuring system has been constructed, and transmitted, reflected and compound light measurement modes have been tested, discussed and the optimum mode identified. A formula has been derived and used to translate the trash content by area into the trash content by mass. MATLAB and its image processing toolbox have been used in image processing and analysis.

Grayscale dilation and erosion are basic transformations of mathematical morphology. Used together or with other transformations, they are very useful tools for image analysis. However, they can be very time consuming, especially with 3D images, and with large structuring elements. Several algorithms have been created to decrease the computation time, some of them with some limitations of shape of structuring element. We have implemented several algorithms, studied their performance in different conditions, and shown that all of them are more efficients than the others in certain conditions. We finally introduce a new structuring element class and a some meta filter designed to select the best algorithm depending on the image and the structuring element, and to smoothely integrate the different algorithms available in the toolkit.

Facile sonochemical preparation of La2Cu2O5 nanostructures, characterization, the evaluation of performance, mechanism, and kinetics of photocatalytic reactions for the removal of toxic pollutants

Interaction energies computed with density functional theory can be divided into physically meaningful components by symmetry-adapted perturbation theory (DFT-SAPT) or the canonical energy decomposition analysis (EDA). In this work, the decomposition results obtained by these schemes were compared for more than 200 hydrogen-, halogen-, and pnicogen-bonded, dispersion-bound, and mixed complexes to investigate their similarity in the evaluation of the nature of noncovalent interactions. BLYP functional with D3(BJ) correction was used for the EDA scheme, whereas asymptotically corrected PBE0 functional for DFT-SAPT provided some of the best combinations for description of noncovalent interactions. Both schemes provide similar results concerning total interaction energies and insight into the individual energy components. For most complexes, the dominant energetic term was identified equally by both decomposition schemes. Because the canonical EDA is computationally less demanding than the DFT-SAPT, the former can be especially used in cases where the systems investigated are very large.

The mathematical morphology was applied to high-speed automaton fault diagnosis in this paper, which a new method was proposed to diagnosis high-speed automaton fault based on mathematical morphology and the combination of fuzzy clustering. Take a high-speed automaton fault data in laboratory tests for example; various types were analyzed for the fault signal. The results demonstrated that the combination of mathematical morphology and fuzzy clustering applied on a high-speed automaton can effectively diagnose faults, providing a new way for high-speed automata fault diagnosis.

Mathematical morphology on l-images

A hybrid reliability evaluation approach is proposed, consisting of the response surface method, the finite-element method, the first-order reliability method, and the linear iterative scheme when the load is applied dynamically to a complicated structural system. The method is especially applicable for realistic structural systems consisting of different types of structural elements and materials. The method was specifically developed to evaluate the reliability of a steel frame and reinforced concrete shear wall structural system subjected to seismic loading. The unique feature of this algorithm is that the earthquake loading can be applied in the time domain, enabling a realistic representation of the seismic loading conditions. The steel members are represented by beam-column elements and the shear walls are represented by plate elements. The deterministic algorithm, discussed in detail in the companion paper, is then extended to consider the uncertainty in the random variables. The reliability of a frame without and with RC shear walls is evaluated for the serviceability performance functions. The results are verified using Monte Carlo simulation. The method estimates the probability of failure very accurately, and is very efficient compared to simulation. The algorithm can be used to estimate the reliability of complicated structural systems consisting of different types of structural elements and materials under dynamic including seismic loading applied in time domain.

A morphological image enhancement method based on the GAN (General Adaptive Neighborhood) structuring elements is proposed for some problems such as low overall contrast, noise and inter-target edge of some remote sensing images. Firstly, a pixel to be processed is selected as a seed point, and an adaptive neighborhood is defined according to the image pixel characteristic and the neighborhood constraint relation to obtain the self-adaptive structuring elements set. A corresponding self-adaptive morphological operation based on the self-adaptive structuring elements set is constructed with reference to the classical morphological operation definition, and the self-adaptive alternative filter is constructed by using the adaptive morphological operation combination so as to realize the enhancement of the remote sensing image. The experimental results show that the method can preserve the accurate positioning of the objects edge while enhancing the image, avoid the loss of information, has better noise removing performance. Compared with the classical morphological filter operator, the single-scale Retinex algorithm and bi-histogram equalization (BHE) algorithm, the contrast ratio and the signal-to-noise ratio of the enhanced image are improved.

An overview of SKIPSM (eparated-Kemel Jinage rocessing using Finite state Machines), a powerful new way to implement many standard image processing operations, is presented in a two companion ape2 This paper describes the application of SKJPSM to grey-level morphology, which involves . in some cases, the reformulation of the grey-level morphology problem as a set of binary morphology operations, . the separation of 2-D morphological operations into a row operation followed by a column operation, . the formulation of these row and column operations in a form compatible with pipelined operation, S the implementation of the resulting operations as simple finite-state machines, and S theautomated generation of the finite-state machine configuration data. Grey-level morphology presents some difficulties to the SKJPSM paradigm having to do with word length. In spite of this, some very useful results can be obtained. Some key features of SKIPSM, as applied to grey-level morphology, are S There is a tradeoffbetween structuring element (SE) size and number of grey levels. . The SEs can be arbitrary . With currently-available components, SEa up to 5x5 and larger can be obtained. S Jfl certain special cases, SEs up to 9x9 and larger can be obtained. . Multiple SEs can be applied simultaneously in a single pipeline pass. S The user specifies the SE or SEs. All other steps can be automated. This paper includes some simple examples of the results and gives implementation feasibility guidelines based on SE size and number of grey levels. The limitations of SKIPSM in this application all relate to the capabilities of the available RAM microchips. As chip capabilities expand, larger SE sizes and greater numbers of grey levels will become feasible. KEYWORDS: image processing, separability, real time, implementations, finite-state machines, grey-level morphology