Basic Mathematical Morphology Operations Research Articles

Neutron–gamma pulse pileup correction based on mathematical morphology and optimized grey model

A new neutron–gamma pulse pileup correction algorithm based on mathematical morphology and optimized grey model is proposed. The pulse characteristic information is extracted through basic mathematical morphology operations to perform pileup discrimination and correction. The hyperbolic tangent function transformation is used to optimize the grey model, and the class ratio dispersion is reduced without reducing the initial sequence smooth ratio, resulting in improved model prediction accuracy. Through experiments, the feasibility of the proposed algorithm is verified and a good correction effect is achieved.

Fault detection for planetary gearbox based on an enhanced average filter and modulation signal bispectrum analysis

Transient impulses are important information for machinery fault diagnosis. However, the transient features contained in the vibration signals generated by planetary gearboxes are usually immersed by a large amount of background noise and harmonic components. Even mathematical morphology (MM) is an excellent anti-noise signal processing method that can directly extract the geometry of impulse features in the time domain, but the four basic operators of MM can only extract one-way impulses while cannot extract the bidirectional impulses effectively at the same time. To accurately extract the impulse feature information, a novel method for fault detection of planetary gearbox based on an enhanced average (EAVG) filter and modulated signal bispectrum (MSB) is proposed. Firstly, the properties of the extracted impulses based on the four basic operators of MM will be divided into two categories of enhanced average operators. The four EAVG filters consist of the average weighted combination of enhanced average operators, and then the best EAVG filter is selected based on correlation coefficient to implement on the original vibration signal. It allows EAVG filter to extract positive and negative impulses of vibration signal, thereby improving the accuracy of planetary gearbox fault detection. Subsequently, the performance of the EAVG filter is influenced by the length of its structural element (SE), which is adaptively determined using an indicator based kurtosis. Then, the EAVG filter selects the optimal SE length to eliminate the interference of background noise and harmonic components to enhance the impulse components of the vibration signal. However, the nonlinear modulation components that are related to the fault types and severities are not extracted exactly and still remained in the filtered signal by EAVG. Finally, the MSB is utilized to the EAVG filtered signal to decompose the modulated components and extract the fault features. The advantages of EAVG over average (AVG) filter are clarified in the simulation study. In addition, the EAVG-MSB is validated by analyzing the vibration signals of planetary gearboxes with sun gear chipped tooth, sun gear misalignment and bearing inner race fault. The results indicate that the EAVG-MSB is effective and accurate in feature extraction compared with the combination morphological filter-hat transform (CMFH) and average combination difference morphological filter (ACDIF), and the feasibility of the EAVG-MSB are proved for planetary gearbox condition monitoring and fault diagnosis.

Balanced morphological filters for horizontal boundaries enhancement of the potential field sources

The enhancement of horizontal boundaries of potential field sources is of great significance for the study of geological structures. Most of the existing filters for horizontal edges enhancement are presented based on the derivatives of potential field data, but these filters often show some shortcomings, for example, the output edges are divergent, strong and weak anomalies cannot be balanced, or some extra false edges appear in the results. In this paper, the edges enhancement filter MMA based on mathematical morphology is first defined by the combination of the basic operators of mathematical morphology. In order to make the filter have the ability to balance different amplitude anomalies, MMAZ and MMAT are proposed, and both of them can be used to delineate the horizontal edges of the field sources by their maxima. The experimental results of synthetic data show that MMAZ and MMAT have good equalization and anti-noise performances. Compared with several traditional filters, the horizontal edges of geological bodies obtained by these two filters are clearer and more convergent, and there are no extra edges in the output results for the complex situations that positive and negative anomalies exist simultaneously. Finally, the two new equalization filters are applied to gravity anomaly data in a potash mine area in Vientiane basin of Laos and the aeromagnetic anomaly of a metal mine in northwest China, the obtained positions of the structures are more accurate and clearer, which further illustrates the effectiveness of the two filtering techniques.

A novel clustering algorithm based on mathematical morphology for wind power generation prediction

Wind power has the characteristic of daily similarity. Furthermore, days with wind power variation trends reflect similar meteorological phenomena. Therefore, wind power prediction accuracy can be improved and computational complexity during model simulation reduced by choosing the historical days whose numerical weather prediction information is similar to that of the predicted day as training samples. This paper proposes a new prediction model based on a novel dilation and erosion (DE) clustering algorithm for wind power generation. In the proposed model, the days with similar numerical weather prediction (NWP) information to the predicted day are selected via the proposed DE clustering algorithm, which is based on the basic operations in mathematical morphology. And the proposed DE clustering algorithm can cluster automatically without supervision. Case study conducted using data from Yilan wind farm in northeast China indicate that the performance of the new generalized regression neural network (GRNN) prediction model based on the proposed DE clustering algorithm (DE clustering-GRNN) is better than that of the DPK-medoids clustering-GRNN, the K-means clustering-GRNN, and the AM-GRNN in terms of day-ahead wind power prediction. Further, the proposed DE clustering-GRNN model is adaptive.

Detection of Age-Related Macular Degeneration in Fundus Images by an Associative Classifier

In this paper we propose the application of a novel associative classifier, the Heaviside's Classifier, for the early detection of Age-Related Macular Degeneration un retinal fundus images. Retinal fundus images are, first, processed by a simple method based on the Homomorphic filtering and some basic mathematical morphology operations; in the second phase we extract relevant features of the images using the Zernike moments, we also apply a feature selection method to select the best features from the original features set. The dataset created from the images with the best features are used to train and test a new classification model whose learning and classification phases are based on the Heaviside's Function. Experimental results show that our method is capable to achieve an accuracy value about the 94.12% with a dataset created from images belonging to famous image repositories.

Adjustment of chest wall thickness of voxel phantom for numerical efficiency calibration of lung counters

A modification method was implemented to adjust the chest wall thickness of human voxel phantom for the purpose of numerical efficiency calibration of lung counters. This method was based on two basic mathematical morphology operations (dilation and erosion) and combined with proper structure elements. The voxel model of LLNL torso phantom was used as a reference to validate the modification process. The chest wall was mathematically modified from the starting phantom with no overlay plate to the target with an overlay plate of 24-mm thickness. The influences of different structure elements on detection efficiency were discussed. When diamond or square structure elements were used, the calculated efficiency was overestimated or underestimated by ∼40 % for 17.5-keV photons, compared with that of target phantom. In contrast, it was shown a good agreement with a deviation of <3 % when the hybrid structure elements were adopted. A similar adjustment method can be used for 3D modification of human voxel phantom to keep the body's anatomical geometry without distortion during the adjustment process.

Digitally Continuous Multivalued Functions, Morphological Operations and Thinning Algorithms

In a recent paper (Escribano et al. in Discrete Geometry for Computer Imagery 2008. Lecture Notes in Computer Science, vol. 4992, pp. 81---92, 2008) we have introduced a notion of continuity in digital spaces which extends the usual notion of digital continuity. Our approach, which uses multivalued functions, provides a better framework to define topological notions, like retractions, in a far more realistic way than by using just single-valued digitally continuous functions. In this work we develop properties of this family of continuous functions, now concentrating on morphological operations and thinning algorithms. We show that our notion of continuity provides a suitable framework for the basic operations in mathematical morphology: erosion, dilation, closing, and opening. On the other hand, concerning thinning algorithms, we give conditions under which the existence of a retraction F:X?X?D guarantees that D is deletable. The converse is not true, in general, although it is in certain particular important cases which are at the basis of many thinning algorithms.

Real-time morphological pipeline architecture using high-capacity programmable logical devices

Mathematical morphology is a very important image analysis area that uses set theory tools to study shapes. The basic operations in mathematical morphology are dilation and erosion, and these can be used to construct more complex operations. Low-level image processing often uses dedicated computing hardware for repetitive processing over large data structures. High-capacity programmable logic devices (HCPLDs) have increasingly been used for the fast development of real-time image processing systems. In this paper we present a pipeline architecture, using high-capacity programmable logic devices, for real-time mathematical morphology operations. The developed architecture can process (512×512) pixel binary images and has flexible stages that can be reprogrammed according to the shape and size of the structuring elements used in the morphological operations. Tests performed over the architecture demonstrated that it performs well when compared to similar architectures and that it is an efficient choice for dedicated morphological image processing operations.

Fast computation of morphological operations with arbitrary structuring elements

This paper presents a general algorithm that performs basic mathematical morphology operations, like erosions and openings, with any arbitrary shaped structuring element in an efficient way. It is shown that our algorithm has a lower or equal complexity but better computing time than all comparable known methods.