Markus Kiderlen, Jan Rataj · ArXiv.org · 2025
Given a convex body $Q$ (structuring element) and a set $A$ in a Euclidean space, we consider the $Q$-Minkowski content of $A$. It is defined as the usual isotropic Minkowski content of $A$, but where the Euclidean ball is replaced by $Q$. When $Q$ is full-dimensional, the existence of the $Q$-Minkowski content can be assured by a sufficient condition which was stated by Ambrosio, Fusco and Pallara in the isotropic case. If $Q$ is not full-dimensional, we show that a weaker condition is sufficient for this purpose. We also consider the outer $Q$-Minkowski content of $A$ yielding the anisotropic perimeter of $A$ and we find a sufficient condition for its existence. Finally, we present an example of a set in three-dimensional Euclidean space, which does not admit the isotropic outer Minkwski content, but it admits the outer $Q$-Minkowski content for all two-dimensional disks $Q$.
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Nicolas Normand · Lecture notes in computer science · 2003
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Aurélie Bouvet, Yoan Paillet, Frédéric Archaux et al. · HAL (Le Centre pour la Communication Scientifique Directe) · 2013
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Xiaopeng Wang, Jing Li, Yue Liu · Optoelectronics Letters · 2014
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Akira Taguchi, Takumi Komori · 1998
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Marc Aiguier, Isabelle Bloch, Ramón Pino Pérez · arXiv (Cornell University) · 2020
A general definition of mathematical morphology has been defined within the algebraic framework of complete lattice theory. In this framework, dealing with deterministic and increasing operators, a dilation (respectively an erosion) is an operation which is distributive over supremum (respectively infimum). From this simple definition of dilation and erosion, we cannot say much about the properties of them. However, when they form an adjunction, many important properties can be derived such as monotonicity, idempotence, and extensivity or anti-extensivity of their composition, preservation of infimum and supremum, etc. Mathematical morphology has been first developed in the setting of sets, and then extended to other algebraic structures such as graphs, hypergraphs or simplicial complexes. For all these algebraic structures, erosion and dilation are usually based on structuring elements. The goal is then to match these structuring elements on given objects either to dilate or erode them. One of the advantages of defining erosion and dilation based on structuring elements is that these operations are adjoint. Based on this observation, this paper proposes to define, at the abstract level of category theory, erosion and dilation based on structuring elements. We then define the notion of morpho-category on which erosion and dilation are defined. We then show that topos and more precisely topos of presheaves are good candidates to generate morpho-categories. However, topos do not allow taking into account the notion of inclusion between substructures but rather are defined by monics up to domain isomorphism. Therefore we define the notion of morpholizable category which allows generating morpho-categories where substructures are defined along inclusion morphisms. {A direct application of this framework is to generalize modal morpho-logic to other algebraic structures than simple sets.
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Neethu M. Sasi, V. K. Jayasree · International Journal of Computer Theory and Engineering · 2017
The application of radioactive isotopes for imaging human body parts developed into nuclear imaging technology, including single photon emission computed tomography imaging (SPECT). Visual inspection and interpretation of SPECT images is a challenging task as there is random scattering of photons during the image reconstruction process which affects its contrast. Recognizing even gradual changes in color intensity aids in the interpretation of images. The paper proposes a new image processing technique to enhance cardiac nuclear images generated by a single photon emission computed tomography device by improving the contrast features. The method utilizes the concept of adaptive techniques in morphology. As an initial step, color space conversion is performed to convert the image to a color space suitable for its processing and each slice or tile corresponding to the gated cardiac cycle is extracted. In the second step, the size of the neighbourhood area is selected for the operation of the structuring element. Morphological processing is done as a final step. This methodology can be used as a pre-processing module for computer aided diagnostic systems. The proposed method employs a novel image dependent technique for the enhancement of cardiac SPECT images making use of morphology in a suitable color space. Qualitative and quantitative evaluations prove the effective performance of the proposed algorithm in enhancing cardiac SPECT images.
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Jin Li, Xiao Xiao, Zi-Jie Liu et al. · WIT transactions on engineering sciences · 2015
Welcome to the WIT Press eLibrary - the home of the Transactions of the Wessex Institute collection, providing on-line access to papers presented at the Institute's prestigious international conferences and from its State-of-the-Art in Science & Engineering publications.
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Sri Huning Anwariningsih · 2010
Morfologi adalah salah satu metode pada pengolahan citra untuk analisa bentuk objek. Pemrosesan citra secara morfologi dilakukan dengan cara menerapkan sebuah structuring element (strel) terhadap sebuah citra dengan cara yang hampir sama dengan konvolusi. Structuring element memegang peranan penting dalam pengolahan citra dengan morfologi. Pemilihan bentuk dan ukuran structuring element sangat berpengaruh terhadap hasil pengolahan citra. Sebuah structuring element yang sesuai digunakan pada sebuah objek, belum tentu sesuai digunakan pada objek lain. Belum ada pedoman baku untuk menentukan bentuk structuring element. Umumnya pemilihan structuring element hanya didasarkan pada kemiripan bentuk dengan objek yang diteliti yang ditentukan secara manual. Pada penelitian ini diusulkan suatu metode estimasi bentuk structuring element berdasar pada representasi bentuk objek yang diteliti. Representasi bentuk yang digunakan berbasis shape matrix. Representasi objek ini akan membantu menentukan bentuk structuring element pada objek yang diteliti karena bentuk structuring element yang digunakan akan sesuai dengan representasi objek yang diteliti. Sedangkan untuk menguji kinerja, bentuk structuring element yang didapatkan diujicobakan untuk deteksi tepi menggunakan operasi morfologi gradien. Hasil uji coba pada 30 sampel data citra sintetis menunjukkan bahwa algoritma deteksi tepi menggunakan metode shape descriptor berbasis shape matrix ini terbukti dapat diandalkan dengan akurasi rata-rata sebesar 99,6 %. Sedangkan pada citra riil, algoritma algoritma deteksi tepi menggunakan metode shape descriptor berbasis shape matrix ini terbukti juga dapat diandalkan dengan akurasi rata-rata sebesar 98,4 %.
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I Gusti Ngurah Agung Pawana, I Made Oka Widyantara, Made Sudarma et al. · International Journal of Advanced Computer Science and Applications · 2025
Coastal monitoring is vital in environmental management, disaster mitigation, and addressing climate change impacts. Traditional methods are time-consuming and error-prone, prompting the need for innovative systems. This study introduces the Coastal Video Monitoring System (CoViMos), a novel framework for real-time shoreline detection in tropical regions, specifically at Kedonganan Beach, Bali. The CoViMos framework utilizes advanced video monitoring and optimized morphological operations to address challenges such as environmental noise and dynamic shoreline behavior. Key innovations include Kapur’s entropy thresholding enhanced with the Grasshopper Optimization Algorithm (GOA) and structuring elements tailored to the beach’s unique features. Sensitivity analysis reveals that a structuring element size of five pixels offers optimal performance, balancing efficiency, and image fidelity. This configuration achieves peak values in quality metrics such as the Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index (SSIM), Complex Wavelet SSIM (CWSSIM), and Feature Similarity Index (FSIM) while minimizing Mean Squared Error (MSE) and reducing processing time. The results demonstrate significant improvements in shoreline detection accuracy, with PSNR increasing by 9.3%, SSIM by 1.4%, CWSSIM by 1.7%, and FSIM by 1.6%. Processing time decreased by 1.3%, emphasizing the system’s computational efficiency. These enhancements ensure more precise shoreline mapping, even in noisy and dynamic environments.
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Yosuke Nabetani, Mitsuji Muneyasu, Akira Asano · 2013
In this paper, we propose an unsupervised design method for optimal structuring element (SE) of morphological filters. We formulate the design of SE as an optimization problem, and estimate an optimal shape and brightness of SE directly from degraded images. We estimated an optimal shape and brightness by using a Genetic Algorithm (GA). Estimation of SE that can remove noise while preserving original signals is achieved by objective function that use Rank-Ordered Logarithmic Differences (ROLD) statistic for the impulse noise detection.
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YANG Wenting, WANG Xiaopeng, FANG Chao · SHILAP Revista de lepidopterología · 2021
Classical mathematical morphology operations use a fixed size and shape structuring element to process the whole image. Due to the diversity of image content and the complexity of target structure, for processed image, its shape may be changed and part of the information may be lost. Therefore, we propose a method for constructing salience adaptive morphological structuring elements based on minimum spanning tree（MST）. First, the gradient image of the input image is calculated, the edge image is obtained by non-maximum suppression（NMS） of the gradient image, and then chamfer distance transformation is performed on the edge image to obtain a salience map（SM）.Second, the radius of structuring element is determined by calculating the maximum and minimum values of SM and then the minimum spanning tree is calculated on the SM. Finally, the radius is used to construct a structuring element whose shape and size adaptively change with the local features of the input image. In addition, the basic morphological operators such as erosion, dilation, opening and closing are redefined using the adaptive structuring elements and then compared with the classical morphological operators. The simulation results show that the proposed method can make full use of the local features of the image and has better processing results in image structure preservation and image filtering.
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Xiangzhi Bai, Fugen Zhou · Signal Processing · 2010
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Kun Li, Xie Chengkun · 2002
Mathematical morphology, which is a set theoretical methodology for image analysis, can rigorously quantify many aspects of the geometrical structure of signals in a way that agrees with human intuition and perception. The paper, which is based on the synthetical idea, analyzes the decomposition of a morphological structuring element. For any N-point structuring element, it concludes that the correct lower bound of decomposition is e/spl middot/lnN.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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Yueh-fang Wu · RIT Scholar Works (Rochester Institute of Technology) · 1999
None provided.
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Louis Bornancin, Isabelle Bonnard, Suzanne C. Mills et al. · Natural Product Reports · 2017
Covering: up to 2017Chemical mediation regulates behavioral interactions between species and thus affects population structure, community organization and ecosystem function. Among marine taxa that have developed chemical mediation strategies, gastropods belong to a diverse group of molluscs found worldwide, including species with a coiled, reduced or absent shell. Most gastropods use natural products to mediate a wide range of behaviors such as defense, prey location or interactions with con- and hetero-geners. Their chemically defended diet, such as cyanobacteria, algae, sponges, bryozoans and tunicates, provides them with a considerable opportunity either as shelter from predators, or as a means to enhance their own chemical defense. In addition to improving their defenses, molluscs also use prey secondary metabolites in complex chemical communication including settlement induction, prey detection and feeding preferences. The assimilation of prey secondary metabolites further provides the opportunity for interactions with conspecifics via diet-derived chemical cues or signals. This review intends to provide an overview on the sequestration, detoxification, and biotransformation of diet-derived natural products, as well as the role of these compounds as chemical mediators in gastropod-prey interactions.
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Ringo Wai-Kit Lam, Horace H. S. Ip, Chi-Kwong Li · 2002
The fast morphological algorithm, overlapping search (OS) algorithm, recently proposed by Lam and Li (1998), can only be applied to a flat structuring element (FSE) whose 1D Euler-Poincare constants, N/sup (1)/(x) and N/sup (1)/(y), at any x or y coordinate are equal to 1. Thus, an arbitrarily shaped structuring element must be decomposed to a set of constrained components before employing the fast algorithm. In the paper, a decomposition algorithm, based on line-scanning process, and an improved algorithm, based on conditionally maximal convex polygon (CMCP), are proposed to generalize the use of the overlapping search morphological algorithm for any arbitrary flat structuring element.
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Felix Weber · 2019
The Future Skills Report about the future of learning and higher Education (Ehlers & Kellermann, 2019) defines a varietyof skills in which the active learner plays a central role. Starting from this perspective, our idea is to promote future
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Guoquan Ren, Yanlong Chen, Chengzhu Li et al. · Shock and Vibration · 2019
In order to solve the disadvantage of conventional structuring element (CSE) where amplitude does not change in accordance with the analyzed signal, the quantum theory is combined and a nonlinear quantum‐inspired weighting structuring element (NQWSE) is proposed. The NQWSE which is utilized to extract the bearing impulse response signal can adjust its amplitude according to the mechanical signal. Firstly, after constructing the multiple quantum bits system for signals, the mapping method which is employed to map the quantum space to the real space is presented and the parameters of the mapping method are set. The nonlinear amplitude probability is calculated based on the stochastic characteristics of the bearing signals, while the dynamic amplitude is calculated based on the local feature of the bearing signals in a subwindow. Then the mathematical formula of NQWSE is derived by incorporating the mathematical expectation into the quantum theory and the mapping method. Finally, the NQWSE is applied to extract the fault information of a failure bearing. The results reveal that NQWSE can extract the bearing impulse response signals exactly.
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Qiong Chen, Zhaowen Chen, Wei Sun et al. · Journal of Vibration and Control · 2013
The condition monitoring and fault diagnosis of rolling element bearings play an important role in the safe and reliable operation of rotating machinery. Feature extraction based on vibration signals is an effective means to identify the operating condition of rolling element bearings. Methods based on multi-scale mathematical morphology (MM) have recently been developed to extract features from one-dimensional signals. In this paper, a new double-dot structuring element (SE) is constructed for multi-scale MM. A pattern spectrum, obtained from the multi-scale MM, is used as a feature extraction index. A correlation analysis gives the final identification result by utilizing information over a whole pattern spectrum. Compared with the most commonly used flat SE, the double-dot SE can extract more features of original signals at different scales. Vibration signals, measured from defective bearings with outer race faults, inner race faults and ball faults, are used to evaluate the fault detection ability of the proposed SE and bearing fault diagnosis method. Results show that faults at different levels can be identified, including ball fault; and the location of outer race fault can also be differentiated.
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