CONTRIBUTIONS OF FRACTIONAL CALCULUS TO EARLY VISION

Fractals ◽  
1994 ◽  
Vol 02 (03) ◽  
pp. 387-390
Author(s):  
FRÉDÉRIC FALZON ◽  
GÉRARD GIRAUDON

As for almost all physical signals, useful information for image understanding is contained in the position and nature of singularities. Consequently, a set of early vision methods has been proposed for locating discontinuities of given derivatives with the aim of solving a large class of features extraction problems. Certain early vision tasks also require a more accurate knowledge of pointwise regularity, mainly for evaluating image roughness. We propose to take these requirements into account, by extending the usual singularity detection methods with the help of fractional calculus.

2011 ◽  
Vol 7 (1) ◽  
pp. 1-4
Author(s):  
Haider Hashim ◽  
Anton Prabuwono ◽  
Siti Norul Huda Abdullah

Pre-processing is very useful in a variety of situations since it helps to suppress information that is not related to the exact image processing or analysis task. Mathematical morphology is used for analysis, understanding and image processing. It is an influential method in the geometric morphological analysis and image understanding. It has befallen a new theory in the digital image processing domain. Edges detection and noise reduction are a crucial and very important pre-processing step. The classical edge detection methods and filtering are less accurate in detecting complex edge and filtering various types of noise. This paper proposed some useful mathematic morphological techniques to detect edge and to filter noise in metal parts image. The experimental result showed that the proposed algorithm helps to increase accuracy of metal parts inspection system.


1998 ◽  
Vol 41 (2) ◽  
pp. 166-177 ◽  
Author(s):  
A. Hof

AbstractIn Bernoulli site percolation on Penrose tilings there are two natural definitions of the critical probability. This paper shows that they are equal on almost all Penrose tilings. It also shows that for almost all Penrose tilings the number of infinite clusters is almost surely 0 or 1. The results generalize to percolation on a large class of aperiodic tilings in arbitrary dimension, to percolation on ergodic subgraphs of ℤd, and to other percolation processes, including Bernoulli bond percolation.


Author(s):  
Daniele Mundici

An AF algebra [Formula: see text] is said to be an AF[Formula: see text] algebra if the Murray–von Neumann order of its projections is a lattice. Many, if not most, of the interesting classes of AF algebras existing in the literature are AF[Formula: see text] algebras. We construct an algorithm which, on input a finite presentation (by generators and relations) of the Elliott semigroup of an AF[Formula: see text] algebra [Formula: see text], generates a Bratteli diagram of [Formula: see text] We generalize this result to the case when [Formula: see text] has an infinite presentation with a decidable word problem, in the sense of the classical theory of recursive group presentations. Applications are given to a large class of AF algebras, including almost all AF algebras whose Bratteli diagram is explicitly described in the literature. The core of our main algorithms is a combinatorial-polyhedral version of the De Concini–Procesi theorem on the elimination of points of indeterminacy in toric varieties.


2014 ◽  
Vol 12 (01) ◽  
pp. 1350014 ◽  
Author(s):  
R. RAKSHAMBIKAI ◽  
N. SRINIVASAN ◽  
RUPALI A. GADKARI

In recent times, zebrafish has garnered lot of popularity as model organism to study human cancers. Despite high evolutionary divergence from humans, zebrafish develops almost all types of human tumors when induced. However, mechanistic details of tumor formation have remained largely unknown. Present study is aimed at analysis of repertoire of kinases in zebrafish proteome to provide insights into various cellular components. Annotation using highly sensitive remote homology detection methods revealed "substantial expansion" of Ser/Thr/Tyr kinase family in zebrafish compared to humans, constituting over 3% of proteome. Subsequent classification of kinases into subfamilies revealed presence of large number of CAMK group of kinases, with massive representation of PIM kinases, important for cell cycle regulation and growth. Extensive sequence comparison between human and zebrafish PIM kinases revealed high conservation of functionally important residues with a few organism specific variations. There are about 300 PIM kinases in zebrafish kinome, while human genome codes for only about 500 kinases altogether. PIM kinases have been implicated in various human cancers and are currently being targeted to explore their therapeutic potentials. Hence, in depth analysis of PIM kinases in zebrafish has opened up new avenues of research to verify the model organism status of zebrafish.


1945 ◽  
Vol 9 (1) ◽  
pp. 56-81 ◽  
Author(s):  
L. Radzinowicz

In 1723 a statute was enacted (9 Geo. I, c. 22) bearing the following title: ‘An Act for the more effectual punishing wicked and evil disposed Persons going armed in Disguise, and doing Injuries and Violences to the Persons and Properties of His Majesty's Subjects, and for the more speedy bringing the Offenders to Justice.’ This statute is commonly known as the Waltham Black Act—a name indicative of the local circumstances which led to its being passed. According to Blackstone, the statute was enacted to stop the depredations which were being committed near Waltham, in Hampshire, by persons in disguise or with their faces blacked; he also observes that the technique of these offenders, who operated in the forests of Waltham, seemed to have been modelled on the criminal activities of the famous band of Roberdsmen, or followers of Robert, or Robin, Hood, who committed great outrages in the reign of Richard the First on the border of England and Scotland. An interesting reference to the Waltham Black Act occurs in Gilbert White's ‘The Natural History and Antiquities of Selborne in the County of Southampton,’ and it is significant that while Blackstone cautiously refrains from expressing any opinion on this statute, White says that it is ‘severe and sanguinary’ and that ‘it comprehends more felonies than any law that ever was framed before.’ Actually, no other single statute passed during the eighteenth century equalled 9 Geo. I, c. 22, in severity, and none appointed the punishment of death in so many cases. The Waltham Black Act may, in fact, be looked upon as a kind of ‘ideological index’ to the large body of laws based on the death penalty which were in force in England at the end of the eighteenth, and the beginning of the nineteenth, centuries. The main features peculiar to this Act reappear, sometimes in a modified form, in almost all the other capital statutes of the period. Thus, an accurate knowledge of the Waltham Black Act is essential if the structure and guiding principles of the capital enactments in general are to be understood; moreover, the fact that the struggle for the repeal of this extraordinary statute was both intense and prolonged, further enhances the symptomatic importance of the Act, which might otherwise seem to be but an obscure enactment designed to meet a purely local emergency.


2021 ◽  
Vol 10 (4) ◽  
pp. 2637-2645

People worldwide are experiencing the most dangerous situation concerning the novel severe acute respiratory syndrome known as coronavirus-2 (SARS-CoV-2), commonly referred to as the novel coronavirus disease-2019 (CoViD-19). Since late December 2019, an epidemic of coronavirus disease 2019 (CoViD-19) occurred in Wuhan, China, and rapidly spread to almost all parts of China. With the growing global burden of the CoViD-19 pandemic, scientists, researchers, and healthcare-related organizations constantly work for a viable vaccine or therapeutics, scalable detection methods, personal protection devices, and novel effective medical solutions. Nanotechnology has recently considerably addressed the many clinical and public healthcare issues that have emerged from the CoViD-19 pandemic. The main focus of this current review article is to explore the possibility and potential of nanotechnology to combat this global pandemic and ongoing mitigation techniques and strategies. Furthermore, novel nanotechnology-based products are currently being developed for the prevention, diagnostic, treatment of CoViD-19, which various researchers or healthcare organizations invent.


Object detection in videos is gaining more attention recently as it is related to video analytics and facilitates image understanding and applicable to . The video object detection methods can be divided into traditional and deep learning based methods. Trajectory classification, low rank sparse matrix, background subtraction and object tracking are considered as traditional object detection methods as they primary focus is informative feature collection, region selection and classification. The deep learning methods are more popular now days as they facilitate high-level features and problem solving in object detection algorithms. We have discussed various object detection methods and challenges in this paper.


Author(s):  
Gioacchino Antonelli ◽  
Andrea Merlo

AbstractThis paper deals with the theory of rectifiability in arbitrary Carnot groups, and in particular with the study of the notion of $$\mathscr {P}$$ P -rectifiable measure. First, we show that in arbitrary Carnot groups the natural infinitesimal definition of rectifiabile measure, i.e., the definition given in terms of the existence of flat tangent measures, is equivalent to the global definition given in terms of coverings with intrinsically differentiable graphs, i.e., graphs with flat Hausdorff tangents. In general we do not have the latter equivalence if we ask the covering to be made of intrinsically Lipschitz graphs. Second, we show a geometric area formula for the centered Hausdorff measure restricted to intrinsically differentiable graphs in arbitrary Carnot groups. The latter formula extends and strengthens other area formulae obtained in the literature in the context of Carnot groups. As an application, our analysis allows us to prove the intrinsic $$C^1$$ C 1 -rectifiability of almost all the preimages of a large class of Lipschitz functions between Carnot groups. In particular, from the latter result, we obtain that any geodesic sphere in a Carnot group equipped with an arbitrary left-invariant homogeneous distance is intrinsic $$C^1$$ C 1 -rectifiable.


Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 43 ◽  
Author(s):  
Min Cai ◽  
Changpin Li

Fractional calculus, albeit a synonym of fractional integrals and derivatives which have two main characteristics—singularity and nonlocality—has attracted increasing interest due to its potential applications in the real world. This mathematical concept reveals underlying principles that govern the behavior of nature. The present paper focuses on numerical approximations to fractional integrals and derivatives. Almost all the results in this respect are included. Existing results, along with some remarks are summarized for the applied scientists and engineering community of fractional calculus.


1857 ◽  
Vol 147 ◽  
pp. 601-620 ◽  

In order to determine whether the act of photo-chemical combination necessitates the production of a certain amount of mechanical effect, for which an equivalent quantity of light is expended, or whether this phenomenon is dependent upon a restoration of equilibrium effected without any corresponding equivalent loss of light, we must study more specially the phenomena occurring at the bounding surfaces, and in the interior of a medium exposed to the chemically active rays. A certain large class of bodies permit the chemical rays to pass through them to a greater or less extent, whilst other substances are opake to these rays. The first class, to which the name “diactinous” maybe given, includes almost all colourless, blue, and violet media; the second class of “anactinous” bodies consists chiefly of opake, and yellow or red substances. Although the terms “diactinous” and “anactinous,” like “diathermanous,” “ diaphanous,” &c., merely represent phases of the same difference, and can therefore bear no strict scientific definition, yet we do not hesitate to employ these terms as a means of avoiding a tedious circumlocution.


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