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This work concerns the Perona-Malik equation, which plays essential role in image processing. The first part gives a survey of results on existance, uniqueness and stability of solutions, the second part introduces discretisations of equation and deals with an analysis of discrete problem. In the last part I present some numerical results, in particular with algorithms applied to real images.
This study aims to reveal the view of Imam Malik about maslahat as an independent proposition in the determination of Islamic law. Trying to explain the terminology of maslahat, uncovering the dimensions of maslahat in the determination of Islamic law, analyzing maslahat as a basis of Islamic law that stands alone to establish Islamic law according to Imam Malik, and citing examples of Imam Malik's fatwa based on consideration of maslahat. This paper is a qualitative descriptive study using a multidisciplinary approach including normative, philosophical, and sociological approaches. This study shows that maslahat contains two sides, namely attracting or bringing benefit and rejecting or avoiding harm in order to maintain the goals of shari'ah, the establishment of Islamic law aims at realizing human benefit that is universal, generally accepted and lasting for all humans and in all circumstances. Imam Malik is of the view that maslahat can be used as a basis for independent legal considerations, without the need for legitimation of the shar'i proposition. For example, Imam Malik establishes the saliva of a holy dog. The fatwa is not in line with the instructions of the hadith that classify it as unclean. Imam Malik was not the first scholar to settle such a law, but his companions had experienced such cases, they then resolved these problems by issuing fatwas that were "contrary to" the instructions of zhahir nas. Therefore, the renewal of Islamic law can be done through maslahat considerations, such as those taken by Imam Malik, in order to provide legal answers to problems faced by the community, so that Islamic law appears to live dynamically in a society that continues to experience changes and developments.
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This article explores the work of the writer, rapper and slam poet Abd Al Malik, who shook up the music world with his message of religious tolerance in the midst of the suburb riots in France in 2005 and the Charlie Hebdo attack in 2015. It shows how he builds on his religious conversions and revelations to pose challenging questions about Islam, its interpretations, and its relationship with French society. In his essays and novel, he challenges the readiness of France to accept Muslim culture in its national and cultural identity. In his last novel, he tells the story of a converted Muslim frontrunner in a national presidential election and his reception by the French population. Malik campaigns in favour of a post-religious France through his music and through his literary works. He dismantles the idea that Islam is a religion of people of colour and insists on its multi-ethnicity. His ideal post-religious France would be based on acceptability and inclusivity, love and universalism. Malik insists that Islam is not radicalism. According to him the Islamist message that he denounces is based on a narrow and ‘ignorant’ interpretation of Islam, which negates both modernity and the Western world. Malik, as a Sufi Muslim, suggests that Islam actually enables religious practices that embrace deep French values and promote the aspiration to ‘vivre ensemble’.
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Anisotropic diffusion is used for both image enhancement and denoising. The Perona-Malik model makes use of anisotropic diffusion to filter out the noise. In Perona-Malik model the rate of diffusion is controlled by edge stopping function. The drawback of Perona-Malik model is that the sharp edges and fine details are not preserved well in the denoised image. But the sharp edges and fine details can be preserved well using appropriate edge stopping function. We have analysed the effect of different edge stopping functions in anisotropic diffusion in terms of how efficient they are in preserving edges. We have found that an edge stopping function which stops diffusion from low image gradient onwards well preserves the sharp edges and fine details. This property of an edge stopping function will also result in lower evolution in case of level set methods. But an edge stopping function which stops diffusion from high image gradient onwards will not preserve sharp edges and fine details, since they are blurred due to diffusion. We have also found that low values of gradient threshold parameter used in edge stopping function well preserves the sharp edges and fine details than high values of threshold parameter. By utilizing an edge stopping function which stops diffusion from low image gradient onwards or which has zero or insignificant value at low image gradient, we can well preserve the sharp edges and fine details in the denoised image.
The globalization era which is full of challenges couldnot be avoided. Therefore, the educational institutions, especially islamic education, should be able to answer those challenges in order to change the direction of educational orientation. One of figures who is serious in building educational thinking paradigm is A. Malik Fadjar. This study aims to explore his educational thinking paradigm and educational concept proposed. A. Malik Fadjar faces the challenge of global era. The result of study showed that his educational thinking paradigm is holistic; in which the education is humanists, liberative, integralistics, multicultural and futuristic, either in the aspect of vision and mision, institution, management, patterns of educational interaction, curriculum, and educator. To face global era, A Malik Fadjar states that there are three big challenges, they are to protect the result achieved, anticipate the global era, and do some changes and adjustment of the national education system.
An impressive and efficient improvement in the classical scale-space analysis was proposed by Perona and Malik (1990) where they describe the diffusion process known as the Perona-Malik (PM) equation. Despite the illposed nature of the PM equation, many of its applications could be carried with success in the signal processing field. On the other hand Weickert and Benamouda (1997) proved the regularization of the PM equation describing and analyzing a model on a semidiscrete system. In this article we present a regularized model of the PM diffusion equation for image segmentation. We start from the hypothesis of well-posedness in the discrete space and the stability conditions. We show two methods for automatic setting of the gradient threshold k, which is changed for each iteration of the partial differential equation (PDE) integration steps. Experimental segmentations are implemented for noise reduction of generic digital images and for segmentation of microcalcifications on X-ray biomedical images.
Original Islam investigates the primacy of Madinan Islam and the madhhab (school of law) of its main exponent, Malik ibn Anas. It contains an annotated translation of Intisar al-faqir al-salik li-tarjih madhhab al-Imam al-kabir Malik, which was written by al-Ra'i, a fifteenth-century Andalusian scholar resident in Cairo.This book includes:a comprehensive section on the scholarly credentials of the great eighth-century Madinan jurist Malik ibn Anas a detailed examination of a number of theoretical and practical disputed legal issues examples of the inter-madhhab rivalry and prejudice prevalent
The so-called first letter of Ibn Ibâḍ was long considered in modern scholarship as an authentic letter of ‘Abd Allâh b. Ibâḍ, the reputed founder of the Ibâḍiyya sect, to the Umayyad caliph ‘Abd al-Malik. This was questioned first by John Wilkinson and then by Michael Cook in his book on Early Muslim Theology, who proposed that the letter was written rather by Jâbir b. Zayd to the Muhallabid amîr ‘Abd al-Malik b. al-Muhallab. In his recent book on Ibadism, John Wilkinson has argued that the letter was addressed to ‘Abd al-Malik, the son of the caliph ‘Umar II, and that Jâbir b. Zayd could not have been its author. It will be argued in this paper that the letter is an authentic letter of ‘Abd Allâh b. Ibâḍ addressed to the son of ‘Umar II. Ibn Ibâḍ was not the founder of the Ibâḍiyya sect, but rather a contemporary and rival of Abû ‘Ubayda Muslim b. Abî Karîma.
In this paper, a hybrid image denoising algorithm based on directional diffusion is proposed. Specifically, we developed a new noise-removal model by combining the modified isotropic diffusion model and the modified Perona-Malik (PM) model. The novel hybrid model can adapt the diffusion process along the tangential direction of edges in the original image via a new control function based on the patch similarity modulus. In addition, the patch similarity modulus is used as the new structure indicator for the modified Perona-Malik model. The feature of second-order directional derivative of edge's tangential direction allows the proposed model to reduce the aliasing and the noise around edge during edge preserving smoothing. The proposed method is thus able to efficiently preserve the edges, textures, thin lines, weak edges, and fine details, meanwhile preventing the staircase effects. Computer experiments on synthetic image and nature images demonstrate that the proposed model achieves a better performance than the conventional partial differential equations models and some recent advanced models.
A new class of anisotropic diffusion models is proposed for image processing which can be viewed either as a novel kind of regularization of the classical Perona--Malik model or, as advocated by the authors, as a new independent model. The models are diffusive in nature and are characterized by the presence of both forward and backward regimes. In contrast to the Perona--Malik model, in the proposed model the backward regime is confined to a bounded region, and gradients are only allowed to grow up to a large but tunable size, thus effectively preventing indiscriminate singularity formation, i.e., staircasing. Extensive numerical experiments demonstrate that the method is a viable denoising/deblurring tool. The method is significantly faster than competing state-of-the-art methods and appears to be particularly effective for simultaneous denoising and deblurring. An application to satellite image enhancement is also presented.
This article introduces generalizations of the Perona-Malik (1990) equation. An edge enhancing functional is proposed for direct edge enhancement. A number of super diffusion operators is introduced for fast and effective smoothing. Statistical information is utilized for robust edge-stopping. Numerical integration is conducted by using a previously developed quasi-interpolating wavelet method. Computer experiments indicate that the present algorithm is very efficient for edge-detecting and noise-removing.
Numismatic evidence is an essential source for reconstructing the visual and textual history of the first eight decades of Islamic rule, particularly the reign of the Marwanid caliph ʿAbd al-Malik, when a large number of coin varieties, many with human representation, were struck. This chapter begins with the premise that when a new coin type was struck the new elements were added as the result of unique historical factors. The increasing use of Arabic in the form of pious phrases and Qurʾanic verses, and of other data such as mint names and dates is one of the hallmarks of this coinage and is traced through the all-epigraphic issues of A.H. 77 and 78. The chapter discusses the emergence of a series of pious phrases found on contemporary coinage, milestones, and tombstones, and in the Dome of the Rock, which have been labeled in all the modern literature as the shahāda.Keywords: ʿAbd al-Malik; coinage; Dome of the Rock; Islam; Qurʾanic verses; shahāda
We prove that for all smooth nonconstant initial data the initial-Neumann boundary value problem for the Perona--Malik equation in image processing possesses infinitely many Lipschitz weak solutions on smooth bounded convex domains in all dimensions. Such existence results have not been known except for the one-dimensional problems. Our approach is motivated by reformulating the Perona--Malik equation as a nonhomogeneous partial differential inclusion with linear constraint but some uncontrollable components of gradient. We establish a general existence result by a suitable Baire category method under a pivotal density hypothesis. We finally fulfill this density hypothesis by convex integration based on certain approximations from an explicit formula of lamination convex hull of some matrix set involved.
This paper introduces a class of adaptive Perona-Malik (PM) diffusion, which combines the PM equation with the heat equation. The PM equation provides a potential algorithm for image segmentation, noise removal, edge detection, and image enhancement. However, the defect of traditional PM model is tending to cause the staircase effect and create new features in the processed image. Utilizing the edge indicator as a variable exponent, we can adaptively control the diffusion mode, which alternates between PM diffusion and Gaussian smoothing in accordance with the image feature. Computer experiments indicate that the present algorithm is very efficient for edge detection and noise removal.
Malik Goes to School: Examining the Language Skills of African American Students From Preschool-5th Grade synthesizes a decade of research by the authors, Holly Craig and Julie Washington, on the oral language and literacy skills of African American children from preschool to fifth grade. Their research has characterized significant influences on the child's use of AAE and the relationship between AAE and aspects of literacy acquisition. The research has also led to the characterization of other nondialectal aspects of language development. The outcome has been a culture-fair, child-centered language evaluation protocol.This very readable volume will be important to students, clinicians, and teachers, learning about and working with, African American children. The book has direct relevance to academic planning, clinical decision-making, curriculum development, and educational policymaking.
Contents: W. Wolfram, Foreword. Preface. Who Is Malik? An Overview of Research on Child AAE. Our School-Based Participants and Sampling Procedures. Features of Child AAE. Distributional Properties of AAE in the Early Grades. Nondialectal Expressive and Receptive Language Skills. Evaluating Language at School Entry. African American Children in Academic Distress. Relationships Among Language and Literacy Skills for African American Students. Summary and Final Thoughts. Appendices.
Abstract We investigate how the Perona‐Malik scheme evolves piecewise smooth initial data in one dimension. By scaling a natural parameter that appears in the scheme in an appropriate way with respect to the grid size, we obtain a meaningful continuum limit. The resulting evolution can be seen as the gradient flow for an energy, just as the discrete evolutions are gradient flows for discrete energies. It involves, except at special isolated times, solving a system of heat equations coupled to each other through nonlinear boundary conditions. At the special times, the solutions experience gradient blowup; nevertheless, there is a natural continuation for the solutions beyond these singular times. © 2001 John Wiley & Sons, Inc.
We propose time regularizations for ill posed evolution equations of the type of the Perona-Malik equation of image processing, prove that they are well posed, and give numerical evidence for their superiority to the widely used space regularizations.