Relevant bibliographies by topics / Calculus of tensors Computer graphics

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Calculus of tensors Computer graphics'

Author: Grafiati
Published: 4 June 2021
Last updated: 13 February 2022

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Journal articles on the topic "Calculus of tensors Computer graphics"

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Wood, Christopher J., Jacob D. Biamonte, and David G. Cory. "Tensor networks and graphical calculus for open quantum systems." Quantum Information and Computation 15, no. 9&10 (July 2015): 759–811. http://dx.doi.org/10.26421/qic15.9-10-3.

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We describe a graphical calculus for completely positive maps and in doing so review the theory of open quantum systems and other fundamental primitives of quantum information theory using the language of tensor networks. In particular we demonstrate the construction of tensor networks to pictographically represent the Liouville-superoperator, Choi-matrix, process-matrix, Kraus, and system-environment representations for the evolution of quantum states, review how these representations interrelate, and illustrate how graphical manipulations of the tensor networks may be used to concisely transform between them. To further demonstrate the utility of the presented graphical calculus we include several examples where we provide arguably simpler graphical proofs of several useful quantities in quantum information theory including the composition and contraction of multipartite channels, a condition for whether an arbitrary bipartite state may be used for ancilla assisted process tomography, and the derivation of expressions for the average gate fidelity and entanglement fidelity of a channel in terms of each of the different representations of the channel.
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Lončarić, Nataša, and Marko Kraljić. "Matrices in computer graphics." Tehnički glasnik 12, no. 2 (June 28, 2018): 120–23. http://dx.doi.org/10.31803/tg-20180119143651.

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In this article, the usage of matrices and matrix operations in computer graphics is shown. A brief overview of geometric transformations in computer graphics is given. The "Matrix - Computer Graphics" application software is created for the representation and easier understanding of relations between geometric transformations and matrix calculus.
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Desbrun, Mathieu. "Applied Geometry:Discrete Differential Calculus for Graphics." Computer Graphics Forum 23, no. 3 (September 2004): 269. http://dx.doi.org/10.1111/j.1467-8659.2004.00756.x.

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Acar, Umut A., Arthur Charguéraud, Mike Rainey, and Filip Sieczkowski. "Dag-calculus: a calculus for parallel computation." ACM SIGPLAN Notices 51, no. 9 (December 5, 2016): 18–32. http://dx.doi.org/10.1145/3022670.2951946.

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Pletinckx, Daniel. "Quaternion calculus as a basic tool in computer graphics." Visual Computer 5, no. 1-2 (January 1989): 2–13. http://dx.doi.org/10.1007/bf01901476.

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Bos, Jan. "RasterCalc: Calculus for Operations on Graphics Colour Rasters." Computer Graphics Forum 6, no. 3 (September 1987): 181–93. http://dx.doi.org/10.1111/j.1467-8659.1987.tb00538.x.

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Oliveira, Bruno C. d. S., Tom Schrijvers, Wontae Choi, Wonchan Lee, and Kwangkeun Yi. "The implicit calculus." ACM SIGPLAN Notices 47, no. 6 (August 6, 2012): 35–44. http://dx.doi.org/10.1145/2345156.2254070.

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Schmitt, Alan, and Jean-Bernard Stefani. "The m-calculus." ACM SIGPLAN Notices 38, no. 1 (January 15, 2003): 50–61. http://dx.doi.org/10.1145/640128.604136.

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Ernst, Erik, Klaus Ostermann, and William R. Cook. "A virtual class calculus." ACM SIGPLAN Notices 41, no. 1 (January 12, 2006): 270–82. http://dx.doi.org/10.1145/1111320.1111062.

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Hayashi, Koby, Grey Ballard, Yujie Jiang, and Michael J. Tobia. "Shared-memory parallelization of MTTKRP for dense tensors." ACM SIGPLAN Notices 53, no. 1 (March 23, 2018): 393–94. http://dx.doi.org/10.1145/3200691.3178522.

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Dissertations / Theses on the topic "Calculus of tensors Computer graphics"

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Ng, Ho Lun. "ROD-TV : surface reconstruction on demand by tensor voting /." View Abstract or Full-Text, 2003. http://library.ust.hk/cgi/db/thesis.pl?COMP%202003%20NG.

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Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2003.
Includes bibliographical references (leaves 123-127). Also available in electronic version. Access restricted to campus users.
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Tong, Dickson Wai Shun. "A complete theory on 3D tensor voting for computer vision and graphics applications /." View abstract or full-text, 2004. http://library.ust.hk/cgi/db/thesis.pl?COMP%202004%20TONG.

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Thesis (Ph. D.)--Hong Kong University of Science and Technology, 2004.
Includes bibliographical references (leaves 158-162). Also available in electronic version. Access restricted to campus users.
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Tall, David Orme. "Building and testing a cognitive approach to the calculus using interactive computer graphics." Thesis, University of Warwick, 1986. http://wrap.warwick.ac.uk/2409/.

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This thesis consists of a theoretical building of a cognitive approach to the calculus and an empirical testing of the theory in the classroom. A cognitive approach to the teaching of a knowledge domain is defined to be one that aims to make the material potentially meaningful at every stage (in the sense of Ausubel). As a resource in such an approach, the notion of a generic organiser is introduced (after Dienes), which is an environment enabling the learner to explore examples of mathematical processes and concepts, providing cognitive experience to assist in the abstraction of higher order concepts embodied by the organiser. This allows the learner to build and test concepts in a mode 1 environment (in the sense of Skemp) rather than the more abstract modes of thinking typical in higher mathematics. The major hypothesis of the thesis is that appropriately designed generic organisers, supported by an appropriate learning environment, are able to provide students with global gestalts for mathematical processes and concepts at an earlier stage than occurs with current teaching methods. The building of the theory involves an in-depth study of cognitive development, of the cultural growth and theoretical content of the mathematics, followed by the design and programming of appropriate organisers for the teaching of the calculus. Generic organisers were designed for differentiation (gradient of a graph), integration (area), and differential equations, to be coherent ends in themselves as well as laying foundations for the formal theories of both standard and non-standard analysis. The testing is concerned with the program GRADIENT, which is designed to give a global gestalt of the dynamic concept of the gradient of a graph. Three experimental classes (one taught by the researcher in conjunction with the regular class teacher) used the software as an adjunct to the normal study of the calculus and five other classes acted as controls. Matched pairs were selected on a pre-test for the purpose of statistical comparison of performance on the post-test. Data was also collected from a third school where the organisers functioned less well, and from university mathematics students who had not used a computer. The generic organiser GRADIENT, supported by appropriate teaching, enabled the experimental students to gain a global gestalt of the gradient concept. They were able to sketch derivatives. for given graphs significantly better than the controls on the post-test, at a level comparable with more able students reading mathematics at university. Their conceptualizations of gradient and tangent transferred to a new situation involving functions given by different formulae on either side of the point in question, performing significantly better than the control students and at least as well, or better, than those at university.
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Mu, Cun. "Structured Tensor Recovery and Decomposition." Thesis, 2017. https://doi.org/10.7916/D8DV1X6M.

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Tensors, a.k.a. multi-dimensional arrays, arise naturally when modeling higher-order objects and relations. Among ubiquitous applications including image processing, collaborative filtering, demand forecasting and higher-order statistics, there are two recurring themes in general: tensor recovery and tensor decomposition. The first one aims to recover the underlying tensor from incomplete information; the second one is to study a variety of tensor decompositions to represent the array more concisely and moreover to capture the salient characteristics of the underlying data. Both topics are respectively addressed in this thesis. Chapter 2 and Chapter 3 focus on low-rank tensor recovery (LRTR) from both theoretical and algorithmic perspectives. In Chapter 2, we first provide a negative result to the sum of nuclear norms (SNN) model---an existing convex model widely used for LRTR; then we propose a novel convex model and prove this new model is better than the SNN model in terms of the number of measurements required to recover the underlying low-rank tensor. In Chapter 3, we first build up the connection between robust low-rank tensor recovery and the compressive principle component pursuit (CPCP), a convex model for robust low-rank matrix recovery. Then we focus on developing convergent and scalable optimization methods to solve the CPCP problem. In specific, our convergent method, proposed by combining classical ideas from Frank-Wolfe and proximal methods, achieves scalability with linear per-iteration cost. Chapter 4 generalizes the successive rank-one approximation (SROA) scheme for matrix eigen-decomposition to a special class of tensors called symmetric and orthogonally decomposable (SOD) tensor. We prove that the SROA scheme can robustly recover the symmetric canonical decomposition of the underlying SOD tensor even in the presence of noise. Perturbation bounds, which can be regarded as a higher-order generalization of the Davis-Kahan theorem, are provided in terms of the noise magnitude.
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Books on the topic "Calculus of tensors Computer graphics"

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Vince, John. Calculus for Computer Graphics. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-11376-6.

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Vince, John. Calculus for Computer Graphics. London: Springer London, 2013. http://dx.doi.org/10.1007/978-1-4471-5466-2.

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M, Christensen Steven, ed. MathTensor: A system for doing tensor analysis by computer. Reading, Mass: Addison-Wesley, 1994.

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Bluston, H. S. Calculus applications of the spectrum / spectrum plus computers, with graphics. Bedford: Energy Consultancy, 1986.

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Tall, David Orme. Building and testing a cognitive approach to the calculus using interactive computer graphics. [s.l.]: typescript, 1986.

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David, Laidlaw, Weickert Joachim, Polthier Konrad, Johnson Christopher R, Hoffman David, Hege Hans-Christian 1954-, Rumpf Martin, and SpringerLink (Online service), eds. Visualization and Processing of Tensor Fields: Advances and Perspectives. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009.

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Schiess, James R. Two algorithms for rational spline interpolation of surfaces. [Washington, D.C.]: National Aeronautics and Space Administration, Scientific and Technical Information Branch, 1986.

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(Editor), Joachim Weickert, and Hans Hagen (Editor), eds. Visualization and Processing of Tensor Fields (Mathematics and Visualization). Springer, 2005.

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John, Vince. Calculus for Computer Graphics. Springer, 2019.

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Calculus For Computer Graphics. Springer London Ltd, 2013.

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Book chapters on the topic "Calculus of tensors Computer graphics"

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Vince, John. "Calculus: Derivatives." In Mathematics for Computer Graphics, 373–429. London: Springer London, 2017. http://dx.doi.org/10.1007/978-1-4471-7336-6_15.

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Vince, John. "Calculus: Integration." In Mathematics for Computer Graphics, 431–70. London: Springer London, 2017. http://dx.doi.org/10.1007/978-1-4471-7336-6_16.

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Vince, John. "Integral Calculus." In Calculus for Computer Graphics, 93–120. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-11376-6_7.

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Vince, John. "Integral Calculus." In Calculus for Computer Graphics, 87–115. London: Springer London, 2013. http://dx.doi.org/10.1007/978-1-4471-5466-2_7.

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Vince, John. "Calculus: Derivatives." In Mathematics for Computer Graphics, 265–317. London: Springer London, 2014. http://dx.doi.org/10.1007/978-1-4471-6290-2_13.

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Vince, John. "Calculus: Integration." In Mathematics for Computer Graphics, 319–60. London: Springer London, 2014. http://dx.doi.org/10.1007/978-1-4471-6290-2_14.

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Vince, John. "Higher Derivatives." In Calculus for Computer Graphics, 71–79. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-11376-6_5.

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Vince, John. "Surface Area." In Calculus for Computer Graphics, 153–78. London: Springer London, 2013. http://dx.doi.org/10.1007/978-1-4471-5466-2_10.

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Vince, John. "Limits and Derivatives." In Calculus for Computer Graphics, 17–30. London: Springer London, 2013. http://dx.doi.org/10.1007/978-1-4471-5466-2_3.

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Vince, John. "Functions." In Calculus for Computer Graphics, 5–18. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-11376-6_2.

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Conference papers on the topic "Calculus of tensors Computer graphics"

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"MODELING WAVELENGTH-DEPENDENT BRDFS AS FACTORED TENSORS FOR REAL-TIME SPECTRAL RENDERING." In International Conference on Computer Graphics Theory and Applications. SciTePress - Science and and Technology Publications, 2010. http://dx.doi.org/10.5220/0002820301650172.

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Nuntawisuttiwong, Taweechai, and Natasha Dejdumrong. "An Educational Game for Learning Calculus." In 2011 Eighth International Conference on Computer Graphics, Imaging and Visualization (CGIV). IEEE, 2011. http://dx.doi.org/10.1109/cgiv.2011.34.

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"PARALLEL SOLVERS COMPARISON FOR AN INVERSE PROBLEM IN FRACTIONAL CALCULUS." In 14th International Conference on Computer Graphics, Visualization, Computer Vision and Image Processing. IADIS Press, 2020. http://dx.doi.org/10.33965/tpmc2020_202011l024.

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Mota, Virgı́nia F., Jefersson A. dos Santos, and Arnaldo De A. Araújo. "FASTensor: A tensor framework for spatiotemporal description." In XXXII Conference on Graphics, Patterns and Images. Sociedade Brasileira de Computação - SBC, 2019. http://dx.doi.org/10.5753/sibgrapi.est.2019.8298.

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Spatiotemporal description is a research field with applications in various areas such as video indexing, surveillance, human-computer interfaces, among others. Big Data problems in large databases are now being treated with Deep Learning tools, however we still have room for improvement in spatiotemporal handcraft description. Moreover, we still have problems that involve small data in which data augmentation and other techniques are not valid. The main contribution of this Ph.D. Thesis 1 is the development of a framework for spatiotemporal representation using orientation tensors enabling dimension reduction and invariance. This is a multipurpose framework called Features As Spatiotemporal Tensors (FASTensor). We evaluate this framework in three different applications: Human Action recognition, Video Pornography classification and Cancer Cell classification. The latter one is also a contribution of this work, since we introduce a new dataset called Melanoma Cancer Cell dataset (MCC). It is a small data that cannot be artificially augmented due the difficulty of extraction and the nature of motion. The results were competitive, while also being fast and simple to implement. Finally, our results in the MCC dataset can be used in other cancer cell treatment analysis.
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Werner, Liss C. "Form and Data from linear Calculus to cybernetic Computation and Interaction." In 37 Education and Research in Computer Aided Architectural Design in Europe and XXIII Iberoamerican Society of Digital Graphics, Joint Conference (N. 1). São Paulo: Editora Blucher, 2019. http://dx.doi.org/10.5151/proceedings-ecaadesigradi2019_667.

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