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Appendix: Useful Mathematical Techniques
"... This appendix contains concise reviews of various mathematical techniques used in this book. We start with formulae useful for solving triangles, both planar and spherical. Next, some aspects of the manipulation of vectors are summarized. These include solution methods for vector equations and conve ..."
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This appendix contains concise reviews of various mathematical techniques used in this book. We start with formulae useful for solving triangles, both planar and spherical. Next, some aspects of the manipulation of vectors are summarized. These include solution methods for vector equations
An axiomatic basis for computer programming
 COMMUNICATIONS OF THE ACM
, 1969
"... In this paper an attempt is made to explore the logical foundations of computer programming by use of techniques which were first applied in the study of geometry and have later been extended to other branches of mathematics. This involves the elucidation of sets of axioms and rules of inference w ..."
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Cited by 1754 (4 self)
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In this paper an attempt is made to explore the logical foundations of computer programming by use of techniques which were first applied in the study of geometry and have later been extended to other branches of mathematics. This involves the elucidation of sets of axioms and rules of inference
ScaleSpace Theory in Computer Vision
, 1994
"... A basic problem when deriving information from measured data, such as images, originates from the fact that objects in the world, and hence image structures, exist as meaningful entities only over certain ranges of scale. "ScaleSpace Theory in Computer Vision" describes a formal theory fo ..."
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Cited by 625 (21 self)
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for representing the notion of scale in image data, and shows how this theory applies to essential problems in computer vision such as computation of image features and cues to surface shape. The subjects range from the mathematical foundation to practical computational techniques. The power of the methodology
Sequence Logos: A New Way to Display Consensus Sequences
 Nucleic Acids Res
, 1990
"... INTRODUCTION A logo is "a single piece of type bearing two or more usually separate elements" [1]. In this paper, we use logos to display aligned sets of sequences. Sequence logos concentrate the following information into a single graphic [2]: 1. The general consensus of the sequences. ..."
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Cited by 650 (28 self)
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. National Cancer Institute, Frederick Cancer Research and Development Center, Laboratory of Mathematical Biology, P. O. Box B, Frederick, MD 21701. Internet addresses: toms@ncifcrf.gov and stephens@ncifcrf.gov. y corresponding author 1 2. The order of predominance of the residues at every position. 3
Mathematical Techniques for Image Interpolation
, 2005
"... We discuss the problem of interpolating visually acceptable images at a higher resolution. We first present the interpolation problem and why linear interpolation filters are inadequate for image data. To represent the major mathematical approaches to image processing, we discuss and evaluate five d ..."
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Cited by 1 (0 self)
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We discuss the problem of interpolating visually acceptable images at a higher resolution. We first present the interpolation problem and why linear interpolation filters are inadequate for image data. To represent the major mathematical approaches to image processing, we discuss and evaluate five
Semantics of ContextFree Languages
 In Mathematical Systems Theory
, 1968
"... "Meaning " may be assigned to a string in a contextfree language by defining "attributes " of the symbols in a derivation tree for that string. The attributes can be defined by functions associated with each production in the grammar. This paper examines the implications of th ..."
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Cited by 569 (0 self)
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specification of semantics which have appeared in the literature. A simple technique for specifying the "meaning " of languages defined by contextfree grammars is introduced in Section 1 of this paper, and its basic mathematical properties are investigated in Sections 2 and 3. An example which
Segmentation of brain MR images through a hidden Markov random field model and the expectationmaximization algorithm
 IEEE TRANSACTIONS ON MEDICAL. IMAGING
, 2001
"... The finite mixture (FM) model is the most commonly used model for statistical segmentation of brain magnetic resonance (MR) images because of its simple mathematical form and the piecewise constant nature of ideal brain MR images. However, being a histogrambased model, the FM has an intrinsic limi ..."
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Cited by 639 (15 self)
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The finite mixture (FM) model is the most commonly used model for statistical segmentation of brain magnetic resonance (MR) images because of its simple mathematical form and the piecewise constant nature of ideal brain MR images. However, being a histogrambased model, the FM has an intrinsic
Handbook of Applied Cryptography
, 1997
"... As we draw near to closing out the twentieth century, we see quite clearly that the informationprocessing and telecommunications revolutions now underway will continue vigorously into the twentyfirst. We interact and transact by directing flocks of digital packets towards each other through cybers ..."
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Cited by 3335 (33 self)
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syllable is bounced off a satellite and smeared over an entire continent? How should a bank know that it really is Bill Gates requesting from his laptop in Fiji a transfer of $10,000,000,000 to another bank? Fortunately, the magical mathematics of cryptography can help. Cryptography provides techniques
Mathematical Techniques of Image Processing
"... I confirm that this is my own work and the use of all material from other sources has been properly and fully acknowledged. This paper investigates various different types of image processing methods and models for image processing: a total variation based approach, a shock filters approach and morp ..."
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I confirm that this is my own work and the use of all material from other sources has been properly and fully acknowledged. This paper investigates various different types of image processing methods and models for image processing: a total variation based approach, a shock filters approach and morphological component analysis. Discretisations of the first two will be seen, as well as various different 1D and 2D examples of their results, and 2D+T (video) examples for Morphological component analysis. Their behaviour and results with different images is compared to contrast the different behaviour
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