There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Introduction to a Transient World. Fourier Kingdom. Discrete Revolution. Time Meets Frequency. Frames. Wavelet Zoom. Wavelet Bases. Wavelet Packet and Local Cosine Bases. An Approximation Tour. Estimations are Approximations. Transform Coding. Appendix A: Mathematical Complements. Appendix B: Software Toolboxes.

http://ahvazdownload.persiangig.com/document/article/39.pdf

A wavelet tour of signal processing

In 1974 an article appeared in Science magazine with the dry-sounding title “Judgment Under Uncertainty: Heuristics and Biases” by a pair of psychologists who were not well known outside their discipline of decision theory. In it Amos Tversky and Daniel Kahneman introduced the world to Prospect Theory, which mapped out how humans actually behave when faced with decisions about gains and losses, in contrast to how economists assumed that people behave. Prospect Theory turned Economics on its head by demonstrating through a series of ingenious experiments that people are much more concerned with losses than they are with gains, and that framing a choice from one perspective or the other will result in decisions that are exactly the opposite of each other, even if the outcomes are monetarily the same. Prospect Theory led cognitive psychology in a new direction that began to uncover other human biases in thinking that are probably not learned but are part of our brain’s wiring.

Thinking fast and slow.

Humans perceive the three-dimensional structure of the world with apparent ease. However, despite all of the recent advances in computer vision research, the dream of having a computer interpret an image at the same level as a two-year old remains elusive. Why is computer vision such a challenging problem and what is the current state of the art? Computer Vision: Algorithms and Applications explores the variety of techniques commonly used to analyze and interpret images. It also describes challenging real-world applications where vision is being successfully used, both for specialized applications such as medical imaging, and for fun, consumer-level tasks such as image editing and stitching, which students can apply to their own personal photos and videos. More than just a source of recipes, this exceptionally authoritative and comprehensive textbook/reference also takes a scientific approach to basic vision problems, formulating physical models of the imaging process before inverting them to produce descriptions of a scene. These problems are also analyzed using statistical models and solved using rigorous engineering techniques Topics and features: structured to support active curricula and project-oriented courses, with tips in the Introduction for using the book in a variety of customized courses; presents exercises at the end of each chapter with a heavy emphasis on testing algorithms and containing numerous suggestions for small mid-term projects; provides additional material and more detailed mathematical topics in the Appendices, which cover linear algebra, numerical techniques, and Bayesian estimation theory; suggests additional reading at the end of each chapter, including the latest research in each sub-field, in addition to a full Bibliography at the end of the book; supplies supplementary course material for students at the associated website, http://szeliski.org/Book/. Suitable for an upper-level undergraduate or graduate-level course in computer science or engineering, this textbook focuses on basic techniques that work under real-world conditions and encourages students to push their creative boundaries. Its design and exposition also make it eminently suitable as a unique reference to the fundamental techniques and current research literature in computer vision.

/pdf/computer-vision-algorithms-and-applications-25dn6wu83j.pdf

Computer Vision: Algorithms and Applications

The limitations of commonly used separable extensions of one-dimensional transforms, such as the Fourier and wavelet transforms, in capturing the geometry of image edges are well known. In this paper, we pursue a "true" two-dimensional transform that can capture the intrinsic geometrical structure that is key in visual information. The main challenge in exploring geometry in images comes from the discrete nature of the data. Thus, unlike other approaches, such as curvelets, that first develop a transform in the continuous domain and then discretize for sampled data, our approach starts with a discrete-domain construction and then studies its convergence to an expansion in the continuous domain. Specifically, we construct a discrete-domain multiresolution and multidirection expansion using nonseparable filter banks, in much the same way that wavelets were derived from filter banks. This construction results in a flexible multiresolution, local, and directional image expansion using contour segments, and, thus, it is named the contourlet transform. The discrete contourlet transform has a fast iterated filter bank algorithm that requires an order N operations for N-pixel images. Furthermore, we establish a precise link between the developed filter bank and the associated continuous-domain contourlet expansion via a directional multiresolution analysis framework. We show that with parabolic scaling and sufficient directional vanishing moments, contourlets achieve the optimal approximation rate for piecewise smooth functions with discontinuities along twice continuously differentiable curves. Finally, we show some numerical experiments demonstrating the potential of contourlets in several image processing applications.

/pdf/the-contourlet-transform-an-efficient-directional-bbl3m3gyb1.pdf

The contourlet transform: an efficient directional multiresolution image representation

The authors consider expansions which give arbitrary orthonormal tilings of the time-frequency plane. These differ from the short-time Fourier transform, wavelet transform, and wavelet packets tilings in that they change over time. They show how this can be achieved using time-varying orthogonal tree structures, which preserve orthogonality, even across transitions. The method is based on the construction of boundary and transition filters; these allow us to construct essentially arbitrary tilings. Time-varying modulated lapped transforms are a special case, where both boundary and overlapping solutions are possible with filters obtained by modulation. They present a double-tree algorithm which for a given signal decides on the best binary segmentation in both time and frequency. That is, it is a joint optimization of time and frequency splitting. The algorithm is optimal for additive cost functions (e.g., rate-distortion), and results in time-varying best bases, the main application of which is for compression of nonstationary signals. Experiments on test signals are presented. >

/pdf/tilings-of-the-time-frequency-plane-construction-of-z51pt8b0sd.pdf

Tilings of the time-frequency plane: construction of arbitrary orthogonal bases and fast tiling algorithms

Despite countless attempts and near-universal desire to replace them, passwords are more widely used and firmly entrenched than ever. The authors' exploration leads them to argue that no silver bullet will meet all requirements-not only will passwords be with us for some time, but in many instances, they're the solution that best fits the scenario of use. Among broad authentication research directions to follow, they first suggest better means to concretely identify actual requirements (surprisingly overlooked to date) and weight their relative importance in target scenarios. Second, for scenarios where passwords appear to be the best-fit solution, they suggest designing better means to support them. The authors also highlight the need for more systematic research and how the premature conclusion that passwords are dead has led to the neglect of important research questions.

/pdf/a-research-agenda-acknowledging-the-persistence-of-passwords-4bjd3cf2i3.pdf

A Research Agenda Acknowledging the Persistence of Passwords

A system and method that facilitates and effectuates detection of malware secreted and/or hidden in plain sight on a machine The system and method in order to achieve its aims generates a list of all loaded modules, identifies from the list a set of modules common to more than a threshold number of processes, and eliminates from the list those modules included in an authentication list The resultant list is prioritized based, in one instance, on the number of occurrences a particular module makes in the resultant list, and thereafter the list is distributed analyst workstations

Spyware detection mechanism

It is shown that infinite impulse response (IIR) filters lead to more general wavelets of infinite support than finite impulse response (FIR) filters. A complete constructive method that yields all orthogonal two channel filter banks, where the filters have rational transfer functions, is given, and it is shown how these can be used to generate orthonormal wavelet bases. A family of orthonormal wavelets that have a maximum number of disappearing moments is shown to be generated by the halfband Butterworth filters. When there is an odd number of zeros at pi it is shown that closed forms for the filters are available without need for factorization. A still larger class of orthonormal wavelet bases having the same moment properties and containing the Daubechies and Butterworth filters as the limiting cases is presented. It is shown that it is possible to have both linear phase and orthogonality in the infinite impulse response case, and a constructive method is given. It is also shown how compactly supported bases may be orthogonalized, and bases for the spline function spaces are constructed. >

/pdf/wavelets-and-recursive-filter-banks-6lsyym25w1.pdf

Wavelets and recursive filter banks

Password meters tell users whether their passwords are "weak" or "strong." We performed a laboratory experiment to examine whether these meters influenced users' password selections when they were forced to change their real passwords, and when they were not told that their passwords were the subject of a study. We observed that the presence of meters yielded significantly stronger passwords. We performed a followup field experiment to test a different scenario: creating a password for an unimportant account. In this scenario, we found that the meters made no observable difference: participants simply reused weak passwords that they used to protect similar low-risk accounts. We conclude that meters result in stronger passwords when users are forced to change existing passwords on "important" accounts and that individual meter design decisions likely have a marginal impact.

/pdf/does-my-password-go-up-to-eleven-the-impact-of-password-3n5n9mvxfj.pdf

Cormac Herley

Papers

Tilings of the time-frequency plane: construction of arbitrary orthogonal bases and fast tiling algorithms

A Research Agenda Acknowledging the Persistence of Passwords

Spyware detection mechanism

Wavelets and recursive filter banks

Does my password go up to eleven?: the impact of password meters on password selection