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

What would a “Science of Security” look like? This question has received considerable attention over the past 10 years No one argues against the desirability of making security research more “scientific” But how would one would go about that? We argue that making progress on this requires clarifying what “scientific” means in the context of computer security, and that has received too little attention We pursue this based on a review of literature in the history and Philosophy of Science and a belief that work under the theme “Science of Security” should align with and ideally, benefit from what has been learned over a few hundred years in science We offer observations and insights, with a view that the security community can benefit from better leveraging past lessons and common practices well-accepted by consensus in the mainstream scientific community—but which appear little recognized in the security community

Science of Security: Combining Theory and Measurement to Reflect the Observable

We consider an image processing pipeline that enables a user to capture and generate high-quality images from a digital camera. In such a system, some image processing tasks are typically implemented within the camera, while others are performed in software on a host computer that controls the output device. We consider the complexity issues and tradeoffs involved in designing several key algorithms in such a system. We also discuss hardware features that accelerate these algorithms.

Image processing considerations for digital photography

We introduce a new image coding algorithm which exploits the idea of space-varying wavelet packets, where the best filter bank representation is chosen from a large library. The filter bank tree representations in the library are free to vary in structure over different segments of the image, and a fast search algorithm is given. In addition we employ the idea of space-frequency quantization, which is a rate-distortion optimized extension of the zero-tree wavelet coder of Shapiro to wavelet packets. The coder thus adaptively chooses the representation to suit the image and adaptively chooses the quantization to suit the representation. We present coding results that confirm the excellent performance of the scheme.

Space-frequency quantization for a space-varying wavelet packet image coder

An Occam filter employs lossy data compression to separate signal from noise. Previously it was shown that Occam filters are useful for filtering random noise from discrete samples of a deterministic and continuous signal. In this paper, we show that Occam filters can also be used to separate two stochastic sources, with the effectiveness of the separation depending on their relative compressibility. We then construct an Occam filter based on singular value decomposition (SVD) and apply it to digital images corrupted with Gaussian noise. We observe that the SVD-based Occam filter outperforms the wavelet-based denoising method of Donoho and Johnstone (1994) and DeVore and Lucier (1992).

Occam filters for stochastic sources with application to digital images

Online guessing attacks against password servers can be hard to address. Approaches that throttle or block repeated guesses on an account (e.g., three strikes type lockout rules) can be effective against depth-first attacks, but are of little help against breadth-first attacks that spread guesses very widely. At large providers with tens, or hundreds, of millions of accounts breadth-first attacks offer a way to send millions or even billions of guesses without ever triggering the depth-first defenses. The absence of labels and non-stationarity of attack traffic make it challenging to apply machine learning techniques. We show how to accurately estimate the odds that an observation x indicates that a request is malicious. Our main assumptions are that successful malicious logins are a small fraction of the total, and that the distribution of x in the legitimate traffic is stationary, or very-slowly varying. From these we show how we can estimate the ratio of bad-to-good traffic among any set of requests; how we can then identify subsets of the request data that contain least (or even no) attack traffic; how these leastattacked subsets allow us to estimate the distribution of values of x over the legitimate data, and hence calculate the odds ratio. A sensitivity analysis shows that even when we fail to identify a subset with little attack traffic our odds ratio estimates are very robust.

Cormac Herley

Papers

Science of Security: Combining Theory and Measurement to Reflect the Observable

Image processing considerations for digital photography

Space-frequency quantization for a space-varying wavelet packet image coder

Occam filters for stochastic sources with application to digital images

Distinguishing Attacks from Legitimate Authentication Traffic at Scale.