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

Counterfactuals (or what-if scenarios) are often employed as security arguments, but the dos and don'ts of their use are poorly understood. They are useful to discuss vulnerability of systems under threats that haven't yet materialized, but they can also be used to justify investment in obscure controls. In this paper, we shed light on the role of counterfactuals in security, and present conditions under which counterfactuals are legitimate arguments, linked to the exclusion or inclusion of the threat environment in security metrics. We provide a new paradigm for security reasoning by deriving essential questions to ask in order to decide on the acceptability of specific counterfactuals as security arguments, which can serve as a basis for further study in this field. We conclude that counterfactuals are a necessary evil in security, which should be carefully controlled.

"If you were attacked, you'd be sorry": Counterfactuals as security arguments

A minimum area rectangle inscription method and system for automatically generating a minimum area rectangle that inscribes and bounds an approximately rectangular object (or “noisy” object) contained within scanned image data. The minimum area rectangle inscription method chooses an interior point located inside the object boundary and determine perimeter points located on the boundary. A convex hull is constructed from at least some of the perimeter points such that each side of the convex hull is convex. Inscribing rectangles, equal in number to the sides of the convex hull, are constructed such that each inscribing rectangle shares a side with the convex hull and circumscribes approximately the entire convex hull. The area of each of the inscribing rectangles is calculated, and the inscribing rectangle having the least amount of area is designated as the minimum area rectangle.

Method and system for automatically inscribing noisy objects in scanned image data within a minimum area rectangle

Many media streams consist of distinct objects that repeat. For example, broadcast television and radio signals contain advertisements, call sign jingles, songs and even whole programs that repeat. The problem we address is to identify explicitly the underlying structure in repetitive streams and deconstruct them into their component objects. Our architecture assumes no a priori knowledge of the streams, and does not require a pre-trained database. Everything the system needs is learned on the fly. We demonstrate that using a modestly capable computer it is perfectly feasible to identify, in realtime, repeating objects that occur days or even weeks apart in audio or video streams. We outline the algorithms, enumerate several applications and present results from real streams.

Extracting repeats from media streams

This paper introduces a novel and very accurate segmentation algorithm. It is very efficient and consumes less than 10% of CPU on a simple desktop PC to segment a stream in real-time. It operates on an audio stream, or on the audio portion of a audio-visual stream. It is very accurate: it accurately detects the positions and durations of objects on an over-the-air broadcast television signal, and songs on both FM and internet radio stations (as checked against labeled ground truth streams). The algorithm does not require any prior information or training. We detail the system design and present results of segmenting broadcast streams.

https://www.microsoft.com/en-us/research/wp-content/uploads/2016/02/mm05.pdf

Accurate repeat finding and object skipping using fingerprints

We describe a method for scaling images which have been acquired with a charge coupled device (CCD) sensor. This method produces enlarged images which are sharper than those produced by bilinear interpolation, for comparable complexity. It is based on the observation that the sampling process of a CCD is not a point sampling process, but instead can be modelled as an averaging filter followed by sampling.

Cormac Herley

Papers

"If you were attacked, you'd be sorry": Counterfactuals as security arguments

Method and system for automatically inscribing noisy objects in scanned image data within a minimum area rectangle

Extracting repeats from media streams

Accurate repeat finding and object skipping using fingerprints

Area-based interpolation for scaling of images from a CCD