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

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

From the Publisher: 
The accessible presentation of this book gives both a general view of the entire computer vision enterprise and also offers sufficient detail to be able to build useful applications. Users learn techniques that have proven to be useful by first-hand experience and a wide range of mathematical methods. A CD-ROM with every copy of the text contains source code for programming practice, color images, and illustrative movies. Comprehensive and up-to-date, this book includes essential topics that either reflect practical significance or are of theoretical importance. Topics are discussed in substantial and increasing depth. Application surveys describe numerous important application areas such as image based rendering and digital libraries. Many important algorithms broken down and illustrated in pseudo code. Appropriate for use by engineers as a comprehensive reference to the computer vision enterprise.

Computer vision : a modern approach = 计算机视觉 : 一种现代的方法

We propose a new optical encoding method of images for security applications. The encoded image is obtained by random-phase encoding in both the input and the Fourier planes. We analyze the statistical properties of this technique and show that the encoding converts the input signal to stationary white noise and that the reconstruction method is robust.

Optical image encryption based on input plane and Fourier plane random encoding.

This Letter reports the production and optical polarimetric verification of codes based on thin-film technology for security applications. Because thin-film structures display distinctive polarization signatures, this data is used to authenticate the message encoded. Samples are analyzed using an imaging ellipsometer able to measure the 16 components of the Mueller matrix. As a result, the behavior of the thin film under polarized light becomes completely characterized. This information is utilized to distinguish among true and false codes by means of correlation. Without the imaging optics the components of the Mueller matrix become noise-like distributions and, consequently, the message encoded is no longer available. Then, a set of Stokes vectors are generated numerically for any polarization state of the illuminating beam and thus, machine learning techniques can be used to perform classification. We show that successful authentication is possible using the k-nearest neighbors algorithm in thin-films codes that have been anisotropically phase-encoded with pseudorandom phase code.

/pdf/optical-security-verification-by-synthesizing-thin-films-5duuh8mzeh.pdf

Optical security verification by synthesizing thin films with unique polarimetric signatures.

Three-Dimensional Video and Display: Devices and Systems

In this paper, we present a 3D photon counting axially distributed image sensing system using statistical approaches, such as a maximum-likelihood estimation and total variation maximum a posteriori expectation maximization, to enhance the visual quality of 2D photon counting images and obtain better 3D reconstructed images. Conventional photon counting integral imaging is implemented by using a lens array, moving an image sensor in lateral (horizontal and vertical) directions, or using an image sensor array to obtain elemental images. To avoid lateral movement of the image sensor, axially distributed sensing is applied to photon counting imaging. A single image sensor is moved along its optical axis to pickup multi-view 2D images with slightly different perspectives which are used for 3D visualization. Axially distributed sensing (ADS) with proper statistical processing can remedy the effect of partial occlusion of the 3D scene. We show that our method can improve the visual quality of 2D photon counting images computationally and obtain the enhanced 3D reconstructed images.

Three-Dimensional Photon Counting Axially Distributed Image Sensing

Conventional multiview imaging systems commonly utilize a planar lenslet array and a rigid, flat image sensor in the pickup stage to capture different views of the scene. In this Letter, we remove this constraint by proposing the concept of three-dimensional (3D) imaging with detector arrays that may conform to arbitrarily shaped surfaces or platforms. A nonplanar detector array configuration can be used in combination with a flexible lenslet array to capture different views. The orientation and optical axes of individual image sensing elements could vary. A point-by-point 3D reconstruction algorithm is described and the feasibility of the proposed approach is demonstrated through simulated imagery.

Three-dimensional imaging with detector arrays on arbitrarily shaped surfaces.

We present the initial results of a novel technique that uses only phase information from a digital hologram for the reconstruction of three-dimensional (3D) objects. Our holograms are created using phase-shift digital holography. Perspectives of the 3D object are usually reconstructed numerically on a computer. For large holograms this can be a computationally intensive task. We believe that the proposed reconstruction technique is promising for 3D display because the phase-encoded digital holograms admit optical, and therefore realtime, reconstructions that use commercially available display devices such as liquid crystal spatial light modulators. Numerical evaluation of the reconstructed 3D object and an experimental demonstration are presented.

/pdf/three-dimensional-object-reconstruction-using-phase-only-466zi1igiz.pdf

Bahram Javidi

Papers

Optical security verification by synthesizing thin films with unique polarimetric signatures.

Three-Dimensional Video and Display: Devices and Systems

Three-Dimensional Photon Counting Axially Distributed Image Sensing

Three-dimensional imaging with detector arrays on arbitrarily shaped surfaces.

Three-dimensional object reconstruction using phase-only information from a digital hologram