On The Continuous Steering of the Scale of Tight Wavelet Frames

In analogy with steerable wavelets, we present a general construction of adaptable tight wavelet frames, with an emphasis on scaling operations. In particular, the derived wavelets can be "dilated" by a procedure comparable to the operation of steering steerable wavelets. The fundamental aspects of the construction are the same: an admissible collection of Fourier multipliers is used to extend a tight wavelet frame, and the "scale" of the wavelets is adapted by scaling the multipliers. As an application, the proposed wavelets can be used to improve the frequency localization. Importantly, the localized frequency bands specified by this construction can be scaled efficiently using matrix multiplication

Multiscale Astronomical Image Processing Based on Nonlinear Partial Differential Equations

Astronomical applications of recent advances in the field of nonastronomical image processing are presented. These innovative methods, applied to multiscale astronomical images, increase signal-to-noise ratio, do not smear point sources or extended diffuse structures, and are thus a highly useful preliminary step for detection of different features including point sources, smoothing of clumpy data, and removal of contaminants from background maps. We show how the new methods, combined with other algorithms of image processing, unveil fine diffuse structures while at the same time enhance detection of localized objects, thus facilitating interactive morphology studies and paving the way for the automated recognition and classification of different features. We have also developed a new application framework for astronomical image processing that implements some recent advances made in computer vision and modern image processing, along with original algorithms based on nonlinear partial differential equations. The framework enables the user to easily set up and customize an image-processing pipeline interactively; it has various common and new visualization features and provides access to many astronomy data archives. Altogether, the results presented here demonstrate the first implementation of a novel synergistic approach based on integration of image processing, image visualization, and image quality assessment

Particle detection and tracking in fluorescence time-lapse imaging: a contrario approach

This paper proposes a probabilistic approach for the detection and the tracking of particles in fluorescent time-lapse imaging. In the presence of a very noised and poor-quality data, particles and trajectories can be characterized by an a contrario model, that estimates the probability of observing the structures of interest in random data. This approach, first introduced in the modeling of human visual perception and then successfully applied in many image processing tasks, leads to algorithms that neither require a previous learning stage, nor a tedious parameter tuning and are very robust to noise. Comparative evaluations against a well-established baseline show that the proposed approach outperforms the state of the art.Comment: Published in Journal of Machine Vision and Application

Improved micro-contact resistance model that considers material deformation, electron transport and thin film characteristics

This paper reports on an improved analytic model forpredicting micro-contact resistance needed for designing microelectro-mechanical systems (MEMS) switches. The originalmodel had two primary considerations: 1) contact materialdeformation (i.e. elastic, plastic, or elastic-plastic) and 2) effectivecontact area radius. The model also assumed that individual aspotswere close together and that their interactions weredependent on each other which led to using the single effective aspotcontact area model. This single effective area model wasused to determine specific electron transport regions (i.e. ballistic,quasi-ballistic, or diffusive) by comparing the effective radius andthe mean free path of an electron. Using this model required thatmicro-switch contact materials be deposited, during devicefabrication, with processes ensuring low surface roughness values(i.e. sputtered films). Sputtered thin film electric contacts,however, do not behave like bulk materials and the effects of thinfilm contacts and spreading resistance must be considered. Theimproved micro-contact resistance model accounts for the twoprimary considerations above, as well as, using thin film,sputtered, electric contact

Isolating contour information from arbitrary images

Aspects of natural vision (physiological and perceptual) serve as a basis for attempting the development of a general processing scheme for contour extraction. Contour information is assumed to be central to visual recognition skills. While the scheme must be regarded as highly preliminary, initial results do compare favorably with the visual perception of structure. The scheme pays special attention to the construction of a smallest scale circular difference-of-Gaussian (DOG) convolution, calibration of multiscale edge detection thresholds with the visual perception of grayscale boundaries, and contour/texture discrimination methods derived from fundamental assumptions of connectivity and the characteristics of printed text. Contour information is required to fall between a minimum connectivity limit and maximum regional spatial density limit at each scale. Results support the idea that contour information, in images possessing good image quality, is (centered at about 10 cyc/deg and 30 cyc/deg). Further, lower spatial frequency channels appear to play a major role only in contour extraction from images with serious global image defects

Curvelet Approach for SAR Image Denoising, Structure Enhancement, and Change Detection

In this paper we present an alternative method for SAR image denoising, structure enhancement, and change detection based on the curvelet transform. Curvelets can be denoted as a two dimensional further development of the well-known wavelets. The original image is decomposed into linear ridge-like structures, that appear in different scales (longer or shorter structures), directions (orientation of the structure) and locations. The influence of these single components on the original image is weighted by the corresponding coefficients. By means of these coefficients one has direct access to the linear structures present in the image. To suppress noise in a given SAR image weak structures indicated by low coefficients can be suppressed by setting the corresponding coefficients to zero. To enhance structures only coefficients in the scale of interest are preserved and all others are set to zero. Two same-sized images assumed even a change detection can be done in the curvelet coefficient domain. The curvelet coefficients of both images are differentiated and manipulated in order to enhance strong and to suppress small scale (pixel-wise) changes. After the inverse curvelet transform the resulting image contains only those structures, that have been chosen via the coefficient manipulation. Our approach is applied to TerraSAR-X High Resolution Spotlight images of the city of Munich. The curvelet transform turns out to be a powerful tool for image enhancement in fine-structured areas, whereas it fails in originally homogeneous areas like grassland. In the change detection context this method is very sensitive towards changes in structures instead of single pixel or large area changes. Therefore, for purely urban structures or construction sites this method provides excellent and robust results. While this approach runs without any interaction of an operator, the interpretation of the detected changes requires still much knowledge about the underlying objects

Detection of Electromagnetic Inclusions using Topological Sensitivity

In this article a topological sensitivity framework for far field detection of a diametrically small electromagnetic inclusion is established. The cases of single and multiple measurements of the electric far field scattering amplitude at a fixed frequency are taken into account. The performance of the algorithm is analyzed theoretically in terms of its resolution and sensitivity for locating an inclusion. The stability of the framework with respect to measurement and medium noises is discussed. Moreover, the quantitative results for signal-to-noise ratio are presented. A few numerical results are presented to illustrate the detection capabilities of the proposed framework with single and multiple measurements.Comment: 31 pages, 5 figure