Sampling and Reconstruction of Shapes with Algebraic Boundaries

We present a sampling theory for a class of binary images with finite rate of innovation (FRI). Every image in our model is the restriction of \mathds{1}_{\{p\leq0\}} to the image plane, where \mathds{1} denotes the indicator function and $p$ is some real bivariate polynomial. This particularly means that the boundaries in the image form a subset of an algebraic curve with the implicit polynomial $p$. We show that the image parameters --i.e., the polynomial coefficients-- satisfy a set of linear annihilation equations with the coefficients being the image moments. The inherent sensitivity of the moments to noise makes the reconstruction process numerically unstable and narrows the choice of the sampling kernels to polynomial reproducing kernels. As a remedy to these problems, we replace conventional moments with more stable \emph{generalized moments} that are adjusted to the given sampling kernel. The benefits are threefold: (1) it relaxes the requirements on the sampling kernels, (2) produces annihilation equations that are robust at numerical precision, and (3) extends the results to images with unbounded boundaries. We further reduce the sensitivity of the reconstruction process to noise by taking into account the sign of the polynomial at certain points, and sequentially enforcing measurement consistency. We consider various numerical experiments to demonstrate the performance of our algorithm in reconstructing binary images, including low to moderate noise levels and a range of realistic sampling kernels.Comment: 12 pages, 14 figure

Automated Optical Inspection and Image Analysis of Superconducting Radio-Frequency Cavities

The inner surface of superconducting cavities plays a crucial role to achieve highest accelerating fields and low losses. For an investigation of this inner surface of more than 100 cavities within the cavity fabrication for the European XFEL and the ILC HiGrade Research Project, an optical inspection robot OBACHT was constructed. To analyze up to 2325 images per cavity, an image processing and analysis code was developed and new variables to describe the cavity surface were obtained. The accuracy of this code is up to 97% and the PPV 99% within the resolution of 15.63 $\mu \mathrm{m}$. The optical obtained surface roughness is in agreement with standard profilometric methods. The image analysis algorithm identified and quantified vendor specific fabrication properties as the electron beam welding speed and the different surface roughness due to the different chemical treatments. In addition, a correlation of $\rho = -0.93$ with a significance of $6\,\sigma$ between an obtained surface variable and the maximal accelerating field was found

The pictures we like are our image: continuous mapping of favorite pictures into self-assessed and attributed personality traits

Flickr allows its users to tag the pictures they like as “favorite”. As a result, many users of the popular photo-sharing platform produce galleries of favorite pictures. This article proposes new approaches, based on Computational Aesthetics, capable to infer the personality traits of Flickr users from the galleries above. In particular, the approaches map low-level features extracted from the pictures into numerical scores corresponding to the Big-Five Traits, both self-assessed and attributed. The experiments were performed over 60,000 pictures tagged as favorite by 300 users (the PsychoFlickr Corpus). The results show that it is possible to predict beyond chance both self-assessed and attributed traits. In line with the state-of-the art of Personality Computing, these latter are predicted with higher effectiveness (correlation up to 0.68 between actual and predicted traits)

Enhancing retinal images by nonlinear registration

Being able to image the human retina in high resolution opens a new era in many important fields, such as pharmacological research for retinal diseases, researches in human cognition, nervous system, metabolism and blood stream, to name a few. In this paper, we propose to share the knowledge acquired in the fields of optics and imaging in solar astrophysics in order to improve the retinal imaging at very high spatial resolution in the perspective to perform a medical diagnosis. The main purpose would be to assist health care practitioners by enhancing retinal images and detect abnormal features. We apply a nonlinear registration method using local correlation tracking to increase the field of view and follow structure evolutions using correlation techniques borrowed from solar astronomy technique expertise. Another purpose is to define the tracer of movements after analyzing local correlations to follow the proper motions of an image from one moment to another, such as changes in optical flows that would be of high interest in a medical diagnosis.Comment: 21 pages, 7 figures, submitted to Optics Communication

A novel astronomical application for formation flying small satellites

OLFAR, Orbiting Low Frequency Antennas for Radio Astronomy, will be a space mission to observe the universe frequencies below 30 MHz, as it was never done before with an orbiting telescope. Because of the ionospheric scintillations below 30 MHz and the opaqueness of the ionosphere below 15 MHz, a space mission is the only opportunity for this as yet unexplored frequency range in radio astronomy. The frequency band is scientifically very interesting for exploring the early cosmos at high hydrogen redshifts, the so-called dark-ages and the epoch of reionization, the discovery of planetary and solar bursts in other solar systems, for obtaining a tomographic view of space weather, ultra-high energy cosmic rays and for many other astronomical areas of interest. Because of the low observing frequency the aperture size of the instrument must be in the order of 100 km. This requires a distributed space mission which is proposed to be implemented using formation flying of small satellites. The individual satellites are broken down in five major subsystems: the spacecraft bus, the antenna design, the frontend, backend and data transport. One of the largest challenges is the inter-satellite communication. In this paper the concept and design considerations of OLFAR are presented