Search Results (4)

The symmetric Kullback–Leibler centroid, also called the Jeffreys centroid, of a set of mutually absolutely continuous probability distributions on a measure space provides a notion of centrality which has proven useful in many tasks, including information retrieval, information fusion, and clustering. However, the Jeffreys centroid is not available in closed form for sets of categorical or multivariate normal distributions, two widely used statistical models, and thus needs to be approximated numerically in practice. In this paper, we first propose the new Jeffreys–Fisher–Rao center defined as the Fisher–Rao midpoint of the sided Kullback–Leibler centroids as a plug-in replacement of the Jeffreys centroid. This Jeffreys–Fisher–Rao center admits a generic formula for uni-parameter exponential family distributions and a closed-form formula for categorical and multivariate normal distributions; it matches exactly the Jeffreys centroid for same-mean normal distributions and is experimentally observed in practice to be close to the Jeffreys centroid. Second, we define a new type of inductive center generalizing the principle of the Gauss arithmetic–geometric double sequence mean for pairs of densities of any given exponential family. This new Gauss–Bregman center is shown experimentally to approximate very well the Jeffreys centroid and is suggested to be used as a replacement for the Jeffreys centroid when the Jeffreys–Fisher–Rao center is not available in closed form. Furthermore, this inductive center always converges and matches the Jeffreys centroid for sets of same-mean normal distributions. We report on our experiments, which first demonstrate how well the closed-form formula of the Jeffreys–Fisher–Rao center for categorical distributions approximates the costly numerical Jeffreys centroid, which relies on the Lambert W function, and second show the fast convergence of the Gauss–Bregman double sequences, which can approximate closely the Jeffreys centroid when truncated to a first few iterations. Finally, we conclude this work by reinterpreting these fast proxy Jeffreys–Fisher–Rao and Gauss–Bregman centers of Jeffreys centroids under the lens of dually flat spaces in information geometry. Full article

Recently, we developed a simple theoretical model for the estimation of the irradiance distribution at the focal plane of commercial off-the-shelf (COTS) camera lenses in case of laser illumination. The purpose of such a model is to predict the incapacitation of imaging sensors when irradiated by laser light. The model is based on closed-form equations that comprise mainly standard parameters of the laser dazzle scenario and those of the main devices involved (laser source, camera lens and imaging sensor). However, the model also includes three non-standard parameters, which describe the scattering of light within the camera lens. In previous work, we have performed measurements to derive these typically unknown scatter parameters for a collection of camera lenses of the Double-Gauss type. In this publication, we compare calculations based on our theoretical model and the measured scatter parameters with the outcome of stray light simulations performed with the optical design software FRED in order to validate the reliability of our theoretical model and of the derived scatter parameters. Full article

We present our efforts on estimating light scattering characteristics from commercial off-the-shelf (COTS) camera lenses in order to deduce thereof a set of generic scattering parameters valid for a specific lens class (double Gauss lenses). In previous investigations, we developed a simplified theoretical light scattering model to estimate the irradiance distribution in the focal plane of a camera lens. This theoretical model is based on a 3-parameter bidirectional scattering distribution function (BSDF), which describes light scattering from rough surfaces of the optical elements. Ordinarily, the three scatter parameters of the BSDF are not known for COTS camera lenses, which makes it necessary to assess them by own experiments. Besides the experimental setup and the measurement process, we present in detail the subsequent data exploitation. From measurements on seven COTS camera lenses, we deduced a generic set of scatter parameters. For a deeper analysis, the results of our measurements have also been compared with the output of an optical engineering software. Together with our theoretical model, now stray light calculations can be accomplished even then, when specific scatter parameters are not available from elsewhere. In addition, the light scattering analyses also allow considering the glare vulnerability of optical systems in terms of laser safety. Full article

In optoacoustic (photoacoustic) systems, different echo signal intensities such as amplitudes, center frequencies, and bandwidths need to be compensated by utilizing variable gain or time-gain compensation amplifiers. However, such electronic components can increase system complexities and signal noise levels. In this paper, we introduce a double-Gauss lens to generate a large field of view with uniform light intensity due to the low chromatic aberrations of the lens, thus obtaining uniform echo signal intensities across the field of view of the optoacoustic system. In order to validate the uniformity of the echo signal intensities in the system, an in-house transducer was placed at various positions above a tissue sample and echo signals were measured and compared with each other. The custom designed double-Gauss lens demonstrated negligible light intensity variation (±1.5%) across the illumination field of view (~2 cm diameter). When the transducer was used to measure echo signal from an eye of a bigeye tuna within a range of ±1 cm, the peak-to-peak amplitude, center frequency, and their −6 dB bandwidth variations were less than 2 mV, 1 MHz, and 6%, respectively. The custom designed double-Gauss lens can provide uniform light beam across a wide area while generating insignificant echo signal variations, and thus can lower the burden of the receiving electronics or signal processing in the optoacoustic system. Full article