Real-Time Anisotropic Diffusion using Space-Variant Vision

Many computer and robot vision applications require multi-scale image analysis. Classically, this has been accomplished through the use of a linear scale-space, which is constructed by convolution of visual input with Gaussian kernels of varying size (scale). This has been shown to be equivalent to the solution of a linear diffusion equation on an infinite domain, as the Gaussian is the Green's function of such a system (Koenderink, 1984). Recently, much work has been focused on the use of a variable conductance function resulting in anisotropic diffusion described by a nonlinear partial differential equation (PDF). The use of anisotropic diffusion with a conductance coefficient which is a decreasing function of the gradient magnitude has been shown to enhance edges, while decreasing some types of noise (Perona and Malik, 1987). Unfortunately, the solution of the anisotropic diffusion equation requires the numerical integration of a nonlinear PDF which is a costly process when carried out on a fixed mesh such as a typical image. In this paper we show that the complex log transformation, variants of which are universally used in mammalian retino-cortical systems, allows the nonlinear diffusion equation to be integrated at exponentially enhanced rates due to the non-uniform mesh spacing inherent in the log domain. The enhanced integration rates, coupled with the intrinsic compression of the complex log transformation, yields a seed increase of between two and three orders of magnitude, providing a means of performing real-time image enhancement using anisotropic diffusion.Office of Naval Research (N00014-95-I-0409

Image Processing Instrumentation for Giardia lamblia Detection

Currently, the identification and enumeration of Giardia Iamblia cysts are based upon microscopic methods requiring individuals proficient in this area. It is a tedious process which consumes time that could be constructively used elsewhere. This project attempts to alleviate that burden by employing a computer to automatically process Indirect Fluorescent Antibody (IFA) prepared slides using digital image processing techniques. A computer controlled frame grabber, in conjunction with a CCD TV camera mounted on the epi-fluorescence microscope phototube, captures the light intensities of the objects in view under the microscope objective. The captured image is stored as pixels, with each pixel having a numerical value that can be altered using linear contrast enhancement and bit-slicing to emphasize the cysts and eliminate the majority of unwanted objects from the image. The altered image is then analyzed by a vector trace routine for typical area and perimeters characteristic to Giardia lamblia cysts. Objects in the image matching these characteristics are most likely cysts and are added to a running tally of the number of cysts present on the slide

Qualitative comparison of several phase correction algorithms in single-image in-line X-ray phase contrast tomography

In recent years, phase contrast has gained importance in the field of X-ray imaging and more particular in high-resolution X-ray computed tomography or micro-CT. For phase propagation imaging, no additional hardware or specific setup is required, which makes the effect inherent to micro-CT where it is manifested as an edge-enhancement effect. As such, it can be beneficial for qualitative analysis of a 3D volume. Nevertheless, it induces unreal gray values and is thus often considered as an imaging artefact which hinders proper quantitative 3D analysis. Several methods exist to reduce this phase contrast effect or to retrieve the phase information from the mixed phase-and-amplitude images. In this presentation, a comparison will be made between 2 phase retrieval algorithms and 2 phase correction algorithms. Of these 2 latter, one can be performed on the reconstructed volume, which clearly facilitates the operation of phase correction

Galaxy density profiles and shapes -- II. selection biases in strong lensing surveys

[Abridged] Many current and future astronomical surveys will rely on samples of strong gravitational lens systems to draw conclusions about galaxy mass distributions. We use a new strong lensing pipeline (presented in Paper I of this series) to explore selection biases that may cause the population of strong lensing systems to differ from the general galaxy population. Our focus is on point-source lensing by early-type galaxies with two mass components (stellar and dark matter) that have a variety of density profiles and shapes motivated by observational and theoretical studies of galaxy properties. We seek not only to quantify but also to understand the physics behind selection biases related to: galaxy mass, orientation and shape; dark matter profile parameters such as inner slope and concentration; and adiabatic contraction. We study how all of these properties affect the lensing Einstein radius, total cross-section, quad/double ratio, and image separation distribution. We find significant (factors of several) selection biases with mass; orientation, for a given galaxy shape at fixed mass; cusped dark matter profile inner slope and concentration; concentration of the stellar and dark matter deprojected Sersic models. Interestingly, the intrinsic shape of a galaxy does not strongly influence its lensing cross-section when we average over viewing angles. Our results are an important first step towards understanding how strong lens systems relate to the general galaxy population.Comment: 26 pages, 15 figures; paper I at arXiv:0808.2493; accepted for publication in MNRAS (minor revisions); PDF file with full resolution figures at http://www.sns.ias.edu/~rmandelb/paper2.pd

Gravitational Microlensing of a Reverberating Quasar Broad Line Region - I. Method and Qualitative Results

The kinematics and morphology of the broad emission line region (BELR) of quasars are the subject of significant debate. The two leading methods for constraining BELR properties are microlensing and reverberation mapping. Here we combine these two methods with a study of the microlensing behaviour of the BELR in Q2237+0305, as a change in continuum emission (a "flare") passes through it. Beginning with some generic models of the BELR - sphere, bicones, disk - we slice in velocity and time to produce brightness profiles of the BELR over the duration of the flare. These are numerically microlensed to determine whether microlensing of reverberation mapping provides new information about the properties of BELRs. We describe our method and show images of the models as they are flaring, and the unlensed and lensed spectra that are produced. Qualitative results and a discussion of the spectra are given in this paper, highlighting some effects that could be observed. Our conclusion is that the influence of microlensing, while not strong, can produce significant observable effects that will help in differentiating the properties of BELRs.Comment: 17 pages, 14 low resolution figures, 1 table, accepted for MNRAS. v2: Corrected velocities p16, 8 to 0.08, 9 to 0.0