A Fisher-Rao metric for paracatadioptric images of lines

In a central paracatadioptric imaging system a perspective camera takes an image of a scene reflected in a paraboloidal mirror. A 360° field of view is obtained, but the image is severely distorted. In particular, straight lines in the scene project to circles in the image. These distortions make it diffcult to detect projected lines using standard image processing algorithms. The distortions are removed using a Fisher-Rao metric which is defined on the space of projected lines in the paracatadioptric image. The space of projected lines is divided into subsets such that on each subset the Fisher-Rao metric is closely approximated by the Euclidean metric. Each subset is sampled at the vertices of a square grid and values are assigned to the sampled points using an adaptation of the trace transform. The result is a set of digital images to which standard image processing algorithms can be applied. The effectiveness of this approach to line detection is illustrated using two algorithms, both of which are based on the Sobel edge operator. The task of line detection is reduced to the task of finding isolated peaks in a Sobel image. An experimental comparison is made between these two algorithms and third algorithm taken from the literature and based on the Hough transform

New algorithmic developments in maximum consensus robust fitting

In many computer vision applications, the task of robustly estimating the set of parameters of a geometric model is a fundamental problem. Despite the longstanding research efforts on robust model fitting, there remains significant scope for investigation. For a large number of geometric estimation tasks in computer vision, maximum consensus is the most popular robust fitting criterion. This thesis makes several contributions in the algorithms for consensus maximization. Randomized hypothesize-and-verify algorithms are arguably the most widely used class of techniques for robust estimation thanks to their simplicity. Though efficient, these randomized heuristic methods do not guarantee finding good maximum consensus estimates. To improve the randomize algorithms, guided sampling approaches have been developed. These methods take advantage of additional domain information, such as descriptor matching scores, to guide the sampling process. Subsets of the data that are more likely to result in good estimates are prioritized for consideration. However, these guided sampling approaches are ineffective when good domain information is not available. This thesis tackles this shortcoming by proposing a new guided sampling algorithm, which is based on the class of LP-type problems and Monte Carlo Tree Search (MCTS). The proposed algorithm relies on a fundamental geometric arrangement of the data to guide the sampling process. Specifically, we take advantage of the underlying tree structure of the maximum consensus problem and apply MCTS to efficiently search the tree. Empirical results show that the new guided sampling strategy outperforms traditional randomized methods. Consensus maximization also plays a key role in robust point set registration. A special case is the registration of deformable shapes. If the surfaces have the same intrinsic shapes, their deformations can be described accurately by a conformal model. The uniformization theorem allows the shapes to be conformally mapped onto a canonical domain, wherein the shapes can be aligned using a M¨obius transformation. The problem of correspondence-free M¨obius alignment of two sets of noisy and partially overlapping point sets can be tackled as a maximum consensus problem. Solving for the M¨obius transformation can be approached by randomized voting-type methods which offers no guarantee of optimality. Local methods such as Iterative Closest Point can be applied, but with the assumption that a good initialization is given or these techniques may converge to a bad local minima. When a globally optimal solution is required, the literature has so far considered only brute-force search. This thesis contributes a new branch-and-bound algorithm that solves for the globally optimal M¨obius transformation much more efficiently. So far, the consensus maximization problems are approached mainly by randomized algorithms, which are efficient but offer no analytical convergence guarantee. On the other hand, there exist exact algorithms that can solve the problem up to global optimality. The global methods, however, are intractable in general due to the NP-hardness of the consensus maximization. To fill the gap between the two extremes, this thesis contributes two novel deterministic algorithms to approximately optimize the maximum consensus criterion. The first method is based on non-smooth penalization supported by a Frank-Wolfe-style optimization scheme, and another algorithm is based on Alternating Direction Method of Multipliers (ADMM). Both of the proposed methods are capable of handling the non-linear geometric residuals commonly used in computer vision. As will be demonstrated, our proposed methods consistently outperform other heuristics and approximate methods.Thesis (Ph.D.) (Research by Publication) -- University of Adelaide, School of Computer Science, 201

Acetylcholine Receptors and Concanavalin A-Binding Sites on Cultured Xenopus Muscle Cells: Electrophoresis, Diffusion, and Aggregation

Using digitally analyzed fluorescence videomicroscopy, we have examined the behavior of acetylcholine receptors and concanavalin A binding sites in response to externally applied electric fields. The distributions of these molecules on cultured Xenopus myoballs were used to test a simple model which assumes that electrophoresis and diffusion are the only important processes involved. The model describes the distribution of concanavalin A sites quite well over a fourfold range of electric field strengths; the results suggest an average diffusion constant of ~2.3 X 10^(-9) cm^2/s. At higher electric field strengths, the asymmetry seen is substantially less than that predicted by the model. Acetylcholine receptors subjected to electric fields show distributions substantially different from those predicted on the basis of simple electrophoresis and diffusion, and evidence a marked tendency to aggregate. Our results suggest that this aggregation is due to lateral migration of surface acetylcholine receptors, and is dependent on surface interactions, rather than the rearrangement of microfilaments or microtubules. The data are consistent with a diffusion-trap mechanism of receptor aggregation, and suggest that the event triggering receptor localization is a local increase in the concentration of acetylcholine receptors, or the electrophoretic concentration of some other molecular species. These observations suggest that, whatever mechanism(s) trigger initial clustering events in vivo, the accumulation of acetylcholine receptors can be substantially enhanced by passive, diffusion-mediated aggregation

Exploring Halo Substructure with Giant Stars IV: The Extended Structure of the Ursa Minor Dwarf Spheroidal

We present a large area photometric survey of the Ursa Minor dSph. We identify UMi giant star candidates extending to ~3 deg from the center of the dSph. Comparison to previous catalogues of stars within the tidal radius of UMi suggests that our photometric luminosity classification is 100% accurate. Over a large fraction of the survey area, blue horizontal branch stars associated with UMi can also be identified. The spatial distribution of both the UMi giant stars and the BHB stars are remarkably similar, and a large fraction of both samples of stars are found outside the tidal radius of UMi. An isodensity contour map of the stars within the tidal radius of UMi reveals two morphological peculiarities: (1) The highest density of dSph stars is offset from the center of symmetry of the outer isodensity contours. (2) The overall shape of the outer contours appear S-shaped. We find that previously determined King profiles with ~50' tidal radii do not fit well the distribution of our UMi stars. A King profile with a larger tidal radius produces a reasonable fit, however a power law with index -3 provides a better fit for radii > 20'. The existence of UMi stars at large distances from the core of the galaxy, the peculiar morphology of the dSph within its tidal radius, and the shape of its surface density profile all suggest that UMi is evolving significantly due to the tidal influence of the Milky Way. However, the photometric data on UMi stars alone does not allow us to determine if the candidate extratidal stars are now unbound or if they remain bound to the dSph within an extended dark matter halo. (Abridged)Comment: accepted by AJ, 32 pages, 15 figures, emulateapj5 styl

Digital hyperplane fitting

International audienceThis paper addresses the hyperplane fitting problem of discrete points in any dimension (i.e. in Z d). For that purpose, we consider a digital model of hyperplane, namely digital hyperplane, and present a combinatorial approach to find the optimal solution of the fitting problem. This method consists in computing all possible digital hyperplanes from a set S of n points, then an exhaustive search enables us to find the optimal hyperplane that best fits S. The method has, however, a high complexity of O(n d), and thus can not be applied for big datasets. To overcome this limitation, we propose another method relying on the Delaunay triangulation of S. By not generating and verifying all possible digital hyperplanes but only those from the elements of the triangula-tion, this leads to a lower complexity of O(n d 2 +1). Experiments in 2D, 3D and 4D are shown to illustrate the efficiency of the proposed method

WFPC2 Observations of the Carina Dwarf Spheroidal Galaxy

We present our analysis of Hubble Space Telescope Wide Field Planetary Camera 2 observations in F555W (~V) and F814W (~I) of the Carina dwarf spheroidal galaxy. The resulting V vs (V-I) color-magnitude diagrams reach V ~ 27.1 mag. The reddening of Carina is estimated to be E(V-I) = 0.08 +- 0.02 mag. A new estimate of the distance modulus of Carina, (m-M)_0 = 19.87 +- 0.11 mag, has been derived primarily from existing photometry in the literature. The apparent distance moduli in V and I were determined to be (m-M)_V = 20.05 +- 0.11 mag and (m-M)_I = 19.98 +- 0.12 mag, respectively. These determinations assumed that Carina has a metallicity of [Fe/H] = -1.9 +- 0.2 dex. This space-based observation, when combined with previous ground-based observations, is consistent with (but does not necessarily prove) the following star formation scenario. The Carina dwarf spheroidal galaxy formed its old stellar population in a short burst (=< 3 Gyr) at about the same time the Milky Way formed its globular clusters. The dominant burst of intermediate-age star formation then began in the central region of the galaxy where stars formed for several billion years before the process of star formation became efficient enough in the outer regions of the galaxy to allow for the formation of large numbers of stars. There has been negligible star formation during the last few billion years. This observation provides evidence that at least some dwarf galaxies can have complex global star formation histories with local variations of the rate of star formation as a function of time and position within the galaxy.Comment: 23 pages (LaTeX+aaspp4.sty), 4 tables and 9 figures (Postscript, gzipped tar file). Postscript version of paper, tables, and full-resolution figures available at http://www.noao.edu/noao/staff/mighell/carina.html To appear in the Astronomical Journa

Segmenting trajectories: A framework and algorithms using spatiotemporal criteria

In this paper we address the problem of segmenting a trajectory based on spatiotemporal criteria. We require that each segment is homogeneous in the sense that a set of spatiotemporal criteria are fulfilled. We define different such criteria including location heading speed velocity curvature sinuosity curviness and shape. We present an algorithmic framework that allows us to segment any trajectory into a minimum number of segments under any of these criteria or any combination of these criteria. In this framework a segmentation can generally be computed in O(n log n) time where n is the number of edges of the trajectory to be segmented. We also discuss the robustness of our approach

Segmenting trajectories: A framework and algorithms using spatiotemporal criteria

In this paper we address the problem of segmenting a trajectory based on spatiotemporal criteria. We require that each segment is homogeneous in the sense that a set of spatiotemporal criteria are fulfilled. We define different such criteria, including location, heading, speed, velocity, curvature, sinuosity, curviness, and shape. We present an algorithmic framework that allows us to segment any trajectory into a minimum number of segments under any of these criteria, or any combination of these criteria. In this framework, a segmentation can generally be computed in O(n log n) time, where n is the number of edges of the trajectory to be segmented. We also discuss the robustness of our approach.Peer ReviewedPostprint (published version

Wide field beamformed observation with MeerKAT

Large-scale beamforming with radio interferometers has the potential to revolutionize the science done with pulsars and fast radio bursts by improving the survey efficiency for these sources. We describe a wide-field beamformer for the MeerKAT radio telescope and outline strategies to optimally design such surveys. A software implementation of these techniques, ${\rm M{\small OSAIC}}$ is introduced and its application in the MeerKAT telescope is presented. We show initial results using the beamformer by observing a globular cluster to track several pulsars simultaneously and demonstrate the source localization capability of this observation