Detection of image structures using the Fisher information and the Rao metric

In many detection problems, the structures to be detected are parameterized by the points of a parameter space. If the conditional probability density function for the measurements is known, then detection can be achieved by sampling the parameter space at a finite number of points and checking each point to see if the corresponding structure is supported by the data. The number of samples and the distances between neighboring samples are calculated using the Rao metric on the parameter space. The Rao metric is obtained from the Fisher information which is, in turn, obtained from the conditional probability density function. An upper bound is obtained for the probability of a false detection. The calculations are simplified in the low noise case by making an asymptotic approximation to the Fisher information. An application to line detection is described. Expressions are obtained for the asymptotic approximation to the Fisher information, the volume of the parameter space, and the number of samples. The time complexity for line detection is estimated. An experimental comparison is made with a Hough transform-based method for detecting lines

Lens distortion correction by analysing the shape of patterns in Hough transform space : a thesis presented in partial fulfilment of the requirements for the degree of Master of Engineering in Electronics and Computer Engineering at Massey University, Manawatu, New Zealand

Many low cost, wide angle lenses suffer from lens distortion, resulting from a radial variation in the lens magnification. As a result, straight lines, particularly those in the periphery, appear curved. The Hough transform is a commonly used linear feature detection technique within an image. In Hough transform space, straight lines and curved lines have different shapes of peaks. This thesis proposes a lens distortion correction method named SLDC based on analysing the shape of patterns in the Hough transform space. It works by reconstructing the distorted line from significant points on the smile-shaped Hough pattern. It then optimises the distortion parameter by mapping the reconstructed curved line into a straight line and minimising the RMSE. From both simulation and correcting real world images, the SLDC provides encouraging results

All-sky search for periodic gravitational waves in LIGO S4 data

We report on an all-sky search with the LIGO detectors for periodic gravitational waves in the frequency range 50-1000 Hz and with the frequency's time derivative in the range -1.0E-8 Hz/s to zero. Data from the fourth LIGO science run (S4) have been used in this search. Three different semi-coherent methods of transforming and summing strain power from Short Fourier Transforms (SFTs) of the calibrated data have been used. The first, known as "StackSlide", averages normalized power from each SFT. A "weighted Hough" scheme is also developed and used, and which also allows for a multi-interferometer search. The third method, known as "PowerFlux", is a variant of the StackSlide method in which the power is weighted before summing. In both the weighted Hough and PowerFlux methods, the weights are chosen according to the noise and detector antenna-pattern to maximize the signal-to-noise ratio. The respective advantages and disadvantages of these methods are discussed. Observing no evidence of periodic gravitational radiation, we report upper limits; we interpret these as limits on this radiation from isolated rotating neutron stars. The best population-based upper limit with 95% confidence on the gravitational-wave strain amplitude, found for simulated sources distributed isotropically across the sky and with isotropically distributed spin-axes, is 4.28E-24 (near 140 Hz). Strict upper limits are also obtained for small patches on the sky for best-case and worst-case inclinations of the spin axes.Comment: 39 pages, 41 figures An error was found in the computation of the C parameter defined in equation 44 which led to its overestimate by 2^(1/4). The correct values for the multi-interferometer, H1 and L1 analyses are 9.2, 9.7, and 9.3, respectively. Figure 32 has been updated accordingly. None of the upper limits presented in the paper were affecte

The Hough transform estimator

This article pursues a statistical study of the Hough transform, the celebrated computer vision algorithm used to detect the presence of lines in a noisy image. We first study asymptotic properties of the Hough transform estimator, whose objective is to find the line that ``best'' fits a set of planar points. In particular, we establish strong consistency and rates of convergence, and characterize the limiting distribution of the Hough transform estimator. While the convergence rates are seen to be slower than those found in some standard regression methods, the Hough transform estimator is shown to be more robust as measured by its breakdown point. We next study the Hough transform in the context of the problem of detecting multiple lines. This is addressed via the framework of excess mass functionals and modality testing. Throughout, several numerical examples help illustrate various properties of the estimator. Relations between the Hough transform and more mainstream statistical paradigms and methods are discussed as well.Comment: Published at http://dx.doi.org/10.1214/009053604000000760 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Direct Observation of Cosmic Strings via their Strong Gravitational Lensing Effect: II. Results from the HST/ACS Image Archive

We have searched 4.5 square degrees of archival HST/ACS images for cosmic strings, identifying close pairs of similar, faint galaxies and selecting groups whose alignment is consistent with gravitational lensing by a long, straight string. We find no evidence for cosmic strings in five large-area HST treasury surveys (covering a total of 2.22 square degrees), or in any of 346 multi-filter guest observer images (1.18 square degrees). Assuming that simulations ccurately predict the number of cosmic strings in the universe, this non-detection allows us to place upper limits on the unitless Universal cosmic string tension of G mu/c^2 < 2.3 x 10^-6, and cosmic string density of Omega_s < 2.1 x 10^-5 at the 95% confidence level (marginalising over the other parameter in each case). We find four dubious cosmic string candidates in 318 single filter guest observer images (1.08 square degrees), which we are unable to conclusively eliminate with existing data. The confirmation of any one of these candidates as cosmic strings would imply G mu/c^2 ~ 10^-6 and Omega_s ~ 10^-5. However, we estimate that there is at least a 92% chance that these string candidates are random alignments of galaxies. If we assume that these candidates are indeed false detections, our final limits on G mu/c^2 and Omega_s fall to 6.5 x 10^-7 and 7.3 x 10^-6. Due to the extensive sky coverage of the HST/ACS image archive, the above limits are universal. They are quite sensitive to the number of fields being searched, and could be further reduced by more than a factor of two using forthcoming HST data.Comment: 21 pages, 18 figure