The Local Structure of Space-Variant Images

Local image structure is widely used in theories of both machine and biological vision. The form of the differential operators describing this structure for space-invariant images has been well documented (e.g. Koenderink, 1984). Although space-variant coordinates are universally used in mammalian visual systems, the form of the operators in the space-variant domain has received little attention. In this report we derive the form of the most common differential operators and surface characteristics in the space-variant domain and show examples of their use. The operators include the Laplacian, the gradient and the divergence, as well as the fundamental forms of the image treated as a surface. We illustrate the use of these results by deriving the space-variant form of corner detection and image enhancement algorithms. The latter is shown to have interesting properties in the complex log domain, implicitly encoding a variable grid-size integration of the underlying PDE, allowing rapid enhancement of large scale peripheral features while preserving high spatial frequencies in the fovea.Office of Naval Research (N00014-95-I-0409

Performance Assessment of Feature Detection Algorithms: A Methodology and Case Study on Corner Detectors

In this paper we describe a generic methodology for evaluating the labeling performance of feature detectors. We describe a method for generating a test set and apply the methodology to the performance assessment of three well-known corner detectors: the Kitchen-Rosenfeld, Paler et al. and Harris-Stephens corner detectors. The labeling deficiencies of each of these detectors is related to their discrimination ability between corners and various of the features which comprise the class of noncorners

A new Edge Detector Based on Parametric Surface Model: Regression Surface Descriptor

In this paper we present a new methodology for edge detection in digital images. The first originality of the proposed method is to consider image content as a parametric surface. Then, an original parametric local model of this surface representing image content is proposed. The few parameters involved in the proposed model are shown to be very sensitive to discontinuities in surface which correspond to edges in image content. This naturally leads to the design of an efficient edge detector. Moreover, a thorough analysis of the proposed model also allows us to explain how these parameters can be used to obtain edge descriptors such as orientations and curvatures. In practice, the proposed methodology offers two main advantages. First, it has high customization possibilities in order to be adjusted to a wide range of different problems, from coarse to fine scale edge detection. Second, it is very robust to blurring process and additive noise. Numerical results are presented to emphasis these properties and to confirm efficiency of the proposed method through a comparative study with other edge detectors.Comment: 21 pages, 13 figures and 2 table

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

Primordial non-Gaussianity and Bispectrum Measurements in the Cosmic Microwave Background and Large-Scale Structure

The most direct probe of non-Gaussian initial conditions has come from bispectrum measurements of temperature fluctuations in the Cosmic Microwave Background and of the matter and galaxy distribution at large scales. Such bispectrum estimators are expected to continue to provide the best constraints on the non-Gaussian parameters in future observations. We review and compare the theoretical and observational problems, current results and future prospects for the detection of a non-vanishing primordial component in the bispectrum of the Cosmic Microwave Background and large-scale structure, and the relation to specific predictions from different inflationary models.Comment: 82 pages, 23 figures; Invited Review for the special issue "Testing the Gaussianity and Statistical Isotropy of the Universe" for Advances in Astronom

From 3D Point Clouds to Pose-Normalised Depth Maps

We consider the problem of generating either pairwise-aligned or pose-normalised depth maps from noisy 3D point clouds in a relatively unrestricted poses. Our system is deployed in a 3D face alignment application and consists of the following four stages: (i) data filtering, (ii) nose tip identification and sub-vertex localisation, (iii) computation of the (relative) face orientation, (iv) generation of either a pose aligned or a pose normalised depth map. We generate an implicit radial basis function (RBF) model of the facial surface and this is employed within all four stages of the process. For example, in stage (ii), construction of novel invariant features is based on sampling this RBF over a set of concentric spheres to give a spherically-sampled RBF (SSR) shape histogram. In stage (iii), a second novel descriptor, called an isoradius contour curvature signal, is defined, which allows rotational alignment to be determined using a simple process of 1D correlation. We test our system on both the University of York (UoY) 3D face dataset and the Face Recognition Grand Challenge (FRGC) 3D data. For the more challenging UoY data, our SSR descriptors significantly outperform three variants of spin images, successfully identifying nose vertices at a rate of 99.6%. Nose localisation performance on the higher quality FRGC data, which has only small pose variations, is 99.9%. Our best system successfully normalises the pose of 3D faces at rates of 99.1% (UoY data) and 99.6% (FRGC data)