On reflection symmetry in natural images

Many new symmetry detection algorithms have been recently developed, thanks to an interest revival on computational symmetry for computer graphics and computer vision applications. Notably, in 2013 the IEEE CVPR Conference organized a dedicated workshop and an accompanying symmetry detection competition. In this paper we propose an approach for symmetric object detection that is based both on the computation of a symmetry measure for each pixel and on saliency. The symmetry value is obtained as the energy balance of the even-odd decomposition of a patch w.r.t. each possible axis. The candidate symmetry axes are then identified through the localization of peaks along the direction perpendicular to each considered axis orientation. These found candidate axes are finally evaluated through a confidence measure that also allow removing redundant detected symmetries. The obtained results within the framework adopted in the aforementioned competition show significant performance improvement

A normalized mirrored correlation measure for data symmetry detection

Symmetry detection algorithms are enjoying a renovated interest in the scientific community, fueled by recent advancements in computer vision and computer graphics applications. This paper is inspired by recent efforts in building a symmetric object detection system in natural images. In particular, it is first shown how correlation can be a core operator that allows finding local reflection symmetry points in 1-D sequences that are optimal in an energetic sense. Then, the importance of 2-D correlation in natural images to correctly align the symmetric object axis is demonstrated. Using the correlation as described is crucial in boosting the performance of the system, as proven by the results on a standard dataset

Twinning of cubic diamond explains reported nanodiamond polymorphs

The unusual physical properties and formation conditions attributed to h-, i-, m-, and n-nanodiamond polymorphs has resulted in their receiving much attention in the materials and planetary science literature. Their identification is based on diffraction features that are absent in ordinary cubic (c-) diamond (space group: Fd-3m). We show, using ultra-high-resolution transmission electron microscope (HRTEM) images of natural and synthetic nanodiamonds, that the diffraction features attributed to the reported polymorphs are consistent with c-diamond containing abundant defects. Combinations of {113} reflection and rotation twins produce HRTEM images and d-spacings that match those attributed to h-, i-, and m-diamond. The diagnostic features of n-diamond in TEM images can arise from thickness effects of c-diamonds. Our data and interpretations strongly suggest that the reported nanodiamond polymorphs are in fact twinned c-diamond. We also report a new type of twin ( rotational), which can give rise to grains with dodecagonal symmetry. Our results show that twins are widespread in diamond nanocrystals. A high density of twins could strongly influence their applications

Symmetry sensitivities of Derivative-of-Gaussian filters

We consider the measurement of image structure using linear filters, in particular derivative-of-Gaussian (DtG) filters, which are an important model of V1 simple cells and widely used in computer vision, and whether such measurements can determine local image symmetry. We show that even a single linear filter can be sensitive to a symmetry, in the sense that specific responses of the filter can rule it out. We state and prove a necessary and sufficient, readily computable, criterion for filter symmetry-sensitivity. We use it to show that the six filters in a second order DtG family have patterns of joint sensitivity which are distinct for 12 different classes of symmetry. This rich symmetry-sensitivity adds to the properties that make DtG filters well-suited for probing local image structure, and provides a set of landmark responses suitable to be the foundation of a nonarbitrary system of feature categories

Sutherland Models for Complex Reflection Groups

There are known to be integrable Sutherland models associated to every real root system -- or, which is almost equivalent, to every real reflection group. Real reflection groups are special cases of complex reflection groups. In this paper we associate certain integrable Sutherland models to the classical family of complex reflection groups. Internal degrees of freedom are introduced, defining dynamical spin chains, and the freezing limit taken to obtain static chains of Haldane-Shastry type. By considering the relation of these models to the usual BC_N case, we are led to systems with both real and complex reflection groups as symmetries. We demonstrate their integrability by means of new Dunkl operators, associated to wreath products of dihedral groups.Comment: 26 pages, 8 figures, latex; v3, acknowledgement adde

Suppression of backscattered diffraction from sub-wavelength ‘moth-eye’ arrays

The eyes and wings of some species of moth are covered with arrays of nanoscale features that dramatically reduce reflection of light. There have been multiple examples where this approach has been adapted for use in antireflection and antiglare technologies with the fabrication of artificial moth-eye surfaces. In this work, the suppression of iridescence caused by the diffraction of light from such artificial regular moth-eye arrays at high angles of incidence is achieved with the use of a new tiled domain design, inspired by the arrangement of features on natural moth-eye surfaces. This bio-mimetic pillar architecture contains high optical rotational symmetry and can achieve high levels of diffraction order power reduction. For example, a tiled design fabricated in silicon and consisting of domains with 9 different orientations of the traditional hexagonal array exhibited a ~96% reduction in the intensity of the ?1 diffraction order. It is suggested natural moth-eye surfaces have evolved a tiled domain structure as it confers efficient antireflection whilst avoiding problems with high angle diffraction. This combination of antireflection and stealth properties increases chances of survival by reducing the risk of the insect being spotted by a predator. Furthermore, the tiled domain design could lead to more effective artificial moth-eye arrays for antiglare and stealth applications

Twinning of cubic diamond explains reported nanodiamond polymorphs

abstract: The unusual physical properties and formation conditions attributed to h-, i-, m-, and n-nanodiamond polymorphs has resulted in their receiving much attention in the materials and planetary science literature. Their identification is based on diffraction features that are absent in ordinary cubic (c-) diamond (space group: Fd-3m). We show, using ultra-high-resolution transmission electron microscope (HRTEM) images of natural and synthetic nanodiamonds, that the diffraction features attributed to the reported polymorphs are consistent with c-diamond containing abundant defects. Combinations of {113} reflection and rotation twins produce HRTEM images and d-spacings that match those attributed to h-, i-, and m-diamond. The diagnostic features of n-diamond in TEM images can arise from thickness effects of c-diamonds. Our data and interpretations strongly suggest that the reported nanodiamond polymorphs are in fact twinned c-diamond. We also report a new type of twin ( rotational), which can give rise to grains with dodecagonal symmetry. Our results show that twins are widespread in diamond nanocrystals. A high density of twins could strongly influence their applications.The final version of this article, as published in Scientific Reports, can be viewed online at: https://www.nature.com/articles/srep1838