No abstract

Abstract-For shapes represented as closed planar contours, we introduce a class of functionals which are invariant with respect to the Euclidean group and which are obtained by performing integral operations. While such integral invariants enjoy some of the desirable properties of their differential counterparts, such as locality of computation (which allows matching under occlusions) and uniqueness of representation (asymptotically), they do not exhibit the noise sensitivity associated with differential quantities and, therefore, do not require presmoothing of the input shape. Our formulation allows the analysis of shapes at multiple scales. Based on integral invariants, we define a notion of distance between shapes. The proposed distance measure can be computed efficiently and allows warping the shape boundaries onto each other; its computation results in optimal point correspondence as an intermediate step.Numerical results on shape matching demonstrate that this framework can match shapes despite the deformation of subparts, missing parts and noise. As a quantitative analysis, we report matching scores for shape retrieval from a database.

For shapes represented as closed planar contours, we introduce a class of functionals that are invariant with respect to the Euclidean and similarity group, obtained by performing integral operations. While such integral invariants enjoy some of the desirable properties of their differential cousins, such as locality of computation (which allows matching under occlusions) and uniqueness of representation (in the limit), they are not as sensitive to noise in the data. We exploit the integral invariants to define a unique signature, from which the original shape can be reconstructed uniquely up to the symmetry group, and a notion of scale-space that allows analysis at multiple levels of resolution. The invariant signature can be used as a basis to define various notions of distance between shapes, and we illustrate the potential of the integral invariant representation for shape matching on real and synthetic data.

We study the effect of extended charge defects in electronic transport properties of graphene. Extended defects are ubiquitous in chemically and epitaxially grown graphene samples due to internal strains associated with the lattice mismatch. We show that at low energies these defects interact quite strongly with the 2D Dirac fermions and have an important effect in the DC-conductivity of these materials.

Textures within real images vary in brightness, contrast, scale and skew as imaging conditions change. To enable recognition of textures in real images, it is necessary to employ a similarity measure which is invariant to these properties. Furthermore, since textures often appear on undulating surfaces, such invariances must necessarily be local rather than global. Despite these requirements, it is only relatively recently that texture recognition algorithms with local scale and affine invariance properties have begun to be reported. Typically, they comprise detecting feature points followed by geometric normalization prior to description. We describe a method based on invariant combinations of linear filters. Unlike previous methods, we introduce a novel family of filters, which provide scale invariance, resulting in a texture description invariant to local changes in orientation, contrast and scale and robust to local skew. Significantly, the family of filters enable local scale invariants to be defined without using a scale selection principle or a large number of filters. A texture discrimination method based on the A2 similarity measure applied to histograms derived from our filter responses outperforms existing methods for retrieval and classification results for both the Brodatz textures and the UIUC database, which has been designed to require local invariance.