A semidiscrete version of the Citti-Petitot-Sarti model as a plausible model for anthropomorphic image reconstruction and pattern recognition

In his beautiful book [66], Jean Petitot proposes a sub-Riemannian model for the primary visual cortex of mammals. This model is neurophysiologically justified. Further developments of this theory lead to efficient algorithms for image reconstruction, based upon the consideration of an associated hypoelliptic diffusion. The sub-Riemannian model of Petitot and Citti-Sarti (or certain of its improvements) is a left-invariant structure over the group $SE(2)$ of rototranslations of the plane. Here, we propose a semi-discrete version of this theory, leading to a left-invariant structure over the group $SE(2,N)$, restricting to a finite number of rotations. This apparently very simple group is in fact quite atypical: it is maximally almost periodic, which leads to much simpler harmonic analysis compared to $SE(2).$ Based upon this semi-discrete model, we improve on previous image-reconstruction algorithms and we develop a pattern-recognition theory that leads also to very efficient algorithms in practice.Comment: 123 pages, revised versio

Data Fusion for Topographic Object Classification

This paper presents research conducted into the automatic recognition of features and objects on topographic maps (for example, buildings, roads, land parcels etc.) using a selection of shape description methods developed mostly in the field of computer vision. In particular the work here focuses on the proposal and evaluation of fusion techniques (at the decision level of representation) for the classification of topographic data. A set of Ordnance Survey large-scale digital data (1:1250 and 1:2500) was used to evaluate the classification performance of the shape recognition methods used. Each technique proved partially successful in distinguishing classes of objects, however, no one technique provided a general solution to the problem. Further outlined experiments combine these techniques, using a data fusion methodology, on the real-world problem of checking and assigning feature codes in large-scale Ordnance Survey digital data

Feature Extraction Methods for Character Recognition

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Applying Computer Vision Techniques to Topographic Objects

Automatic structuring (feature coding and object recognition) of topographic data, such as that derived from air survey or raster scanning large-scale paper maps, requires the classification of objects such as buildings, roads, rivers, fields and railways. The recognition of objects is largely based on the matching of descriptions of shapes. Fourier descriptors, moment invariants, boundary chain coding and scalar descriptors are widely used in image processing and computer vision to describe and classify shapes. They have been developed to describe shape irrespective of position, orientation and scale. The applicability of the above four methods to topographic shapes is described and their usefulness evaluated.

Band selection and disentanglement using maximally-localized Wannier functions: the cases of Co impurities in bulk copper and the Cu (111) surface

We have adapted the maximally-localized Wannier function approach of [I. Souza, N. Marzari and D. Vanderbilt, Phys. Rev. B 65, 035109 (2002)] to the density functional theory based Siesta method [J. M. Soler et al., J. Phys.: Cond. Mat. 14, 2745 (2002)] and applied it to the study of Co substitutional impurities in bulk copper as well as to the Cu (111) surface. In the Co impurity case, we have reduced the problem to the Co d-electrons and the Cu sp-band, permitting us to obtain an Anderson-like Hamiltonian from well defined density functional parameters in a fully orthonormal basis set. In order to test the quality of the Wannier approach to surfaces, we have studied the electronic structure of the Cu (111) surface by again transforming the density functional problem into the Wannier representation. An excellent description of the Shockley surface state is attained, permitting us to be confident in the application of this method to future studies of magnetic adsorbates in the presence of an extended surface state

Topographic Object Recognition Through Shape

Automatic structuring (feature coding and object recognition) of topographic data, such as that derived from air survey or raster scanning large-scale paper maps, requires the classification of objects such as buildings, roads, rivers, fields and railways. The recognition of objects in computer vision is largely based on the matching of descriptions of shapes. Fourier descriptors, moment invariants, boundary chain coding and scalar descriptors are methods that have been widely used and have been developed to describe shape irrespective of position, orientation and scale. The applicability of the above four methods to topographic shapes is described and their usefulness evaluated. All methods derive descriptors consisting of a small number of real values from the object's polygonal boundary. Two large corpora representing data sets from Ordnance Survey maps of Purbeck and Plymouth were available. The effectiveness of each description technique was evaluated by using one corpus as a training-set to derive distributions for the values for supervised learning. This was then used to reclassify the objects in both data sets using each individual descriptor to evaluate their effectiveness. No individual descriptor or method produced consistent correct classification. Various models for the fusion of the classification results from individual descriptors were implemented. These were used to experiment with different combinations of descriptors in order to improve results. Overall results show that Moment Invariants fused with the minfusion rule gave the best performance with the two data sets. Much further work remains to be done as enumerated in the concluding section

Comparative Analysis of Techniques Used to Detect Copy-Move Tampering for Real-World Electronic Images

Evolution of high computational powerful computers, easy availability of several innovative editing software package and high-definition quality-based image capturing tools follows to effortless result in producing image forgery. Though, threats for security and misinterpretation of digital images and scenes have been observed to be happened since a long period and also a lot of research has been established in developing diverse techniques to authenticate the digital images. On the contrary, the research in this region is not limited to checking the validity of digital photos but also to exploring the specific signs of distortion or forgery. This analysis would not require additional prior information of intrinsic content of corresponding digital image or prior embedding of watermarks. In this paper, recent growth in the area of digital image tampering identification have been discussed along with benchmarking study has been shown with qualitative and quantitative results. With variety of methodologies and concepts, different applications of forgery detection have been discussed with corresponding outcomes especially using machine and deep learning methods in order to develop efficient automated forgery detection system. The future applications and development of advanced soft-computing based techniques in digital image forgery tampering has been discussed