Hopf Map and Quantization on Sphere

Quantization of a system constrained to move on a sphere is considered by taking a square root of the ``on sphere condition''. We arrive at the fibre bundle structure of the Hopf map in the cases of $S^{2}$and $S^{4}$. This leads to more geometrical understanding of monopole and instanton gauge structures that emerge in the course of quantization.Comment: 9 pages, LaTeX2e, uses amsmath.st

Inequivalent Quantization in the Skyrme Model

Quantum mechanics on manifolds is not unique and in general infinite number of inequivalent quantizations can be considered. They are specified by the induced spin and the induced gauge structures on the manifold. The configuration space of collective mode in the Skyrme model can be identified with $S^{3}$ and thus the quantization is not unique. This leads to the different predictions for the physical observables.Comment: 16 pages, LaTeX2

Lost equivalence of nonlinear sigma and CP1CP^{1} models on noncommutative space

We show that the equivalence of nonlinear sigma and $CP^{1}$ models which is valid on the commutative space is broken on the noncommutative space. This conclusion is arrived at through investigation of new BPS solitons that do not exist in the commutative limit.Comment: 17 pages, LaTeX2

Anveshak - A Groundtruth Generation Tool for Foreground Regions of Document Images

We propose a graphical user interface based groundtruth generation tool in this paper. Here, annotation of an input document image is done based on the foreground pixels. Foreground pixels are grouped together with user interaction to form labeling units. These units are then labeled by the user with the user defined labels. The output produced by the tool is an image with an XML file containing its metadata information. This annotated data can be further used in different applications of document image analysis.Comment: Accepted in DAR 201

COCO_TS Dataset: Pixel-level Annotations Based on Weak Supervision for Scene Text Segmentation

The absence of large scale datasets with pixel-level supervisions is a significant obstacle for the training of deep convolutional networks for scene text segmentation. For this reason, synthetic data generation is normally employed to enlarge the training dataset. Nonetheless, synthetic data cannot reproduce the complexity and variability of natural images. In this paper, a weakly supervised learning approach is used to reduce the shift between training on real and synthetic data. Pixel-level supervisions for a text detection dataset (i.e. where only bounding-box annotations are available) are generated. In particular, the COCO-Text-Segmentation (COCO_TS) dataset, which provides pixel-level supervisions for the COCO-Text dataset, is created and released. The generated annotations are used to train a deep convolutional neural network for semantic segmentation. Experiments show that the proposed dataset can be used instead of synthetic data, allowing us to use only a fraction of the training samples and significantly improving the performances

Berry Connections and Induced Gauge Fields in Quantum Mechanics on Sphere

Quantum mechanics on sphere $S^{n}$ is studied from the viewpoint that the Berry's connection has to appear as a topological term in the effective action. Furthermore we show that this term is the Chern-Simons term of gauge variables that correspond to the extra degrees of freedom of the enlarged space.Comment: 12 pages, LaTeX2

Noncommutative Chern-Simons Soliton

We have studied the noncommutative extension of the relativistic Chern-Simons-Higgs model, in the first non-trivial order in $\theta$, with only spatial noncommutativity. Both Lagrangian and Hamiltonian formulations of the problem have been discussed, with the focus being on the canonical and symmetric forms of the energy-momentum tensor. In the Hamiltonian scheme, constraint analysis and the induced Dirac brackets have been provided. The spacetime translation generators and their actions on the fields are discussed in detail. The effects of noncommutativity on the soliton solutions have been analysed thoroughly and we have come up with some interesting observations. Considering the {\it{relative}} strength of the noncommutative effects, we have shown that there is a universal character in the noncommutative correction to the magnetic field - it depends {\it{only}} on $\theta$. On the other hand, in the cases of all other observables of physical interest, such as the potential profile, soliton mass or the electric field, $\theta$ as well as $\tau$, (comprising solely of commutative Chern-Simons-Higgs model parameters), appear on similar footings. This phenomenon is a new finding which has come up in the present analysis. Lastly, we have pointed out a generic problem in the NC extension of the models, in the form of a mismatch between the BPS dynamical equation and the full variational equations of motion, to $O(\theta)$. This mismatch indicates that the analysis is not complete as it brings in to fore the ambiguities in the definition of the energy-momentum tensor in a noncommutative theory.Comment: 21 page