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A piece of text that basically describes a graphic (or diagram) often appears in many branches of science and engineering. Researchers have attempted to involve machine in drawing the underlying graphics after automatically understanding the text but automatic evaluation of the accuracy of such drawing remained unexplored. This paper aims at measuring the accuracy of the graphic which comes from a text-to-graphic conversion process. Experiments show that this evaluation problem poses several challenges which have not been addressed before and hence calls for new initiatives. School level geometry problems have been taken as reference to demonstrate the underlying challenges and related issues.

A fast and efficient algorithm for segmentation of the articulated components of 3D objects is proposed. The algorithm is marked by several novel features, such as DCEL-based fast orthogonal slicing, weighted Reeb graph with slice areas as vertex weights, and graph cut by exponential averaging. Each of the three sets of orthogonal slices obtained from the object is represented by a vertex-weighted Reeb graph of low complexity, as the slicing is done with an appropriate grid resolution. Each linear subgraph in a Reeb graph is traversed from its leaf node up to an articulation node or up to a node whose weight exceeds a dynamically-set threshold, based on exponential averaging of the predecessor weights in the concerned subgraph. The nodes visited in each linear subgraph are marked by a unique component number, thereby helping the inverse mapping for marking the articulated regions during final segmentation. Theoretical analysis shows that the algorithm runs faster for objects with smaller surface area and for larger grid resolutions. The algorithm is stable, invariant to rotation, and leads to natural segmentation, as evidenced by experimentation with a varied dataset.

We present the mathematical model for TPBS parameters via Fourier Grid Hamiltonian method after second quantization on a K-G lattice is done with Bosonic operators. This study is realistic to understand quantum localization by nonlinearity that is essential for many small-structured nano-devices. An eigenspectrum is shown that indicates two-phonon QB state separated at upper segment of energy from a single-phonon continuum. Hence, the objective of this paper is to explore whether the switching is easier at a particular point of nonlinearity by quantum calculations hitherto not done on lithium tantalite.

The goal of this paper is to explore whether SRR system, through engineering of their geometry (i.e. change of coupling) and permittivity, shows any sensitivity on the femtosecond response of quantum breathers by quantum calculations hitherto not done in metamaterials. This study is quite realistic to understand quantum localization by nonlinearity that is essential for many small-structured nano-devices. Therefore, this study should be viewed as working towards understanding of many nano structured devices.

An orthopedic X-ray captures bone images along with surrounding flesh and muscle components. Segmentation of the bone component with a sharp contour is a challenging task as the bone and flesh regions often have pixels with overlapping intensity range. In this paper, we propose a new technique of contour extraction by integrating an entropy-based segmentation approach with adaptive thresholding. The method eliminates the shortcomings of earlier derivative or deformable model based approaches, and can be fully automated. Experiments with several digital X-ray images reveal encouraging results especially for long-bone X-ray images.

Shortest path algorithms are finding interesting applications in recent times in various emerging areas of image analysis and computer vision. Such algorithms are designed to solve shortest path problems with variegated need-based constraints. We present here an efficient combinatorial algorithm to find a/the shortest isothetic path (SIP) between two grid points in a digital object such that the SIP lies entirely inside the object. The algorithm first obtains the inner isothetic cover (simple and without holes) of the object and then applies certain combinatorial rules to construct the SIP and its constituent monotone sub-paths. For a given grid size, the entire algorithm runs in O(n logn) time, n being the number of grid points on the border of the cover. Experimental results show the effectiveness of the algorithm and its further prospects in shape analysis.

A combinatorial algorithm to find the intersection of an axis-parallel slicing plane with the orthogonal cover of a digital object is presented in this paper. The orthogonal cover is the smallest-volume 3D orthogonal polyhedron containing the object and stored in a doubly connected edge list (DCEL). Its intersection with the slicing plane consists of one or more isothetic polygons that provide topological information about the cover. The algorithm traverses the vertices on the polyhedron boundary and lying on the slicing plane, and the direction of next move from a vertex is determined by a set of linear equations in the integer domain. Results for few objects with successive slicing planes are presented to demonstrate the effectiveness and elegance of the algorithm.

A fast and efficient algorithm to obtain an orthogonally convex decomposition of a digital object is presented. The algorithm reports a sub-optimal solution and runs in O(n log n) time for a hole-free object whose boundary consists of n pixels. The approximate/rough decomposition of the object is achieved by partitioning the inner cover (an orthogonal polygon) of the object into a set of orthogonal convex components. A set of rules is formulated based on the combinatorial cases and the decomposition is obtained by applying these rules while considering the concavities of the inner cover. Experimental results on different shapes have been presented to demonstrate the efficacy, elegance, and robustness of the proposed technique.

The orthogonal cover of a 3D digital object is a minimum-volume 3D polytope having surfaces parallel to the coordinate planes, and containing the entire object so as to capture its approximate shape information. An efficient algorithm for construction of such an orthogonal cover imposed on a background grid is presented in this paper. A combinatorial technique is used to classify the grid faces constituting the polytope while traversing along the surface of the object in a breadthfirst manner. The eligible grid faces are stored in a doubly connected edge list, using which the faces are finally merged to derive the isothetic polygons parallel to the coordinate planes, thereby obtaining the orthogonal cover of the object. The complexity of the cover decreases with increasing grid size. The algorithm requires computations in integer domain only and runs in a time linear in the number of voxels constituting the object surface. Experimental results demonstrate the effectiveness of the algorithm.

Understanding of graphic objects has become a problem of pertinence in today's context of digital documentation and document digitization, since graphic information in a document image may be present in several forms, such as engineering drawings, architectural plans, musical scores, tables, charts, extended objects, hand-drawn sketches, etc. There exist quite a few approaches for segmentation of graphics from text, and also a separate set of techniques for recognizing a graphics and its characteristic features. This paper introduces a novel geometric algorithm that performs the task of segmenting out all the graphic objects in a document image and subsequently also works as a high-level tool to classify various graphic types. Given a document image, it performs the text-graphics segmentation by analyzing the geometric features of the minimum-area isothetic polygonal covers of all the objects for varying grid spacing, g. As the shape and size of a polygonal cover depends on g, and each isothetic polygon is represented by an ordered sequence of its vertices, the spatial relationship of the polygons corresponding to a higher grid spacing with those corresponding to a lower spacing, is used for graphics segmentation and subsequent classification. Experimental results demonstrate its efficiency, elegance, and versatility.

A combinatorial algorithm to compute the orthogonal hull of a digital object imposed on a background grid is presented in this paper. The resolution and complexity of the orthogonal hull can be controlled by varying the grid spacing, which may be used for a multiresolution analysis of a given object. Existing algorithms on finding the convex hull are based on divide and conquer strategy, sweepline approach, etc., whereas the proposed algorithm is combinatorial in nature whose time complexity depends on the object perimeter instead of the object area. For a larger grid spacing, the perimeter of an object decreases in length in terms of grid units, and hence the runtime of the algorithm reduces significantly. The algorithm uses only comparison and addition in the integer domain, thereby making it amenable to usage in real-world applications where speed is a prime factor. Experimental results including the CPU time demonstrate the elegance and efficacy of the proposed algorithm.

A novel technique for shape coding of a digital object based on its inner and/or outer isothetic polygonal shape, is proposed. The method uses a multigrid background for several applications including digital image visualization and retrieval with varying levels of accuracy. The elegance of the proposed shape code lies in capturing the shape of the objects present in an image from their gross appearances to finer details with a set of hierarchical isothetic polygons that tightly envelop (cover) the objects from outside (inside). Experimental results demonstrate the strength and efficiency of the proposed scheme.

Determination of an isothetic polygonal approximation of the outer or inner contour of an object is a challenging problem with numerous applications to pattern recognition and image processing. In this paper, a novel algorithm is presented for constructing the outer (or inner) tight isothetic polygon(s) containing (or filling) an arbitrarily shaped 2D object on a background grid, using a classical labeling technique. The background grid may consist of uniformly or non-uniformly spaced horizontal and vertical lines. Experimental results for both uniform and non-uniform grids of varying sizes have been reported to demonstrate the applicability and efficiency of the proposed algorithm.

The problem of constructing a tight isothetic outer (or inner) polygon covering an arbitrarily shaped 2D object on a background grid, is addressed in this paper, and a novel algorithm is proposed. Such covers have many applications to image mining, rough sets, computational geometry, and robotics. Designing efficient algorithms for these cover problems was an open problem in the literature. The elegance of the proposed algorithm lies in utilizing the inherent combinatoral properties of the relative arrangement of the object and the grid lines. The shape and the relative error of the polygonal cover can be controlled by changing the granularity of the grid. Experimental results on various complex objects with variable grid sizes have been reported to demonstrate the versatility, correctness, and speed of the algorithm.