Shyamosree Pal

Estimation of discrete curvature based on chain-code pairing and digital straightness

Estimation of discrete curvature is a challenging problem, since a mere replacement of functional derivatives by numerical differences fails to produce the desired result. Several algorithms have been proposed so far, which are mostly based on the concepts of real geometry and hence are computationally expensive. The existing measure of k-curvature, though easy to compute, is crippled with some unwanted syndromes arising out of improper consideration of chain codes. Hence, an improved algorithm for estimating k-curvature is proposed, which is marked by its inherent simplicity and computational attractiveness, and produces the expected estimate, whether the concerned point has an extreme (high or low) curvature or the concerned segment has a constant or changing curvature. Examples and experimental results demonstrate the fitness and effectiveness of the proposed technique for digital curves of arbitrary shapes.

Determining Digital Circularity Using Integer Intervals

Digital circularity is a well-researched topic for its real-world practicality to circularity measure, estimation of discrete curvature, circular arc segmentation, etc. The proposed work reveals a novel technique to determine whether a digital curve segment is digitally circular using the correspondence of its constituent runs with the square numbers in integer intervals. The notion of radii nesting is used to successively analyze these runs of digital points. Two algorithms have been proposed along with their demonstrations and detailed analysis, and a simple-yet-effective solution has been provided to expedite them using infimum circle and supremum circles that bound the initial range of radii. We have also shown how the proposed technique can be used for segmentation of an arbitrary digital curve segment into a sequence of circular arcs. Experimental results have been given to demonstrate the efficiency and elegance of the proposed technique.

CIRCULAR ARC SEGMENTATION BY CURVATURE ESTIMATION AND GEOMETRIC VALIDATION

A novel algorithm to detect circular arcs from a digital image is proposed. The algorithm is based on discrete curvature estimated for the constituent points of digital curve segments, followed by a fast geometric analysis. The curvature information is used in the initial stage to find the potentially circular segments. In the final stage, the circular arcs are merged and maximized in length using the radius and center information of the potentially circular segments. Triplets of longer segments are given higher priorities; doublets and singleton arcs are processed at the end. Detailed experimental results on benchmark datasets demonstrate its efficiency and robustness.

FACET: A Fast Approximate Circularity Estimation Technique

A fast algorithm that approximately estimates the circularity of a digital object is proposed. The algorithm is shown to be capable of incorporating the existing empirical measures of circularity, which are mostly based on area and perimeter computation. The minimum-area orthogonal cover of the object is obtained by a fast combinatorial technique that simultaneously provides approximate measures of the area and the perimeter of the object, wherein lies its strength and novelty. Exhaustive experimentation has been performed to verify the robustness of the algorithm, and some results are furnished in this paper to demonstrate its efficacy and elegance.

Cubic approximation of curve-shaped objects in ℤ2: a generalized approach based on discrete curvature

Abstract Approximation of arbitrary curves and curve-shaped objects on the digital plane, ℤ2, is a captivating problem with potential usages in many computer-aided applications, such as image processing and image analysis, pattern recognition, computer vision, etc. The simplest approximation is linear in nature, and for improving the quality of approximation, higher order curves are used. Hence, to obtain the desired approximation, we have used a set of cubic B-splines, which are constructed based on control points judiciously selected from the input digital curve based on estimated curvatures at the constituent points of the curve. For estimation of discrete curvature, several algorithms have been proposed so far, which are mostly based on the concepts of real geometry and hence are computationally expensive. The existing measure of k-curvature, although computationally attractive, is crippled with some unwanted syndromes, as revealed in this paper. Hence, an improved algorithm for estimating k-curvature is also proposed. Exhaustive testing and experimental results demonstrate the strength and elegance of our method.

GOAL: towards understanding of graphic objects from architectural to line drawings

Understanding of graphic objects has become a problem of pertinence in todays 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.

Faster circularity estimation by randomization

A fast algorithm that approximately estimates the circularity of a digital object is proposed. The algorithm is shown to be capable of incorporating the existing empirical measures of circularity, which are mostly based on area and perimeter computation. The minimum-area orthogonal cover of the object is obtained by a fast combinatorial technique that simultaneously provides approximate measures of the area and the perimeter of the object, wherein lies its strength and novelty. A randomization technique has also been incorporated to make the algorithm more efficient in terms of its running time. Exhaustive experimentation has been performed to verify the robustness of the algorithm, and some results are furnished in this paper to demonstrate its efficacy and elegance.

Recognition of Hand-Drawn Graphs Using Digital-Geometric Techniques

A novel algorithm to recognize hand-drawn graphs is proposed. The algorithm uses properties of digital-geometric straightness combined with a new idea of Farey sequence, followed by geometric refinement, in order to speed up the recognition of graph edges. In the next phase, the nodes of the graph — which, being hand-drawn, are very grossly circular — are recognized using the annular regions containing the vertices of their corresponding isothetic covers. Results of the two phases are finally compiled using interval search to output the adjacency list of the graph. The problems of jaggedness, waviness, and similar unforeseen aberrations usually present in a hand-drawn graph are well-tackled by the adopted techniques, as verified by our experimentation on various hand-drawn graphs. Some results have been given in this paper to show the usability and efficiency of the proposed algorithm.

Understanding Digital Documents Using Gestalt Properties of Isothetic Components

This paper introduces how Gestalt properties can be used for identifying various components in a document image. That the human mind makes a holistic approach to vision rather than a disintegrated approach is shown to be useful for document analysis. Since the major constituent components textual or non-textual in a document page are arranged in a rectilinear fashion, rectilinear/isothetic decomposition of different components are made on a document page. After representing the page as a feature set of its polygonal covers corresponding to the distinct regions of interest, each polygon is iteratively decomposed into the sub-polygons tightly enclosing the corresponding sub-components to capture the overall information as well as the necessary details to the desired level of precision. Subsequently, these components and sub-components are analyzed using Gestalt laws/properties, which have been explained in detail in the context of this work. Text regions, tabular structures, and various graphic objects readily admit some of the Gestalt properties. We have tested our algorithm on several benchmark datasets, and some relevant results have been produced here to demonstrate the effectiveness and elegance of the proposed method.