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AbstractApproximation 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.

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.