Partha Bhowmick

Fast Polygonal Approximation of Digital Curves Using Relaxed Straightness Properties

Several existing digital straight line segment (DSS) recognition algorithms can be used to determine the digital straightness of a given one-pixel-thick digital curve. Because of the inherent geometric constraints of digital straightness, these algorithms often produce a large number of segments to cover a given digital curve representing a real-life object/image. Thus, a curve segment, which is not exactly digitally straight but appears to be visually straight, is fragmented into multiple DSS when these algorithms are run. In this paper, a new concept of approximate straightness is introduced by relaxing certain conditions of DSS, and an algorithm is described to extract those segments from a digital curve. The number of such segments required to cover the curve is found to be significantly fewer than that of the exact DSS cover. As a result, the data set required for representing a curve also reduces to a large extent. The extracted set of segments can further be combined to determine a compact polygonal approximation of a digital curve based on certain approximation criteria and a specified error tolerance. The proposed algorithm involves only primitive integer operations and, thus, runs very fast compared to those based on exact DSS. The overall time complexity becomes linear in the number of points present in the representative set. Experimental results on several digital curves demonstrate the speed, elegance, and efficacy of the proposed method.

TIPS: on finding a tight isothetic polygonal shape covering a 2d object

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.

Number-theoretic interpretation and construction of a digital circle

This paper presents a new interpretation of a digital circle in terms of the distribution of square numbers in discrete intervals. The number-theoretic analysis that leads to many important properties of a digital circle succinctly captures the original perspectives of digital calculus and digital geometry for its visualization and characterization. To demonstrate the capability and efficacy of the proposed method, two simple algorithms for the construction of digital circles, based on simple number-theoretic concepts, have been reported. Both the algorithms require only a few primitive operations and are completely devoid of any floating-point computation. To speed up the computation, especially for circular arcs of high radii, a hybridized version of these two algorithms has been given. Experimental results have been furnished to elucidate the analytical power and algorithmic efficiency of the proposed approach. It has been also shown, how and why, for sufficiently high radius, the number-theoretic technique can expedite a circle construction algorithm.

Reconstruction of torn documents using contour maps

Efficient and successful joining of torn pieces of papers to reconstruct the original documents is an important and challenging issue in many disciplines, especially in forensics and investigation sciences. Automation of the process by means of appropriate techniques can speed up the problem solving substantially. In this paper, we propose a fast, efficient, and useful technique for the reconstruction of hand-torn pages of documents from their images, using contour descriptors for shape-based matching. Chain code of the closed digital arc representing a contour, and its Minkowski sum, have been exploited in our reconstruction work. Experimental results demonstrate the strength and robustness of the method.

Recognition of Bangla compound characters using structural decomposition

In this paper we propose a novel character recognition method for Bangla compound characters. Accurate recognition of compound characters is a difficult problem due to their complex shapes. Our strategy is to decompose a compound character into skeletal segments. The compound character is then recognized by extracting the convex shape primitives and using a template matching scheme. The novelty of our approach lies in the formulation of appropriate rules of character decomposition for segmenting the character skeleton into stroke segments and then grouping them for extraction of meaningful shape components. Our technique is applicable to both printed and handwritten characters. The proposed method performs well for complex-shaped compound characters, which were confusing to the existing methods. HighlightsThe proper recognition of compound characters is a difficult problem due to their complex shapes.In this paper, we propose a novel character recognition method for Bangla compound characters.Our strategy is to decompose the compound character into simpler shape components.Our technique is applicable to printed and handwritten characters.Experiment is done on printed and handwritten Bangla compound characters.

Approximate fingerprint matching using kd-tree

Fast and robust fingerprint matching is a challenging task today in fingerprint-based biometric systems. A fingerprint matching algorithm compares two given fingerprints and returns either a degree of similarity or a binary decision. Minutiae-based fingerprint matching is the most well-known and widely used method. This paper reveals a new technique of fingerprint matching, using an efficient data structure, combining the minutiae representation with the individual usefulness of each minutia, to make the matching more powerful. Experimental results exhibit the strength of this method.

Handwritten Bangla character recognition in machine-printed forms using gradient information and Haar wavelet

A robust and efficient algorithm to recognize handwritten Bangla (Bengali) characters in machine-printed forms is proposed. It is based on the combination of gradient features and Haar wavelet coefficients. The gradient feature is used to capture local characteristics, and for its sensitivity to the usual deformation and idiosyncrasy of handwritten characters, wavelet transform is used for multi-resolution analysis of character images. Such a strategy with combined features captures adequate global characteristics in different scales. Two feature-combination schemes are devised and tested on test images of 4372 instances of 49 characters and 10 numerals, after being trained by a set of 59×25 = 1475 images. Finally, a k-NN classifier is used for the character recognition, which shows 87.65% and 88.95% recognition accuracies for the two schemes.

Recognition of Bengali Handwritten Characters Using Skeletal Convexity and Dynamic Programming

The main challenge in recognizing handwritten characters is to handle large-scale shape variations in the handwriting of different individuals. In this paper, we present a novel handwritten character recognition method based on the structural shape of a character irrespective of the viewing direction on the 2D plane. Structural shape of a character is described by different skeletal convexities of character strokes. Such skeletal convexity acts as an invariant feature for character recognition. Longest common subsequence matching is used for recognition. We have tested out method on a benchmark dataset of handwritten Bengali character images. Preliminary results demonstrate the efficacy of our approach.

Word Segmentation and Baseline Detection in Handwritten Documents Using Isothetic Covers

A novel approach towards word segmentation and baseline detection in a handwritten document is proposed. It is based on certain structural properties of isothetic covers tightly enclosing the words in a handwritten document. For an appropriate grid size, the isothetic covers successfully segregates the words so that each cover corresponds to a particular word. By analyzing the horizontal chords of these covers, the corresponding baselines are extracted. The method is fast, robust, and efficient by dint of its traversal strategy along the word boundaries in a combinatorial manner and usage of limited operations strictly in the integer domain. Some results on several Bengali and English handwritings have been given to demonstrate its strength and elegance.

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.