Sanjoy Pratihar

A Thinning-free Algorithm for Straight Edge Detection in a Gray-scale Image

An efficient algorithm to detect the straight edges present in a gray-scale image is proposed.Algorithms to detect curvilinear edges (of possibly uneven thickness) and algorithms to segment a one-pixel thick digital curve into a sequence of straight pieces are found in the literature in several varieties and in several paradigms. However, to the best of our knowledge, there exists no algorithm till date that can detect straight edges in a gray-scale image without thinning. The proposed algorithm uses the novel idea of exponential averaging to achieve a carry-forward of previous edge strengths along the traversed straight edge. The process is computationally attractive, since the underlying operations at an edge point effectively reduce to one right shift and one integer addition. The straightness of an edge is verified from classical chain code properties realizable by simple integer operations, thereby making the algorithm easy for implementation and fast in execution. Experimental results demonstrate its efficiency and robustness.

SKEW CORRECTION OF DOCUMENT IMAGES BY RANK ANALYSIS IN FAREY SEQUENCE

Skew correction of a scanned document page is an important preprocessing step in document image analysis. We propose here a fast and robust skew estimation algorithm based on rank analysis in Farey sequence. Our target document class comprises two major Indian scripts with headlines, namely Devnagari and Bangla. At the beginning, straight edge segments from the edge map of the document page are detected by our algorithm using properties of digital straightness. Straight edges derived in this manner are binned by Farey ranks in correspondence with their slopes. The principal bin, identified from these bins using the strength of accumulated edge points, represents the principal direction along the direction of headlines, from which the gross skew angle is estimated. A fast refinement algorithm is then applied with a finer tuning of Farey ranks, to detect the skew up to the desired level of precision. The algorithm has been tested on a diverse set of document images, containing Bangla and Devnagari scripts. Experimental results are quite encouraging in terms of accuracy, sensitivity to non-textual objects, effectiveness in dealing with unrestricted layouts, and computational efficiency.

Removal of hand-drawn annotation lines from document images by digital-geometric analysis and inpainting

Performance of an OCR system is badly affected due to presence of hand-drawn annotation lines in various forms, such as underlines, circular lines, and other text-surrounding curves. Such annotation lines are drawn by a reader usually in free hand in order to summarize some text or to mark the keywords within a document page. In this paper, we propose a generalized scheme for detection and removal of these hand-drawn annotations from a scanned document page. An underline drawn by hand is roughly horizontal or has a tolerable undulation, whereas for a hand-drawn curved line, the slope usually changes at a gradual pace. Based on this observation, we detect the cover of an annotation object-be it straight or curved-as a sequence of straight edge segments. The novelty of the proposed method lies in its ability to compute the exact cover of the annotation object, even when it touches or passes through any text character. After getting the annotation cover, an effective method of inpainting is used to quantify the regions where text reconstruction is needed. We have done our experimentation with various documents written in English, and some results are presented here to show the efficiency and robustness of the proposed method.

Vectorization of thick digital lines using Farey sequence and geometric refinement

A novel algorithm for vectorization of line-shaped objects present in a gray-scale image is proposed. The algorithm derives the straight edges of maximal length from the object boundary using the notion of Farey sequence, and subsequently vectorizes them by an efficient technique of geometric refinement. The method would be computationally attractive when vectorization of a large database of grayscale images is in question. Experimental results on several datasets including road maps demonstrate the usefulness, efficiency, and elegance of the proposed algorithm.

Shape decomposition using Farey sequence and saddle points

A novel algorithm for boundary-based shape decomposition is proposed. The algorithm uses Farey sequence for determining several measures, such as slopes of edges and turn types at vertices of the polygonal cover P corresponding to the concerned shape. The fraction ranks (indices) in the Farey sequence have been used in the related procedures to enable computations in the integer domain while merging straight edges of P, which are almost collinear, and to perform turn checking at the vertices of P. Such turn checking aids in extracting the saddle points and constructing the visibility graph to finally output the decomposition. Experimental results demonstrate the efficiency and elegance of the proposed algorithm.

On the Farey sequence and its augmentation for applications to image analysis

Abstract We introduce a novel concept of the augmented Farey table (AFT). Its purpose is to store the ranks of fractions of a Farey sequence in an efficient manner so as to return the rank of any query fraction in constant time. As a result, computations on the digital plane can be crafted down to simple integer operations; for example, the tasks like determining the extent of collinearity of integer points or of parallelism of straight lines—often required to solve many image-analytic problems—can be made fast and efficient through an appropriate AFT-based tool. We derive certain interesting characterizations of an AFT for its efficient generation. We also show how, for a fraction not present in a Farey sequence, the rank of the nearest fraction in that sequence can efficiently be obtained by the regula falsi method from the AFT concerned. To assert its merit, we show its use in two applications—one in polygonal approximation of digital curves and the other in skew correction of engineering drawings in document images. Experimental results indicate the potential of the AFT in such image-analytic applications.

Detection and removal of hand-drawn underlines in a document image using approximate digital straightness

A novel algorithm for detection and removal of underlines present in a scanned document page is proposed. The underlines treated here are hand-drawn and of various patterns. One of the important features of these underlines is that they are drawn by hand in almost a horizontal fashion. To locate these underlines, we detect the edges of their covers as a sequence of approximately straight segments, which are grown horizontally. The novelty of the algorithm lies in the detection of almost straight segments from the boundary edge map of the underline parts. After getting the exact cover of the underlines, an effective strategy is taken for underline removal. Experimental results are given to show the efficiency and robustness of the method.

Fast and Direct Polygonization for Gray-Scale Images Using Digital Straightness and Exponential Averaging

Although there exist various algorithms for polygonization of objects present in a digital image, most of them cannot directly be applied on a gray-scale image without resorting to edge map computation, thinning, etc. Hence, with the aim of applying polygonization directly on a gray-scale image, we propose here an improved algorithm. It is based on a novel proposition of exponential averaging of estimated edge strengths, which is used to extract (thinned) digitally straight edges directly from a gray-scale image. These straight edges are subsequently used as input for a fast polygonization based on simple primitive operations in the integer domain. Procedural advantages and implementation details of the proposed method are explained in this paper to adjudge its fitness in the context of polygonization. Experimental results have been furnished to demonstrate the usefulness, efficiency, and robustness of the proposed technique.

Skew correction of engineering drawings by digital-geometric analysis of Farey ranks

A novel algorithm for detection and correction of skews present in scanned engineering drawings is proposed. The novelty of the algorithm lies in the usage of certain periodic properties of digital straightness directly on gray-scale images, in tandem with the ranks of fractions in a Farey sequence. Straight edges derived in this manner are binned by their Farey ranks, which, in turn, are analyzed to obtain the principal bin from the sums of lengths of the edges in a sequence of bins. The principal bin corresponds to the principal direction, from which the skew angle is estimated to finally correct the skew. Owing to primitive operations in the integer domain and a linear-time clustering procedure, the algorithm runs significantly fast with the desired level of precision, even for document pages with text-graphics mix or containing tabular structures with boundary lines. Experimental results on several datasets demonstrate its elegance, efficiency, and robustness.

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.