Bimal Kumar Ray

Determination of optimal polygon from digital curve using L1 norm

Abstract A technique to determine optimal polygons of digital curves is proposed. It determines the longest possible line segments with the minimum possible error. The L 1 norm is used to measure the closeness of a polygon to a digital curve. The algorithm runs in linear time. The procedure is applied to several digital curves and promising results are obtained.

An algorithm for detection of dominant points and polygonal approximation of digitized curves

Abstract A new technique for the detection of dominant points and polygonal approximation of digitized curves is proposed. The procedure needs no input parameter and remains reliable even when features of multiple size are present. Unlike the existing algorithms, the present technique introduces the concept of an asymmetric region of support and k - l -cosine. The dominant points are the local maxima of k - l -cosine. The polygon is obtained joining the dominant points successively.

A new split-and-merge technique for polygonal approximation of chain coded curves

Abstract In all split-and-merge techniques the fundamental problem is the initial segmentation. In this paper the initial segmentation is done by introducing the concept of rank of a point. The split-and-merge is done using two criteria functions, namely, the ratio of the arc length to the length of the line segment and the ratio of the distance from a point to the line segment (not the perpendicular distance) to the length of the line segment. The procedure generates polygons that are insensitive to rotation and scales and remains reliable in presence of noise.

A non-parametric sequential method for polygonal approximation of digital curves

Abstract A non-parametric sequential technique for polygonal approximation of digital curves is proposed. The procedure looks for the longest possible line segments by maximising an objective function which comprises of the length of the line segment and the integral square error along the line segment. The vertices of the polygon are those points where this function attains a local maximum. Though the procedure is sequential and one pass, neither does it round off sharp turnings nor does it dislocate the vertices near the other turnings.

ACORD—an adaptive corner detector for planar curves

Abstract In contrast to the conventional method of smoothing a curve at multiple scales and integrating the information at various scales, a technique for smoothing a curve adaptively based on the roughness present in the curve is suggested. The procedure does not require smoothing at all levels of detail and it does not require construction of complete scale space map and representation of the map by tree. The procedure has been applied on a number of digital curves and the results have been compared with those of the recent work.

Corner detection using iterative Gaussian smoothing with constant window size

Abstract In contrast to the existing Gaussian smoothing process with varying window size, an iterative Gaussian convolution with constant window size is proposed. The iterative process is shown to converge as the norm of the convolution matrix is less than unity. For a closed digital curve the number of iterations is shown to be related to the number of points on the curve. The Gaussian filter coefficients that are used to smooth the curve are shown to enjoy the scale-space property. A scale-space map showing the location of the maxima of absolute curvature over iterations is proposed. The map is converted into a tree organization on the basis of an analysis of the scale-space behavior of different corner models such as Γ models, END models and STAIR models. Corners are detected in a process of interpreting the tree. The corner detector has been applied successfully on different digital curves even in presence of additive white Gaussian noise and at varying orientations.

Scale-space analysis and corner detection on digital curves using a discrete scale-space kernel

This paper shows the application of the discrete scale-space kernel T(n;t) with continuous parameter to scale-space analysis of digital curves. The numerical problems that arise in the implementation are addressed in sequence and feasible solutions are proposed. The scale-space analysis is applied to corner detection. The corner detector is shown to operate successfully on noisy curves and at varying orientation.

Polygonal approximation of digital planar curve using local integral deviation

An algorithm for polygonal approximation based on local integral deviation is presented. The algorithm is tested on various shapes with varying number of dominant points. A comparative study of the proposed procedure with other iterative methods shows that the proposed procedure produces polygon from a digital curve approximating high as well as low curvature regions with almost equal precision.

POLYGONAL APPROXIMATION OF DIGITAL CURVE BASED ON REVERSE ENGINEERING CONCEPT

This paper applies reverse engineering on the Bresenhams line drawing algorithm [J. E. Bresenham, IBM System Journal, 4, 106–111 (1965)] for polygonal approximation of digital curve. The proposed method has a number of features, namely, it is sequential and runs in linear time, produces symmetric approximation from symmetric digital curve, is an automatic algorithm and the approximating polygon has the least non-zero approximation error as compared to other algorithms.

An iterative point elimination technique to retain significant vertices on digital planar curves

This paper presents a technique that uses distance to a point as a metric to measure the collinearity to delete quasi linear points on a digital curve. The technique described here iteratively deletes points whose deviation is minimal from the line segment joining its neighbours. The results of the proposed technique are compared with recent iterative point elimination techniques. The comparative results show that the proposed technique produces the polygon by preserving the significant vertices such as sharp turning, with less approximation error.