T. Pavlidis and S. Horowitz. Segmentation of plane curves. In IEEE Transactions on Computers, volume C-23, pages 860 -- 870, 1984.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....or eigen vectors of the covariance matrix [4] A general optimization of the objective function may be computationally expensive and prone to get stuck in local minima. Therefore, most of popular polygonal approximation algorithms look for an optimal solution with the help of a greedy algorithm [6, 9]. They primarily exploit the advantage that the points in the set are connected and ordered. Dynamic Strip Algorithm is one such algorithm [6] which is a fast polygonal approximation algorithm. Hopfield neural network based algorithms also have been reported for polygonal approximation [2] Some ....

T. Pavlidis and S. Horowitz. Segmentation of plane curves. In IEEE Transactions on Computers, volume C-23, pages 860 -- 870, 1984.

....we have tested the indexing system with somewhat ideal groups, in which automatically located features are formed into groups by hand. We begin model building by running an edge detector[4] on many images of the object. We find corner features by making straight line approximations to the edges[21], and lo cating a corner where nearby lines have a stable intersection point, when extended. We 14 then form by hand groups of three to five points that are formed by a set of convex lines (see [13] and [12] for discussion of the value of convex groups) The convexity of the group orders the ....

Pavlidis, T. and Horowitz, S., 1974. "Segmentation of Plane Curves." IEEE Trans. on Comp., C(23):860-870.

....the sample points as observations. This, however, would lead to large models in order to be able to describe the dynamics of the dioeerent wave classes. In this work we have chosen as observations the slope of a wave in some proper points. To choose these points we used a split and merge algorithm [25] with a piecewise linear approximation of a wave. This algorithm aims to segment the wave into minimum number of segments so that every point of the wave is within some threshold distance from the straight line connecting the endpoints of that segment. Let S 1 ; S 2 ; S nr be the ....

Pavlidis, T., and Horowitz, S. L. (1974), "Segmentation of Plane Curves", IEEE Transactions on Computers, Ser. C, 23, 860-869.

....on such graphical data are very complicated and expensive. An error criterion de nes the goodness of t in terms of the deviations between the approximated and approximating objects. Di erent error criteria have been used in solving various polygonal curve approximation problems (e.g. see [1, 2, 5, 7 18, 21 28]) In this paper, we consider two commonly used error criteria for studying polygonal curve approximations: The error criterion used in [5, 12,14,18] which we call the tolerance zone criterion, and the criterion used in [9, 14,24] which we call the in nite beam criterion (the in nite beam ....

T. Pavlidis and S. Horowitz. Segmentation of plane curves. IEEE Trans. Comput., C-23(8):860-870, 1974.

....by a plane always lead to a unique solution. 5 Experiments To test the scheme we took pictures of a number of roughly planar objects. We first processed these images using Canny s edge detector [7] We then constructed polygonal approximations to the edges using Pavlidis and Horowitz s [20] split and merge algorithm. The resulting polygons approximate the original edges to within two pixels. Then, we extracted the roughly convex structures using Jacobs s grouping system [16] The matching between the regions was specified manually. Finally, the transformations relating these images ....

Pavlidis, T. and S. Horowitz, 1974, "Segmentation of Plane Curves," IEEE Trans. on Computers, C(23):860-870.

....we achieve will be proportional to the square of compression rate. In addition, it will allow us to search huge time series in main memory without having to swap in and out small subsections. There are many well known segmentation algorithms in the literature, many of which were pioneered by Pavlidis (1974). It should be emphasized that the distance measures, and search techniques presented in the rest of this paper will work with any segmentation algorithm. For completeness, however, we present a variant of the bottom up algorithm which not only produces a segmentation, but chooses K, the number ....

Pavlidis, T., Horowitz, S., `Segmentation of Plane Curves', IEEE Transactions on Computers, Vol. C-23, NO 8, August 1974.

....success, but all have shortcomings, including sensitivity to noise, lack of intuitiveness, and the need to fine tune many parameters. Piece wise linear segmentation, which attempts to model the data as sequences of straight lines, as in Figure 2) has innumerable advantages as a representation. Pavlidis and Horowitz (1974) point out that it provides a useful form of data compression and noise filtering. Shatkay and Zdonik (1996) describe a method for fuzzy queries on linear (and higher order polynomial) segments. Keogh and Smyth (1997) further demonstrate a framework for probabilistic pattern matching using linear ....

....are used for relevance feedback, and section 4 describes a classification algorithm which takes advantage of our representation to greatly boost accuracy. 2. 0 Representation of time series There are numerous algorithms available for segmenting time series, many of which where pioneered by Pavlidis and Horowitz (1974). An open question is how to best choose K, the optimal number of segments used to represent a particular time series. This problem involves a trade off between accuracy and compactness, and clearly has no general solution. For this paper, we utilize the segmentation algorithm proposed in Keogh ....

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Pavlidis, T., Horowitz, S., (1974). Segmentation of plane curves. IEEE Transactions on Computers, Vol. C-23, No 8, August.

....changes of direction. Such features come in very handy when we want to distinguish between similar shapes. For example, it seems that the only way to differentiate between D and O or 5 and S , is to use contour corners. An alternative approach which was pursued by Pavlidis and Horowitz [58] is the polygonal approximation of the contour. Its principal advantage is robustness against noise and generality. Essentially, the contour is approximated by piecewise polynomial functions, where the breakpoints are adjusted at a later stage, in order to fit the data and to provide for the ....

T. Pavlidis and S. L. Horowitz. Segmentation of plane curves. IEEE Trans. Computers, C-23:860--870, Aug. 1974.

....success, but all have shortcomings, including sensitivity to noise, lack of intuitiveness, and the need to fine tune many parameters. Piece wise linear segmentation, which attempts to model the data as sequences of straight lines, as in Figure 2) has innumerable advantages as a representation. Pavlidis and Horowitz (1974) point out that it provides a useful form of data compression and noise filtering. Shatkay and Zdonik (1996) describe a method for fuzzy queries on linear (and higher order polynomial) segments. Keogh and Smyth (1997) further demonstrate a framework for probabilistic pattern matching using linear ....

....piece wise linear segments to represent the shape of a time series, and a weight vector that contains the relative importance of each individual linear segment. 2. 0 Representation of time series There are numerous algorithms available for segmenting time series, many of which where pioneered by Pavlidis and Horowitz (1974). An open question is how to best choose K, the optimal number of segments used to represent a particular time series. This problem involves a trade off between accuracy and compactness, and clearly has no general solution. For this paper, we utilize the segmentation algorithm proposed in Keogh ....

Pavlidis, T., Horowitz, S., (1974). Segmentation of plane curves.

....have been proposed, and we refer the interested reader to [10] for a detailed discussion of their rival merits. Piece wise linear segmentation, which attempts to model the data as sequences of straight lines, as in Figure 2) has many advantages as a representation. Pavlidis and Horowitz [14] point out that it provides a useful form of data compression and noise filtering. Shatkay and Zdonik [7] describe a method for fuzzy queries on linear (and higher order polynomial) segments. Keogh and Smyth [11] further demonstrate a framework for probabilistic pattern matching using linear ....

Pavlidis, T., Horowitz, S., (1974). Segmentation of plane curves. IEEE Transactions on Computers, Vol. C-23, No 8, August.

....representations have been proposed, including Discrete Fourier Transformations [8] 1] 24] 25] Relational Trees [22] and envelope matching R trees [2] Here, we explore indexing with a piecewise linear representation. This representation has numerous advantages. Pavlidis and Horowitz [19] point out that it provides a useful form of data compression and noise filtering. Shatkay and Zdonik [11] describe a method for fuzzy queries on linear (and higher order polynomial) segments. Furthermore, in previous work we have demonstrated a framework for probabilistic pattern matching using ....

....with longer and shorter queries. Section 5 contains a discussion of how we select a key parameter, and Section 6 surveys related work. 2. Piecewise Linear Representation There are numerous algorithms available for segmenting time series, many of which where pioneered by Pavlidis and Horowitz [19]. An open question is how to best choose K, the optimal number of segments used to represent a particular time series. This problem involves a trade off between accuracy and compactness, and clearly has no general solution. For this paper, we utilize the segmentation algorithm proposed in Keogh ....

Pavlidis, T., & Horowitz, S., (1974). Segmentation of plane curves. IEEE Transactions on Computers, Vol. C23, No 8, August.

....the data within the bins to reduce search times. While both these approaches greatly speed up query times for Euclidean distance queries, many real world applications require non Euclidean notions of similarity. The idea of using piecewise linear segments to approximate time series dates back to Pavlidis and Horowitz (1974). Later researchers, including Hagit and Zdonik (1996) and Keogh and Pazzani (1998) considered methods to exploit this representation to support various non Euclidean distance measures, however this paper is the first to demonstrate the possibility of supporting time warped queries with linear ....

Pavlidis, T., Horowitz, S. (1974). Segmentation of plane curves. IEEE Transactions on Computers, Vol. C-23, NO 8, August.

....above two level aggregations. The filtering of curve segments at level I involves choosing an appropriate threshold for segmentation. We will discuss next the technical issues in computing a stable segmentation. 3. 1 Curve Segmentation We use curve fitting technique and split and merge algorithm [9, 2, 15] to segment curves. Because iso bar curves are generally smooth, we use constant curvature curves (straight lines and circular arcs) to fit iso bar curves, i.e. we first transform an iso bar curve into Gamma S space ( the angle made between the tangent to the curve and a fixed line; S: the ....

T. Pavlidis and S.L. Horowitz. Segmentation of plane curves. IEEE Trans. Computer, C-22:860--870, 1974.

....z(x 0 Gamma 1; y 0 )j jz(x 0 ; y 0 ) Gamma z(x 0 1; y 0 )j, then we assign the break point to its left and otherwise to its right neigboring line segment. It is well known that the simple splitting method of Duda and Hart produces sometimes superfluous line segments. Pavlidis and Horowitz [21] tried to solve this problem by introducing a merge step. As stated in [7] however, this algorithm is computationally much more expensive. For complex curves, it produces sometimes worse results than the simple splitting method. As the second stage of our segmentation algorithm is based on region ....

T. Pavlidis, S. L. Horowitz, Segmentation of plane curves, IEEE Trans. on Comput. Vol. C-23, 860--870, 1974.

....algorithm proceeds recursively until the approximation error e max doesn t exceed the threshold ffl. It is well known that the simple splitting method of Duda and Hart produces sometimes spurious segments. For the problem of piecewise linear approximation of curves, Pavlidis and Horowitz [27] tried to solve this problem by introducing a merge step. As stated in [10] however, this algorithm is computationally rather expensive. For complex curves, it produces sometimes worse results than the simple splitting method. For the partitioning into quadratic curve segments, the usefulness of ....

T. Pavlidis, S.L. Horowitz, Segmentation of plane curves, IEEE Trans. on Computers, C23, 860--870, 1974.

....the convex sequences of line segments the algorithm will produce, and introduce some useful notation. The system begins with line segments that we obtain by running a Canny edge detector[9] in the experiments shown, oe = 2) and then using a split and merge algorithm based on Horowitz and Pavlidis[40] to approximate these edges with straight lines. This system approximates curves with lines whose end points are on the curves, such that the curves are no more than three pixels from the line segments. We call a line segment oriented when one endpoint is distinguished as the first endpoint. If ....

Pavlidis, T. and S. Horowitz, 1974, "Segmentation of Plane Curves," IEEE Transactions on Computers, C(23):860-870.

....by an operating grant from the Natural Sciences and Engineering Research Council of Canada. 1 Introduction Planar shape modeling has broad applications to various signal understanding and computer vision tasks, such as shape matching, feature extraction, data compression, or noise filtering [1][2] 3] 4] Planar shapes are defined by their outline curves. It is desirable to be able to derive a parametric curve representation from a set of sample points which define a planar contour. This can be done by either Fourier descriptors or spatial domain models. One of the most commonly used ....

T.Pavlidis & S.L. Horowitz, "Segmentation of Plane Curves", IEEE Trans. Comput. 23,1974, 860--870.

....using a standard technique. We connect the start and end of a connected string of edge pixels with a line, then break this line at the point of maximum deviation. We then repeat this process recursively, until each line approximates edge contours to within two pixels (see Pavlidis and Horowitz[29] for a description of this type of algorithm) In the remainder of this section we describe GROPER s indexing and verification. Figure 12: Two edges are in bold. Five parameters describe their relationship. Indexing determines the sets of edges from modeled objects that might have produced a set ....

Pavlidis, T. and Horowitz, S., 1974. "Segmentation of Plane Curves." IEEE Transactions on Computers, C(23):860-870.

.... the number of vertices of the polygons while retaining their inherent shape using polygonal approximation methods in order to reduce the complexity of subsequent algorithms applied to the polygons. Such an approach was applied to character recognition by Pavlidis and his colleagues [PA75] [PH74]. Here again is an area where computational geometry has great potential and is playing an ever increasing role. Smoothing and enhancement can be carried out for example by deleting carefully chosen branches of the medial axis of the polygon [Le82] Given a polygonal planar curve P= p 1 ,p 2 ....

Pavlidis, T. and Horowitz, S. L., "Segmentation of plane curves," IEEE Transactions on Computers, vol. C-23, August 1974, pp. 860-870.

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T. Pavlidis and S. Horowitz. Segmentation of plane curves. In IEEE Transactions on Computers, volume C-23, pages 860 -- 870, 1984.

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T. Pavlidis and S. L. Horowitz, "Segmentation of plane curves," IEEE Transactions on Computers, vol. c23(8), pp. 860--870, 1974.

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T. Pavlidis and S. L. Horowitz, "Segmentation of plane curves," IEEE Transactions on Computers, vol. c23(8), pp. 860--870, 1974.

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# T. Pavlidis and S.L. Horowitz, "Segmentation of Plane Curves," IEEE Trans. Computers, vol. 23, no. 8, p. 860, 1974.

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T. Pavlidis and S. L. Horowitz, "Segmentation of Plane Curves," in IEEE Trans. on Computers, Vol. C-23(8), pp. 860--870, August 1974.

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Pavlidis, T. and Horowitz, S. L. (1974). Segmentation of plane curves. IEEE Trans. on Computers, 23(8):860--870.

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