P.L. Rosin, "Techniques for Assessing Polygonal Approximation of Curves", Pattern Analysis and Machine Intelligence (PAMI), 19(6) : 659-666, 1997.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....geometry. Given a curve as a chain of line segments, a simplification algorithm generates an approximation of it with a smaller number of vertices. For our application, we chose Lowe s algorithm [6] which outperforms other algorithms for curve simplification according to an assessment [8]. The algorithm approximates the polygonal chain by selecting a subset of vertices from the original chain. Fig. 1. Curve simplification. Left column) step by step visualization of the simplification with a given error tolerance. Right column) Results of the simplification to the same curve but ....

P. L. Rosin. Techniques for assessing polygonal approximations of curve. IEEE Transactions on Pattern Recognition and Machine Intelligence, 19(6):659 -- 666, 1997.

.... of the stroke (i.e. endpoints of linear segments) There are, by design, no vertices marked on curved portions of the stroke because we want to handle these separately, modeling them with curves (as described below) This is unlike the well studied problem of piecewise linear approximation [13]. Figure 2: Stroke representing a square. Our approach takes advantage of the interactive nature of sketching, combining information from both stroke direction and speed data. Consider as an example the square in Fig. 2; Fig. 3 shows the direction, curvature (change in direction with respect to ....

R. Rosin. Techniques for assessing polygonal approximations of curves. 7th British Machine Vision Conf., Edinburgh, 1996.

.... the approximation within some threshold range of the original curve s area, to nding the dominant points on the curve based on Gaussian scale space [Rattarangsi and Chin 1992] The di erent techniques employed by each of these algorithms provide di erent advantages to di erent types of input data [Rosin 1997]. The algorithm published by Douglas and Peuker [1973] is a good example of an algorithm which is suited to a particular task. Kraak and Ormeling [1996] note that it has been implemented in many GIS packages to perform generalisations. Cartographers need a generalisation when maps become ....

....c 45 c 46 c 47 c 48 Figure 2.1: An example of a curve C = fc i j 1 i 48g before approximation to congestion of features and symbols. Kraak and Ormeling [1996] also note that the Douglas Peucker algorithm is considered one of the best generalisation algorithms, but is slow in processing. Rosin [1997] evaluated various algorithms, including the Douglas Peucker algorithm. However the task performed and the measure of eciency used in this research were not based on the requirements of cartography. The study showed the relative performance of a number of other algorithms, many of which performed ....

[Article contains additional citation context not shown here]

P. Rosin. Techniques for assessing polygonal approximations of curves. IEEE Transactions on Pattern Analysis and Machine Intelligence, 19(6):659-666, June 1997.

....stroke. During the vertex detection process, we want to avoid picking points on the curved regions as much as possible. Piecewise linear approximation algorithms don t satisfy this requirement. Vertex localization is a frequent subject in the extensive literature on graphics recognition (e.g. [16] compares 21 methods) Unfortunately these methods produce piecewise linear approximations. Our approach takes advantage of the interactive nature of sketching by combining information from both curvature and speed data for detecting corners while avoiding a piecewise linear approximation. For ....

R. Rosin. Techniques for assessing polygonal approximations of curves. 7th British Machine Vision Conf., Edinburgh, 1996.

....so that it best matches another shape (optimization problem) in whole or in part. Shape approximation and simplification: construct a shape of fewer elements (points, segments, triangles, etc. that is still similar to the original. There are many heuristics for approximating polygonal curves [45] and polyhedral surfaces [26] Optimal methods construct an approximation with the fewest elements given a maximal dissimilarity, or with the smallest dissimilarity given the maximal number of elements. Checking the former dissimilarity is a decision problem, the latter is a computation ....

P. L. Rosin. Techniques for assessing polygonal approximations of curves. IEEE Transactions on Pattern Recognition and Machine Intelligence, 19(5):659--666, 1997.

....curved world of modern vision however, they are inadequate. Although curved edges may be approximated to an arbitrary degree of accuracy by piecewise linear segments, the resulting descriptions are inherently unstable. Despite this, research is still active into the problems of line segmentation [29, 70, 71, 100, 107], indicating that even for this relatively simple case, a best practice algorithm has not been agreed. 2.4.2 Conic sections The importance of conic sections in computer vision has always been recognised, as they arise naturally as the perspective projection of the circle. They are also one of ....

P. L. Rosin. Techniques for assessing polygonal approximations of curves. In Proceedings, British Machine Vision Conference, pages 153--162, 1996.

....points left. Then, the tree of possible segments is traversed and the method keeps those segments maximizing a measure of significance, which is defined as a ratio between the maximum deviation and the length of the segment. Recently, Rosin has proposed other possible measures of significance [18], and we plan to explore this further in the coming months. We have also used for many years an iterative method, that of Wall and Danielsson [23] enhanced in our team with a direction change marking procedure to preserve the angular points. The method only needs a single threshold, on the ratio ....

....many segments [1] Also, as already said, the approximation will be precise with respect to the original curve, which does not necessarily correspond to the expected line, as we have seen with the displacement of junctions in a skeleton. Possible improvements include better significance criteria [18] and the use of postprocessing steps (x 6) 6 Post processing In the two steps described until now, we have never used any explicit knowledge about what vectors are supposed to be in a graphical document. The line finding methods working on the binary image only use simple topological and ....

P. L. Rosin. Techniques for Assessing Polygonal Approximation of Curves. IEEE Transactions on PAMI, 19(6):659--666, June 1997.

....of vertices. An implicit de nition of the curve, A : f(x; y) 0, is less often used in matching. Polylines from real world applications often contain many spurious vertices, which can be removed by approximating the polygon. There are many heuristics for approximating polygonal curves, see e.g. Ros97] for a comparison. Two methods of optimal approximation are the following: Given a polyline A and a number k, construct an approximation polyline A k of k vertices, minimizing the approximation error, or dissimilarity, d(A; A k ) Given a polyline and an error bound , construct an ....

Paul L. Rosin. Techniques for assessing polygonal approximations of curves. IEEE Transactions on Pattern Recognition and Machine Intelligence, 19(5):659-666, 1997.

....results of evaluating the performance of our breakpoint detector against that of Lowe s algorithm [7] using both synthetic data and RADIUS data. 4 Lowe s algorithm for digital segmentation has been widely cited and was found superior to most breakpoint detection algorithms available [13] [12], 5] 5.1 Synthetic Curves First we evaluate the performance of Lowe s algorithm and ours using synthetic curves for polygonal approximation. Synthetic curves were generated by sampling the original model curve consisting of piecewise linear line segments and by perturbing each sampled pixel ....

P. L. Rosin. Techniques for assessing polygonal approximations of curves. IEEE Trans. on Pattern Analysis and Machine Intelligence, 19(6):659--666, 1997.

....using both synthetic data and RADIUS data. The criterion used for the evaluation include both visual inspection, and false alarm and misdetection rates when groundtruth data are available. Lowe s algorithm has been widely cited and was found superior to most corner detection algorithms available [8] [7] 3] 5.1. Synthetic curves Here we evaluate the performance of the two algorithms using the synthetic curves for polygonal approximation. Synthetic curves were generated by sampling the original model curve consisting of piecewise linear line segments and by perturbing each sampled pixel ....

R. L. Rosin. Techniques for assessing polygonal approximations of curves. 7th British Machine Vision Conf., Edinburgh, 1996, 1996.

....the model and data. Fitting is performed by finding a polygonal approximation of the boundary. Dynamic programming is used to find the optimal three line polygon approximation minimising E = P i d i , the summed L 1 error, where d i is the shortest Euclidean distance from p i to the triangle [7]. Since this is computationally expensive the data is first subsampled by a factor of five. The final triangularity measure is TA = 1 E where A is the area of the region. 4.3. Projections (T P ) A computationally more efficient approach to fitting the triangle model is to work with the ....

P.L. Rosin. Techniques for assessing polygonal approximations of curves. IEEE Transactions on Pattern Analysis and Machine Intelligence, 19(6):659--666, 1997.

....the Behaviour of Polygonal Approximation Algorithms Paul L. Rosin Department of Information Systems and Computing Brunel University Middlesex UK Paul.Rosin brunel.ac. uk Abstract In a recent paper we described a method for assessing the accuracy of polygonal approximation algorithms [16]. Here we develop several measures to assess the stability of such approximation algorithms under variations in their scale parameters. A monotonicity index is introduced that can be applied to analyse the change in the approximation error or the number of line segments against increasing ....

....into account (in a rudimentary manner) the number of humans that selected similar breakpoints, and the degree of certainty of the human s selection. To measure the algorithms robustness their performance was measured on input data which was transformed by rotation, scaling, and reflection. Rosin [16] compared various algorithms according to criteria such as integral squared error (ISE) maximum deviation, etc. Previously a problem with this approach was that if the algorithms produced different numbers of breakpoints their errors could not be meaningfully compared. This was circumvented by ....

[Article contains additional citation context not shown here]

P.L. Rosin. Techniques for assessing polygonal approximations of curves. IEEE Trans. PAMI, 19(6):659--666, 1997.

No context found.

P.L. Rosin, "Techniques for Assessing Polygonal Approximation of Curves", Pattern Analysis and Machine Intelligence (PAMI), 19(6) : 659-666, 1997.

No context found.

P.L. Rosin. Techniques for Assessing Polygonal Approximation of Curves. Pattern Analysis and Machine Intelligence (PAMI), 19(6) : 659-666, 1997.

No context found.

# P.L. Rosin, "Techniques for Assessing Polygonal Approximations of Curves," Seventh British Machine Vision Conf., Edinburgh, 1996.

No context found.

P. L. Rosin. Techniques for Assessing Polygonal Approximation of Curves. IEEE Transactions on PAMI, 19(6):659--666, June 1997.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC