Results 1  10
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22
Techniques for Assessing Polygonal Approximations of Curves
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1996
"... Given the enormous number of available methods for finding polygonal approximations to curves techniques are required to assess different algorithms. Some of the standard approaches are shown to be unsuitable if the approximations contain varying numbers of lines. Instead, we suggest assessing an al ..."
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Cited by 56 (3 self)
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Given the enormous number of available methods for finding polygonal approximations to curves techniques are required to assess different algorithms. Some of the standard approaches are shown to be unsuitable if the approximations contain varying numbers of lines. Instead, we suggest assessing an algorithm's results relative to an optimal polygon, and describe a measure which combines the relative fidelity and efficiency of a curve segmentation. We use this measure to compare the application of fifteen algorithms to a curve first used by Teh and Chin [31]; their ISEs are assessed relative to the optimal ISE. In addition, using an example of pose estimation, it is shown how goaldirected evaluation can be used to select an appropriate assessment criterion.
A simple and efficient algorithm for detection of high curvature points in planar curves
, 1999
"... A new algorithm is proposed for detection of corners and other high curvature points in planar curves. A corner is defined as a location where a triangle with specified opening angle and size can be inscribed in the curve. The tests compare the new algorithm to four alternative algorithms for corner ..."
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Cited by 39 (0 self)
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A new algorithm is proposed for detection of corners and other high curvature points in planar curves. A corner is defined as a location where a triangle with specified opening angle and size can be inscribed in the curve. The tests compare the new algorithm to four alternative algorithms for corner detection.
A PseudoMetric for Weighted Point Sets

, 2002
"... We present a pseudometric for weighted point sets. There are numerous situations, for example in the shape description domain, where the individual points in a feature point set have an associated attribute, a weight. A distance function that incorporates this extra information apart from the point ..."
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Cited by 22 (8 self)
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We present a pseudometric for weighted point sets. There are numerous situations, for example in the shape description domain, where the individual points in a feature point set have an associated attribute, a weight. A distance function that incorporates this extra information apart from the points' position can be very useful for matching and retrieval purposes. There are two main approaches to do this. One approach is to interpret the point sets as fuzzy sets. However, a distance measure for fuzzy sets that is a metric, invariant under rigid motion and respects scaling of the underlying ground distance, does not exist. In addition,
Corner Detection via Topographic Analysis of Vector Potential
, 1998
"... This paper describes how corner detection can be realised using a new feature representation that has recently been successfully exploited for edge and symmetry detection. The feature representation based on an magnetostatic analogy. The idea is to compute a vector potential by appealing to an a ..."
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Cited by 21 (5 self)
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This paper describes how corner detection can be realised using a new feature representation that has recently been successfully exploited for edge and symmetry detection. The feature representation based on an magnetostatic analogy. The idea is to compute a vector potential by appealing to an analogy in which the Canny edgemap is regarded as an elementary current density residing on the image plane. In our previous work we demonstrated that edges are the local maxima of the vector potential while points of symmetry correspond to the local minimum. In this paper we demonstrate that corners are located at the saddle points of the magnitude of the vector potential.
A comparative study on 2d curvature estimators
, 2006
"... Abstract. Curvature is a frequently used property in twodimensional (2D) shape analysis, directly or for derived features such as corners or convex and concave arcs. This paper presents curvature estimators which follow approaches in differential geometry. Digitalstraight segment approximation (as ..."
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Cited by 10 (0 self)
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Abstract. Curvature is a frequently used property in twodimensional (2D) shape analysis, directly or for derived features such as corners or convex and concave arcs. This paper presents curvature estimators which follow approaches in differential geometry. Digitalstraight segment approximation (as known from digital geometry) is used in those estimators. Results of multigrid experiments are evaluated leading to a comparative performance analysis of several curvature estimators. 1
Curvature Morphology
 PROCEEDINGS OF VISION INTERFACE ’89
, 1988
"... The notion of curvature of planar curves has emerged as one of the most powerful for the representation and interpretation of objects in an image. Although curvature extraction from a digitized object contour would seem to be a rather simple task, few methods exist that are at the same time easy ..."
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Cited by 9 (1 self)
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The notion of curvature of planar curves has emerged as one of the most powerful for the representation and interpretation of objects in an image. Although curvature extraction from a digitized object contour would seem to be a rather simple task, few methods exist that are at the same time easy to implement, fast, and reliable in the presence of noise. In this paper we first briefly present a scheme for obtaining the discrete curvature function of planar contours based on the chaincode representation of a boundary. Secondly, we propose a method for extracting important features from the curvature function such as extrema or peaks, and segments of constant curvature. We use mathematical morphological operations on functions to achieve this. Finally, on the basis of these morphological operations, we suggest a new scalespace representation for curvature named the Morphological Curvature ScaleSpace. Advantages over the usual scalespace approaches are shown.
The Viterbi Optimal RunlengthConstrained Approximation Nonlinear Filter
, 1995
"... Simple nonlinear filters are often used to enforce "hard" syntactic constraints while remaining close to the observation data; e.g., in the binary case it is common practice to employ iterations of a suitable median, or a onepass recursive median, openclose, or closopen filter to impose a minimum s ..."
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Cited by 6 (3 self)
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Simple nonlinear filters are often used to enforce "hard" syntactic constraints while remaining close to the observation data; e.g., in the binary case it is common practice to employ iterations of a suitable median, or a onepass recursive median, openclose, or closopen filter to impose a minimum symbol runlength constraint while remaining "faithful" to the observation. Unfortunately, these filters are  in general  suboptimal. Motivated by this observation, we pose the following optimization: Given a finitealphabet sequence of finite extent, y = fy(n)g N \Gamma1 n=0 , find a sequence, b x = fbx(n)g N \Gamma1 n=0 , which minimizes d(x; y) = P N \Gamma1 n=0 dn (y(n); x(n)) subject to: x is piecewise constant of plateau runlength M . We show how a suitable reformulation of the problem naturally leads to a simple and efficient Viterbitype optimal algorithmic solution. We call the resulting nonlinear inputoutput operator the Viterbi Optimal RunlengthConstrained Approximation...
Global curvature estimation for corner detection
 In International conference on image and vision computing (IVCNZ), Dunedin/New Zealand
, 2005
"... The paper starts with presenting three curvature estimators which follow definitions (approaches) in differential geometry. Digitalstraight segment (DSS) approximation is used in those estimators, we point to problems caused by this approach, and propose simple ways for eliminating those problems. ..."
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Cited by 4 (0 self)
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The paper starts with presenting three curvature estimators which follow definitions (approaches) in differential geometry. Digitalstraight segment (DSS) approximation is used in those estimators, we point to problems caused by this approach, and propose simple ways for eliminating those problems. The paper then informs about multigrid analysis experiments, where all estimators appear to be multigrid convergent when digitizing an ellipse. The paper also applies these estimators for corner detection and compares their performance with a recently published heuristic cornerdetection approach by means of multigrid analysis. Experiments indicate that corner detectors (based on curvature estimation) perform about as good as the heuristic method for large grid resolutions, and one detector might be even superior.