Discrete Curvature Based on Osculating Circle Estimation

Cœurjolly, David; Miguet, Serge; Tougne, Laure

doi:10.1007/3-540-45129-3_27

Cited by 60 publications

(53 citation statements)

References 10 publications

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“…Coeurjolly et al [14] presented a purely discrete algorithm to compute curvature in images based on discrete osculating circles as an extension to the method classification done by Worring and Smeulders [4].…”

Section: Comparison With a Segmentation Based Approachmentioning

confidence: 99%

“…The acceleration is related to the curvature of the spatiotemporal space curve formed by the moving spots. The acceleration can be computed from the 4-D image with the notation as in Section I-A as follows [26]: (14) (15) This is the classical expression of the tangential and the normal components of the acceleration.…”

Section: Applicationsmentioning

confidence: 99%

“…In 2-D, the use of the double angle method is well-known [1], [10], but in 3-D it remained an obstacle that prevented the computation of curvature in 3-D. Therefore, traditional 3-D methods are applied to segmented images, or even on curves represented by ordered points, which enables one to fit a parametric model to the curve [11]- [14]. These methods rely heavily on the preceding segmentation, labeling, and orderings steps, which may fail due to noise or the presence of a bundle of space curves comparable to a lock of hair.…”

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confidence: 99%

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Curvature of n-dimensional space curves in grey-value images

Rieger

Vliet

2002

IEEE Trans. on Image Process.

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Abstract-Local curvature represents an important shape parameter of space curves which are well described by differential geometry. We have developed an estimator for local curvature of space curves embedded in -dimensional ( -D) grey-value images. There is neither a segmentation of the curve needed nor a parametric model assumed. Our estimator works on the orientation field of the space curve. This orientation field and a description of local structure is obtained by the gradient structure tensor. The orientation field has discontinuities; walking around a closed contour yields two such discontinuities in orientation. This field is mapped via the Knutsson mapping to a continuous representation; from a -D vector to a symmetric 2 -D tensor field. The curvature of a space curve, a coordinate invariant property, is computed in this tensor field representation. An extensive evaluation shows that our curvature estimation is unbiased even in the presence of noise, independent of the scale of the object and furthermore the relative error stays small.

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Section: Comparison With a Segmentation Based Approachmentioning

confidence: 99%

Section: Applicationsmentioning

confidence: 99%

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confidence: 99%

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Curvature of n-dimensional space curves in grey-value images

Rieger

Vliet

2002

IEEE Trans. on Image Process.

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“…and Debled-Rennesson [7] follows the same concept than the estimator proposed by Coeurjolly et al [6] (called CC estimator). The latter is based on the estimation of osculating circles.…”

Section: Estimator Based On Osculating Circles (Cc and Ndc)mentioning

confidence: 95%

“…First Nguyen et al extend the estimator of osculating circles proposed by Coeurjolly et al [6] by using blurred segments [1]. By this way, the estimation of osculating circles had a better behavior on noisy contours and was also meaningful for a non connected (but ordered) set of points.…”

Section: Introductionmentioning

confidence: 99%

Comparison of Discrete Curvature Estimators and Application to Corner Detection

Kerautret

Lachaud

Naegel

2008

Advances in Visual Computing

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Abstract. Several curvature estimators along digital contours were proposed in recent works [1][2][3]. These estimators are adapted to non perfect digitization process and can process noisy contours. In this paper, we compare and analyse the performances of these estimators on several types of contours and we measure execution time on both perfect and noisy shapes. In a second part, we evaluate these estimators in the context of corner detection. Finally to evaluate the performance of a non curvature based approach, we compare the results with a morphological corner detector [4].

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Estimation of Curvature along Curves with Application to Fibres in 3D Images of Paper

Cœurjolly¹,

Svensson²

2003

Lecture Notes in Computer Science

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Space curves can be used to represent elongated objects in 3D images and furthermore to facilitate the computation of shape measures for the represented objects. In our specific application (fibres in 3D images of paper), we want to analyze the fibre network on a voxel level with respect to elongation and bending. For this purpose, it is of interest to estimate the curvature in each voxel along a curve. We present a new discrete curvature estimator fulfilling the multigrid convergence property. Moreover, we present results from a study where curvature together with other shape measures are used to analyze the fibre network.

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Discrete Curvature Based on Osculating Circle Estimation

Cited by 60 publications

References 10 publications

Curvature of n-dimensional space curves in grey-value images

Curvature of n-dimensional space curves in grey-value images

Comparison of Discrete Curvature Estimators and Application to Corner Detection

Estimation of Curvature along Curves with Application to Fibres in 3D Images of Paper

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