[NE08] Nicolas Normand and Pierre Evenou. Medial axis lookup table and test neighborhood computation for 3D chamfer norms. Pattern Recognition, page 20 pages, 2008. To appear.
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[EVEN2019] Philippe Even, Phuc Ngo and Bertrand Kerautret. Thick Line Segment Detection with Fast Directional Tracking ICIAP 2019, To appears.

Keywords: line and segment detection,
[FM05] Céline Fouard and Grégoire Malandain. 3-d chamfer distances and norms in anisotropic grids. Image and Vision Computing, 23(2):143-158, February 2005.
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Chamfer distances are widely used in image analysis and many authors have investigated the computation of optimal chamfer mask coefficients. Unfortunately, these methods are not systematized: calculations have to be conducted manually for every mask size or image anisotropy. Since image acquisition (e.g. medical imaging) can lead to discrete anisotropic grids with unpredictable anisotropy value, automated calculation of chamfer mask coefficients becomes mandatory for e cient distance map computations. This article presents an automatic construction for chamfer masks of arbitrary sizes. This allows, first, to derive analytically the relative error with respect to the Euclidean distance, in any 3-D anisotropic lattice, and second, to compute optimal chamfer coefficients. In addition, the resulting chamfer map verifies discrete norm conditions.

Keywords: chamfer distance, anisotropic lattice, Farey triangulation
[MF05] Grégoire Malandain and Céline Fouard. On optimal chamfer masks and coefficients. Research Report 5566, INRIA, 2005.
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This report describes the calculation of local errors in Chamfer masks both in two- and in three-dimensional anisotropic spaces. For these errors, closed forms are given that can be related to the Chamfer mask geometry. Thanks to these calculation, it can be obsrved that the usual Chamfer masks (i.e. 3x3x3 or 5x5x5) have an inhomogeneously distributed error. Moreover, it allows us to design dedicated Chamfer masks by controlling either the complexity of the computation of the distance map (or equivalently the number of vectors in the mask), or the error of the mask in Z2 or in Z3. Last, since Chamfer distances are usually computed with integer weights (and approximate the Euclidean distance up to a multiplicative factor), we demonstrate that the knowledge of the local errors allows a very efficient computation of these weights.

Keywords: Chamfer distance, anisotropic lattice, Farey triangulation
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Keywords: binary image; chamfer; chessboard; city block; computational complexity; computer vision; distance maps; Euclidean; Euclidean distance; Euclidean distance transform; image processing; machine vision; matrix searching; octagonal
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