Chamfer masks: discrete distance functions, geometrical properties and optimization

Thiel, Edouard; Montanvert, Annick

doi:10.1109/icpr.1992.201971

Cited by 24 publications

(17 citation statements)

References 9 publications

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“…Some results concerning the geometry of large chamfer masks have been obtained in [7]. In this paper, we optimize such large chamfer masks by minimizing the maximum absolute error.…”

Section: Optimal Local Distances For 5 5 Neighborhoodmentioning

confidence: 99%

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Optimum design of chamfer distance transforms

Butt

Maragos²

1998

IEEE Trans. on Image Process.

127

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Abstract-The distance transform has found many applications in image analysis. Chamfer distance transforms are a class of discrete algorithms that offer a good approximation to the desired Euclidean distance transform at a lower computational cost. They can also give integer-valued distances that are more suitable for several digital image processing tasks. The local distances used to compute a chamfer distance transform are selected to minimize an approximation error. In this paper, a new geometric approach is developed to find optimal local distances. This new approach is easier to visualize than the approaches found in previous work, and can be easily extended to chamfer metrics that use large neighborhoods. A new concept of critical local distances is presented which reduces the computational complexity of the chamfer distance transform without increasing the maximum approximation error.

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“…Some results concerning the geometry of large chamfer masks have been obtained in [7]. In this paper, we optimize such large chamfer masks by minimizing the maximum absolute error.…”

Section: Optimal Local Distances For 5 5 Neighborhoodmentioning

confidence: 99%

“…For a 5 5 neighborhood, such optimal combinations of integer local distances and normalizing constant are given in Table II. V. OPTIMAL LOCAL DISTANCES FOR 7 7 AND LARGER NEIGHBORHOODS…”

Section: Optimal Local Distances For 5 5 Neighborhoodmentioning

confidence: 99%

Optimum design of chamfer distance transforms

Butt

Maragos²

1998

IEEE Trans. on Image Process.

127

View full text Add to dashboard Cite

show abstract

“…1). Of course the result of the graph-search could be improved by taking a larger neighborhood as structuring element, giving better approximations of the distance in some directions (like √ 2 for the diagonals) (Borgefors, 1984;Thiel and Montanvert, 1992).…”

Section: Graph Search Algorithms and Metrication Errormentioning

confidence: 99%

Global minimum for active contour models: a minimal path approach

Cohen

Kimmel

1996

Proceedings CVPR IEEE Computer Society Conference on Computer Vision and Pattern Recognition

327

565

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Abstract.A new boundary detection approach for shape modeling is presented. It detects the global minimum of an active contour model's energy between two end points. Initialization is made easier and the curve is not trapped at a local minimum by spurious edges. We modify the "snake" energy by including the internal regularization term in the external potential term. Our method is based on finding a path of minimal length in a Riemannian metric. We then make use of a new efficient numerical method to find this shortest path.It is shown that the proposed energy, though based only on a potential integrated along the curve, imposes a regularization effect like snakes. We explore the relation between the maximum curvature along the resulting contour and the potential generated from the image.The method is capable to close contours, given only one point on the objects' boundary by using a topology-based saddle search routine.We show examples of our method applied to real aerial and medical images.

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“…Each error term ∆(Π c (p i ), Z c ) in (7) determines the distance from the projection Π c (p i ) of a point p i into view c, to the nearest point on the object boundary Z c . In order to speed up this common calculation, we pre-calculate a lookup table for ∆ by means of the well known distance transform to obtain a Chamfer image [22]. Each pixel in a Chamfer image contains the distance from this pixel to the nearest point on the segmented curve Z c in view c. Calculating the Chamfer images has to be done only once and runs in linear time.…”

Section: Multiple View Fittingmentioning

confidence: 99%

MCMC-Based Multiview Reconstruction of Piecewise Smooth Subdivision Curves with a Variable Number of Control Points

Kaess

Zboinski

Dellaert

2004

Lecture Notes in Computer Science

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Abstract. We investigate the automated reconstruction of piecewise smooth 3D curves, using subdivision curves as a simple but flexible curve representation. This representation allows tagging corners to model nonsmooth features along otherwise smooth curves. We present a reversible jump Markov chain Monte Carlo approach which obtains an approximate posterior distribution over the number of control points and tags. In a Rao-Blackwellization scheme, we integrate out the control point locations, reducing the variance of the resulting sampler. We apply this general methodology to the reconstruction of piecewise smooth curves from multiple calibrated views, in which the object is segmented from the background using a Markov random field approach. Results are shown for multiple images of two pot shards as would be encountered in archaeological applications.

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Chamfer masks: discrete distance functions, geometrical properties and optimization

Cited by 24 publications

References 9 publications

Optimum design of chamfer distance transforms

Optimum design of chamfer distance transforms

Global minimum for active contour models: a minimal path approach

MCMC-Based Multiview Reconstruction of Piecewise Smooth Subdivision Curves with a Variable Number of Control Points

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