Shape Representation by Multiscale Contour Approximation

@article{Bengtsson1991ShapeRB,
  title={Shape Representation by Multiscale Contour Approximation},
  author={Ann Bengtsson and J. O. Eklundh},
  journal={IEEE Trans. Pattern Anal. Mach. Intell.},
  year={1991},
  volume={13},
  pages={85-93}
}
An approach is presented for deriving qualitative descriptions of contours containing structures at different (unknown) scales. The descriptions are in terms of straight arcs, curved arcs with sign of curvature, corners, and points delimiting the arcs: inflexion points and transitions from straight to curved. Furthermore, the tangents at these points are derived. The approach is based on the construction of a hierarchic family of polygons, having the scale-space property of causality; structure… 

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References

SHOWING 1-10 OF 25 REFERENCES

Organization of smooth image curves at multiple scales

  • D. Lowe
  • Computer Science
    [1988 Proceedings] Second International Conference on Computer Vision
  • 1988
A method is presented for describing linked edge points at a range of scales by selecting intervals of the curve and scales of smoothing that are most likely to represent the underlying structure of the scene.

The Organization Of Curve Detection: Coarse Tangent Fields And Fine Spline Coverings

  • S. Zucker
  • Computer Science, Mathematics
    [1988 Proceedings] Second International Conference on Computer Vision
  • 1988
We propose a new paradigm for curve detection in which an autonomous and atomic description is computed between measurements on the image and global curves. The description takes the form of a

On the computation of a scale-space primal sketch

Using Symmetries For Analysis Of Shape From Contour

  • F. UlupinarR. Nevatia
  • Computer Science, Mathematics
    [1988 Proceedings] Second International Conference on Computer Vision
  • 1988
One of the mathematical results is that for a cone, the surface shape can be constructed uniquely under very simple assumptions, and some preliminary results on extraction of symmetries from real images are shown.

Toward a computational theory of shape

Although the shape of objects is a key to their recognition, viable theories for representing and describing shape have been elusive. We propose a framework that unifies competing approaches to

The Recovery of Three-Dimensional Structure from Image Curves

  • D. LoweT. Binford
  • Computer Science
    IEEE Transactions on Pattern Analysis and Machine Intelligence
  • 1985
A class of inferences is described which allows the recovery of three-dimensional structures from the two-dimensional curves in an image and it can be shown that many potential interpretations of image curves are highly improbable.

The renormalized curvature scale space and the evolution properties of planar curves

  • Alan K. MackworthF. Mokhtarian
  • Mathematics, Physics
    Proceedings CVPR '88: The Computer Society Conference on Computer Vision and Pattern Recognition
  • 1988
The curvature scale-space image of a planar curve is computed by convolving a path-based parametric representation of the curve with a Gaussian function of variance sigma /sup 2/, extracting the

Curve Fitting with Conic Splines

It is shown theoretically that exact knot placement at the optimal locations is less important for higher order splines than for polygons, andisons with other methods suggest that conic splines require no more knots than cubic splines for similar quality of approximation.

Scale-space filtering: A new approach to multi-scale description

Scale-space filtering is a method that describes signals qualitatively, managing the ambiguity of scale in an organized and natural way.