Refining Surface Curvature with Relaxation Labeling

@inproceedings{Wilson1997RefiningSC,
  title={Refining Surface Curvature with Relaxation Labeling},
  author={Richard C. Wilson and Edwin R. Hancock},
  booktitle={ICIAP},
  year={1997}
}
Our main contributions in this paper are twofold. In the first instance, we demonstrate how H - K surface labelling can be realised using dictionary-based probabilistic relaxation. To facilitate this implementation we have developed a dictionary of feasible surface-label configurations. These configurations observe certain constraints on the contiguity of elliptic and hyperbolic regions, and, on the continuity and thinness of parabolic lines. The second contribution is to develop a statistical… 
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References

SHOWING 1-10 OF 19 REFERENCES

Edge-Labeling Using Dictionary-Based Relaxation

TLDR
An improved application of probabilistic relaxation to edge labeling is presented, which uses a dictionary to represent permitted labelings of the entire context-conveying neighborhood of each pixel.

Inferring Surface Trace and Differential Structure from 3-D Images

TLDR
A functional minimization algorithm utilizing overlapping local charts to refine surface points and curvature estimates is presented, and an implementation as an iterative constraint satisfaction procedure based on local surface smoothness properties is developed.

Segmentation through Variable-Order Surface Fitting

  • P. BeslR. Jain
  • Computer Science
    IEEE Trans. Pattern Anal. Mach. Intell.
  • 1988
TLDR
A piecewise-smooth surface model for image data that possesses surface coherence properties is used to develop an algorithm that simultaneously segments a large class of images into regions of arbitrary shape and approximates image data with bivariate functions so that it is possible to compute a complete, noiseless image reconstruction based on the extracted functions and regions.

Using Uncertainty to Link 3D Edge Detection and Local Surface Modelling

TLDR
A method for computing typical curvature features from 3D medical images by quantitatively analyzing the uncertainty in edge position, orientation and magnitude produced by the multidimensional (2-D and 3-D) versions of the Monga-Deriche-Canny recursive separable edge-detector.

Using differential geometry in R/sup 4/ to extract typical features in 3D density images

  • O. MongaS. Benayoun
  • Mathematics
    [1992] Proceedings. 11th IAPR International Conference on Pattern Recognition
  • 1992
TLDR
A method involving computing the curvatures on the edge points from the second partial derivatives of the image to avoid the need to find links between 3D edge detection and local surface approximation is proposed.

Algebraic error analysis for surface curvatures and segmentation of 3-D range images

Statistics of surface curvature estimates

TLDR
A model of the relationship between the variance of curvature estimates and the image noise is presented and it is concluded that any pixel-by-pixel thresholding will produce poor results.

Surface shape and curvature scales

Feature tracking by multi-frame relaxation

Recursive Filtering and Edge Closing: two primary tools for 3-D edge detection

TLDR
3D edge tracking/closing enables to extract many edges not provided by the filtering stage without introducing noisy edges, and some efficient 3D edge detection algorithms having a low computational cost are obtained.