Edge localization in surface reconstruction using optimal estimation theory

Many relaxation based smoothing methods used in surface reconstruction algorithms filter out the effect of noise in image data, but result in the elimination of important discontinuity information as well. In this paper the inter-pixel interaction during relaxation is shown to be equivalent to a multiple measurement fusion problem which can be solved using optimal estimation theory. Pixels in a given neighbourhood act as noisy information sources, combining their information to update the state of that neighbourhood. By formulating discontinuities as another "noise" source in the image, and by using the so-called Curvature Consistency reconstruction algorithm on range images, it is shown that optimal estimation theory offers a method for the automatic and adaptive localization of discontinuities while providing a smooth piece wise continuous surface description.

[1]  Demetri Terzopoulos,et al.  Regularization of Inverse Visual Problems Involving Discontinuities , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[2]  B. Frieden.  A new restoring algorithm for the preferential enhancement of edge gradients , 1976 .

[3]  Thomas S. Huang,et al.  A fast two-dimensional median filtering algorithm , 1979 .

[4]  Demetri Terzopoulos,et al.  Image Analysis Using Multigrid Relaxation Methods , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[5]  Frank P. Ferrie,et al.  Deriving course 3D models of objects , 1988, Proceedings CVPR '88: The Computer Society Conference on Computer Vision and Pattern Recognition.

[6]  Tomaso Poggio,et al.  Computational vision and regularization theory , 1985, Nature.

[7]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[8]  Joachim Heel,et al.  Temporally integrated surface reconstruction , 1990, [1990] Proceedings Third International Conference on Computer Vision.

[9]  John W. Woods,et al.  Multiple model recursive estimation of images , 1979, ICASSP.

[10]  Y. J. Tejwani,et al.  Robot vision , 1989, IEEE International Symposium on Circuits and Systems,.

[11]  Philippe Saint-Marc,et al.  Adaptive smoothing: a general tool for early vision , 1989, Proceedings CVPR '89: IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[12]  Stan Z. Li,et al.  Reconstruction without discontinuities , 1990, [1990] Proceedings Third International Conference on Computer Vision.

[13]  Jitendra Malik,et al.  Scale-Space and Edge Detection Using Anisotropic Diffusion , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[14]  Richard Szeliski.  Estimating Motion From Sparse Range Data Without Correspondence , 1988, [1988 Proceedings] Second International Conference on Computer Vision.

[15]  Frank P. Ferrie,et al.  Curvature consistency improves local shading analysis , 1992, CVGIP Image Underst..

[16]  JOHN w. WOODS,et al.  Kalman filtering in two dimensions , 1977, IEEE Trans. Inf. Theory.

[17]  M.D. Levine,et al.  Where and Why Local Shading Analysis Works , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[18]  W. Eric L. Grimson,et al.  An implementation of a computational theory of visual surface interpolation , 1983, Comput. Vis. Graph. Image Process..

[19]  Andrew Blake,et al.  Visual Reconstruction , 1987, Deep Learning for EEG-Based Brain–Computer Interfaces.

[20]  Martin D. Levine,et al.  Structured edge map of curved objects in a range image , 1989, Proceedings CVPR '89: IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[21]  Jean W. Lagarde,et al.  CONSTRAINTS AND THEIR SATISFACTION IN THE RECOVERY OF LOCAL SURFACE STRUCTURE , 1999 .

[22]  Frank P. Ferrie,et al.  Darboux Frames, Snakes, and Super-Quadrics: Geometry from the Bottom Up , 1993, IEEE Trans. Pattern Anal. Mach. Intell..

[23]  Arthur Gelb,et al.  Applied Optimal Estimation , 1974 .

[24]  Jong-Sen Lee,et al.  Digital Image Enhancement and Noise Filtering by Use of Local Statistics , 1980, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[25]  Federico Girosi,et al.  Parallel and deterministic algorithms from MRFs: surface reconstruction and integration , 1990, ECCV.

[26]  David C. Wang,et al.  Gradient inverse weighted smoothing scheme and the evaluation of its performance , 1981 .

[27]  Ramesh C. Jain,et al.  Segmentation through Variable-Order Surface Fitting , 1988, IEEE Trans. Pattern Anal. Mach. Intell..

[28]  Edward J. Delp,et al.  Viewpoint invariant recovery of visual surfaces from sparse data , 1990, [1990] Proceedings Third International Conference on Computer Vision.

[29]  Brian G. Schunck,et al.  Discontinuity preserving surface reconstruction , 1989, Proceedings CVPR '89: IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[30]  Steven W. Zucker,et al.  On the Foundations of Relaxation Labeling Processes , 1983, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[31]  Steven W. Zucker,et al.  Inferring Surface Trace and Differential Structure from 3-D Images , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[32]  Demetri Terzopoulos,et al.  Multilevel computational processes for visual surface reconstruction , 1983, Comput. Vis. Graph. Image Process..

[33]  W. Eric L. Grimson,et al.  From images to surfaces , 1981 .

[34]  Manfredo P. do Carmo,et al.  Differential geometry of curves and surfaces , 1976 .