Length estimators for digitized contours
Computer Vision, Graphics, and Image Processing
Digital topology: introduction and survey
Computer Vision, Graphics, and Image Processing
Discrete multidimensional Jordan surfaces
CVGIP: Graphical Models and Image Processing
Topology preservation within digital surfaces
Graphical Models
Fast computation of the normal vector field of the surface of a 3-D discrete object
DCGA '96 Proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery
A concise characterization of 3D simple points
Discrete Applied Mathematics
A Comparative Evaluation of Length Estimators of Digital Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fast, accurate and convergent tangent estimation on digital contours
Image and Vision Computing
Surface Shading in the Cuberille Environment
IEEE Computer Graphics and Applications
Multigrid convergence and surface area estimation
Proceedings of the 11th international conference on Theoretical foundations of computer vision
Normals and curvature estimation for digital surfaces based on convolutions
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
Binomial convolutions and derivatives estimation from noisy discretizations
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
Discrete surfaces segmentation into discrete planes
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
Smooth 2D coordinate systems on discrete surfaces
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Convergence of binomial-based derivative estimation for C2 noisy discretized curves
Theoretical Computer Science
Mesh Parameterization with Generalized Discrete Conformal Maps
Journal of Mathematical Imaging and Vision
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In this paper, we present a method that we call on-surface convolution which extends the classical notion of a 2D digital filter to the case of digital surfaces (following the cuberille model). We also define an averaging mask with local support which, when applied with the iterated convolution operator, behaves like an averaging with large support. The interesting property of the latter averaging is the way the resulting weights are distributed: given a digital surface obtained by discretization of a differentiable surface of R^3, the masks isocurves are close to the Riemannian isodistance curves from the center of the mask. We eventually use the iterated averaging followed by convolutions with differentiation masks to estimate partial derivatives and then normal vectors over a surface. The number of iterations required to achieve a good estimate is determined experimentally on digitized spheres and tori. The precision of the normal estimation is also investigated according to the digitization step.