Discrete Geometry for Computer Imagery, 14 conf., DGCI 2008

Cover......Page p0001.djvu
Lecture Notes in Computer Science 4992......Page p0002.djvu
Discrete Geometry for Computer Imagery......Page p0003.djvu
Preface......Page p0005.djvu
Organization......Page p0006.djvu
Table of Contents......Page p0008.djvu
Introduction......Page p0013.djvu
References......Page p0015.djvu
Introduction......Page p0016.djvu
Consequences of Shannon\'s Sampling Theorem......Page p0017.djvu
Geometric Sampling Theorems......Page p0021.djvu
Error Analysis of Segmentation Methods......Page p0025.djvu
Conclusions......Page p0030.djvu
Weak Rational Computing for Digital Geometry......Page p0032.djvu
Introduction......Page p0033.djvu
Theoretical Framework......Page p0034.djvu
Origin of the Reveillès Discrete Analytical Line......Page p0035.djvu
Bases of Nonstandard Analysis on N and Z......Page p0036.djvu
The System A......Page p0038.djvu
Constructive Mathematics, Proofs and Programs......Page p0039.djvu
A Discrete Nonstandard Constructive Model of R......Page p0040.djvu
Conclusion......Page p0043.djvu
Generation and Recognition of Digital PlanesUsing Multi-dimensional Continued Fractions......Page p0045.djvu
Stepped Planes and Dual Maps......Page p0046.djvu
Brun Expansions of Real Vectors......Page p0049.djvu
Generation of Stepped Planes......Page p0050.djvu
Brun Expansions of Stepped Planes......Page p0051.djvu
Brun Expansions of Binary Functions......Page p0053.djvu
Recognition of Stepped Planes......Page p0054.djvu
Introduction......Page p0057.djvu
Frequencies of the (m,n)-cubes......Page p0058.djvu
Application to Local Estimators......Page p0063.djvu
Conclusion......Page p0067.djvu
Introduction......Page p0069.djvu
Preliminaries......Page p0070.djvu
Combinatorics on Words......Page p0071.djvu
Christoffel Words......Page p0072.djvu
Digital Convexity......Page p0073.djvu
Algorithm to Check Word Convexity......Page p0076.djvu
The Final Algorithm......Page p0077.djvu
Concluding Remarks......Page p0078.djvu
Introduction......Page p0081.djvu
Mathematical Preliminaries......Page p0082.djvu
Matrix Ring over the Kronecker Product and Matrix Addition ......Page p0085.djvu
Averages in the Neighbourhood......Page p0086.djvu
Operations in Z3......Page p0087.djvu
Discrete Gaussian Kernel......Page p0090.djvu
Conclusions ......Page p0091.djvu
Digitally Continuous Multivalued Functions......Page p0093.djvu
Digital Spaces......Page p0095.djvu
Continuous Multivalued Functions......Page p0096.djvu
Continuous Multivalued Functions and Simple Points......Page p0098.djvu
Multivalued Digital Retractions......Page p0102.djvu
Digital Version of Hahn-Mazurkiewicz Theorem......Page p0103.djvu
About This Paper......Page p0105.djvu
Earlier Developments......Page p0106.djvu
Earlier Results by Uscka-Wehlou (2007) huw......Page p0107.djvu
Main Result......Page p0109.djvu
Slopes with Periodic CF Expansions......Page p0113.djvu
Slopes with Non-periodic CF Expansions......Page p0114.djvu
Conclusion......Page p0115.djvu
New Characterizations of Simple Points,Minimal Non-simple Sets and P-Simple Pointsin 2D, 3D and 4D Discrete Spaces......Page p0117.djvu
Cubical Complexes......Page p0118.djvu
Collapse and Simple Sets......Page p0120.djvu
Confluences......Page p0122.djvu
New Characterization of Simple Cells......Page p0123.djvu
Critical Kernels......Page p0124.djvu
Minimal Non-simple Sets......Page p0125.djvu
Conclusion......Page p0127.djvu
Introduction......Page p0129.djvu
Background Notions......Page p0130.djvu
Morse Functions......Page p0131.djvu
Morse and Morse-Smale Complexes......Page p0132.djvu
Cancellations in Morse-Smale and Morse Complexes......Page p0133.djvu
Quasi-Morse Complexes......Page p0136.djvu
Dual Representation of Morse Complexes......Page p0137.djvu
Concluding Remarks......Page p0139.djvu
Introduction......Page p0141.djvu
Neighbourhoods in Toric Spaces......Page p0143.djvu
Loops in Toric Spaces......Page p0144.djvu
Fundamental Group......Page p0145.djvu
Algorithm for Detecting Wrapped Subsets of Tn......Page p0146.djvu
Wrapping Vector of a Loop......Page p0148.djvu
Equivalence between Homotopy Classes and Wrapping Vector......Page p0149.djvu
Proof of Alg. 1......Page p0150.djvu
Annex......Page p0151.djvu
Introduction......Page p0153.djvu
Generalized Maps......Page p0154.djvu
Removal and Contraction Operations......Page p0156.djvu
Dimension 1: 0-insertion......Page p0157.djvu
Dimension 2......Page p0158.djvu
Dimension n......Page p0159.djvu
Expansion......Page p0161.djvu
Generalisation......Page p0162.djvu
Conclusion and Perspectives......Page p0163.djvu
Introduction......Page p0165.djvu
Conformal Structure......Page p0166.djvu
De Rham Cohomology......Page p0169.djvu
Hodge Star......Page p0171.djvu
The Real Case......Page p0173.djvu
Non Real Conformal Structure......Page p0174.djvu
Conclusions and Acknowledgments......Page p0175.djvu
Introduction......Page p0177.djvu
Cubical Complexes......Page p0179.djvu
Topology Preserving Operations......Page p0181.djvu
Minimal Simple Pairs in F3......Page p0182.djvu
Some Properties of Minimal Simple Pairs......Page p0184.djvu
Conclusion......Page p0186.djvu
Appendix: Simple Equivalence and MSPs......Page p0188.djvu
Determining Whether a Simplicial 3-ComplexCollapses to a 1-Complex Is NP-Complete......Page p0189.djvu
Collapsing......Page p0190.djvu
The 2D Case......Page p0194.djvu
The 3D Collapsing Problem......Page p0195.djvu
Conclusion......Page p0199.djvu
Introduction......Page p0201.djvu
Chamfer Distances......Page p0202.djvu
Geometry of the Chamfer Ball......Page p0203.djvu
Chamfer Medial Axis......Page p0204.djvu
General H-Polytopes ziegler2001......Page p0205.djvu
Chamfer H-Polytopes......Page p0206.djvu
LUT Mask......Page p0209.djvu
Conclusion and Future Works......Page p0211.djvu
Introduction......Page p0213.djvu
Basic Notions and Previous Results......Page p0214.djvu
Metricity of the Distance Functions......Page p0216.djvu
The fcc Grid......Page p0217.djvu
The bcc Grid......Page p0218.djvu
Metricity......Page p0219.djvu
Algorithm to Find a Minimal Cost-Path between Two Points......Page p0220.djvu
Conclusions......Page p0223.djvu
Introduction......Page p0225.djvu
Recall ECC......Page p0226.djvu
Properties of Eccentric Points......Page p0227.djvu
Recall Discrete Circles......Page p0228.djvu
Shape Bounded Single Source Distance Transform......Page p0229.djvu
Progressive Refinement Eccentricity Transform......Page p0230.djvu
New Algorithm (ECC08)......Page p0231.djvu
Experimental Results......Page p0232.djvu
Conclusion......Page p0235.djvu
Introduction......Page p0237.djvu
Statistical Template Matching......Page p0239.djvu
STM under Geometric Transformations......Page p0240.djvu
Adaptive Subpixel STM......Page p0242.djvu
Experiments......Page p0244.djvu
References......Page p0248.djvu
Introduction......Page p0250.djvu
A Simple Approach Based on the Complete Voronoi Diagram Implementation......Page p0251.djvu
A d-Dimensional Algorithm for I-DT......Page p0254.djvu
Experiments......Page p0257.djvu
Conclusion and Future Works......Page p0260.djvu
Introduction......Page p0262.djvu
Definition......Page p0263.djvu
General Properties......Page p0264.djvu
Self-similarity......Page p0265.djvu
Constructive Results on Sturmian Words......Page p0266.djvu
Grid Configurations from Rotation Words......Page p0268.djvu
Application to C/4......Page p0269.djvu
Perspectives......Page p0271.djvu
Introduction......Page p0274.djvu
Skeleton Definition......Page p0275.djvu
Simplified Skeletons......Page p0276.djvu
Computing Simplified Skeletons......Page p0277.djvu
Computing the Y-network......Page p0279.djvu
Y-network Decomposition......Page p0280.djvu
Skeleton Segmentation......Page p0281.djvu
Results and Discussion......Page p0283.djvu
Conclusion......Page p0285.djvu
Introduction......Page p0287.djvu
Width- Discrete Patches......Page p0288.djvu
Width- Normal......Page p0290.djvu
Width- Patch Area......Page p0292.djvu
Patch Outline......Page p0293.djvu
Concave and Convex Parts......Page p0294.djvu
Conclusion......Page p0297.djvu
Introduction......Page p0299.djvu
Adjacency Relations between Surfels an Surfels Neighborhoods......Page p0300.djvu
On-Surface Convolution......Page p0301.djvu
The Averaging Filter......Page p0302.djvu
Surface Normal Estimation......Page p0303.djvu
Comparison with Papier\'s Averaging Process......Page p0304.djvu
Experiments......Page p0305.djvu
Second Derivatives Operators......Page p0307.djvu
Experiment......Page p0308.djvu
Conclusion......Page p0309.djvu
Introduction......Page p0311.djvu
Continuous and Discrete Moments of Inertia......Page p0312.djvu
Properties of Roundest Discrete Sets......Page p0313.djvu
Roundest Discrete Sets Are Strongly Convex......Page p0314.djvu
Roundest Discrete Sets Are Discrete Quasi-Discs......Page p0315.djvu
Generation of Roundest Discrete Sets According to Size......Page p0316.djvu
Concluding Remarks......Page p0318.djvu
Introduction......Page p0322.djvu
Digital Plane Recognition Problems......Page p0323.djvu
The Preimage Polyotope......Page p0324.djvu
The Vertices of preimage+(S) and preimage -(S)......Page p0325.djvu
The Vertices of preimage0(S) : Chords and Visibility Cone......Page p0326.djvu
The Faces of the Preimage......Page p0328.djvu
From a Starting Point to a Starting Facet......Page p0329.djvu
Gift-Wrapping on the Chords Set SS......Page p0330.djvu
Complexity Analysis......Page p0331.djvu
Conclusion......Page p0332.djvu
Introduction......Page p0334.djvu
Preimages of a Digital Plane Patch......Page p0335.djvu
Linear LGP Generation by Arithmetic Planes......Page p0336.djvu
Feasible Normal Vectors and Discrete Gaussian Spheres......Page p0338.djvu
Feasible Normal Vectors of Each LGP......Page p0339.djvu
Discrete Gaussian Spheres......Page p0341.djvu
Unified Discrete Gaussian Images......Page p0342.djvu
Algorithm......Page p0343.djvu
Experimental Results......Page p0344.djvu
Conclusion......Page p0345.djvu
Introduction......Page p0346.djvu
Tangential Cover and Tangent Space......Page p0349.djvu
Curvature Computation by Optimization......Page p0350.djvu
Tangential Cover of Noisy Digital Contours......Page p0352.djvu
Experimental Validation......Page p0354.djvu
Conclusion......Page p0356.djvu
Introduction......Page p0358.djvu
Definitions and Notations......Page p0359.djvu
Introduction......Page p0360.djvu
Subgradient Computation......Page p0361.djvu
Studying the Solution Space......Page p0362.djvu
Sketching the Method......Page p0363.djvu
Improving Valid Cuts......Page p0366.djvu
Experimental Results......Page p0367.djvu
Conclusion......Page p0368.djvu
Introduction......Page p0370.djvu
-Thick Segments......Page p0371.djvu
Tangential Cover for Closed Discrete Curves......Page p0372.djvu
Isothetic Thickness Computation......Page p0374.djvu
Convex Hull Maintenance......Page p0375.djvu
Putting All Together......Page p0376.djvu
Thick Digital Curves......Page p0378.djvu
Conclusion......Page p0380.djvu
Introduction......Page p0382.djvu
Principle......Page p0383.djvu
Convergence......Page p0385.djvu
Higher Order Derivatives......Page p0386.djvu
Derivatives Estimation for Parametrized Curves......Page p0387.djvu
Pixel Length Parametrization......Page p0388.djvu
Experimental Results......Page p0389.djvu
Conclusion......Page p0391.djvu
Introduction......Page p0392.djvu
Method......Page p0394.djvu
Results......Page p0398.djvu
Conclusion......Page p0402.djvu
Introduction and Notations......Page p0404.djvu
Principle of the Reduction......Page p0405.djvu
Going Back and Forth from Instance I to Instance I\'......Page p0407.djvu
From a Solution of I to a Solution of I\'......Page p0408.djvu
From a Solution of I Back to a Solution of I\'......Page p0409.djvu
Conclusion......Page p0412.djvu
Introduction......Page p0413.djvu
The Mojette Transform (MT)......Page p0414.djvu
The Finite Radon Transform (FRT)......Page p0415.djvu
Ghosts in the FRT......Page p0416.djvu
The Mojette Ghost-Recovery Algorithm (MGR)......Page p0417.djvu
Results......Page p0420.djvu
Further Work......Page p0421.djvu
Conclusion......Page p0423.djvu
Introduction......Page p0425.djvu
Definitions and Properties......Page p0426.djvu
Reconstructing a hv-Convex Matrix Respecting One Projection hv-Convex(V)......Page p0427.djvu
Reconstructing a Nearly h-Convex Matrix Respecting the Horizontal Projection h-Convex(H,w) ......Page p0428.djvu
Heuristic......Page p0430.djvu
hv-Convex Images......Page p0431.djvu
Conclusion......Page p0433.djvu
Introduction......Page p0435.djvu
Constrained Connectivity Relations......Page p0436.djvu
Alpha,Omega)-Connectivity......Page p0437.djvu
Representative Value......Page p0438.djvu
Partition Filtering......Page p0439.djvu
Filtering Procedures......Page p0440.djvu
Experiments......Page p0441.djvu
Concluding Remarks and Perspectives......Page p0442.djvu
On Watershed Cuts and Thinnings......Page p0446.djvu
Basic Notions for Edge Weighted Graphs......Page p0447.djvu
Extensions and Graph Cuts......Page p0448.djvu
Watersheds......Page p0449.djvu
Minimum Spanning Forests and Watershed Optimality......Page p0450.djvu
Border Thinnings and Watersheds......Page p0451.djvu
Linear-Time Algorithm for Border Cut......Page p0452.djvu
Introduction......Page p0458.djvu
Preliminaries......Page p0459.djvu
Connectivity Measure......Page p0462.djvu
Connected Components......Page p0463.djvu
Tree Representation......Page p0464.djvu
Connected Filters......Page p0466.djvu
Illustrative Example......Page p0467.djvu
Conclusion......Page p0468.djvu
Introduction......Page p0470.djvu
Basic Morphological Directional Transformations......Page p0471.djvu
Line-Segment and Orientation Functions......Page p0472.djvu
Non-parametric Algorithm to Build the Line-Segment and Orientation Functions and the Limits of the Approach......Page p0474.djvu
The Limits of the Approach......Page p0476.djvu
Image Segmentation Using Directional Morphology and the Watershed Transformation......Page p0477.djvu
Conclusion......Page p0480.djvu
Introduction......Page p0482.djvu
Digitizing an Image into Pixels......Page p0483.djvu
Discrete Epipolar Line......Page p0484.djvu
Identifying the Boundaries Using the Fundamental Matrix......Page p0485.djvu
Corresponding Pixels in Two Views and a Third View......Page p0486.djvu
Identifying the Corresponding Region......Page p0487.djvu
Experiments......Page p0489.djvu
Concluding Remarks......Page p0492.djvu
Introduction......Page p0494.djvu
Related Work......Page p0495.djvu
Our Model......Page p0496.djvu
Runoff......Page p0497.djvu
Algorithm......Page p0498.djvu
Equilibrating Flow Calculation......Page p0499.djvu
Transport......Page p0501.djvu
Visual Result of Soil Fragments Transport......Page p0502.djvu
Conclusion and Future Work......Page p0504.djvu
Introduction......Page p0507.djvu
Function Classes......Page p0508.djvu
Shaped Operators......Page p0511.djvu
The Optimal Operator......Page p0512.djvu
Optimal Operator Selection......Page p0513.djvu
How to Select Function Class and Window Size?......Page p0514.djvu
Evaluation......Page p0515.djvu
Computation of the Difference Operator......Page p0516.djvu
Concluding Remarks......Page p0518.djvu
Introduction......Page p0519.djvu
Combinatorial Map......Page p0520.djvu
3D Images and Intervoxel Elements......Page p0521.djvu
Topological Map......Page p0522.djvu
Operation of Segmentation......Page p0523.djvu
Criterion Used in the Segmentation Process......Page p0524.djvu
Algorithm......Page p0525.djvu
Results and Analysis......Page p0527.djvu
Conclusion......Page p0529.djvu
Introduction......Page p0531.djvu
Discrete Geodesic Time......Page p0533.djvu
Adaptive Neighbourhoods......Page p0534.djvu
Similarity Measures and Filtering Kernels......Page p0535.djvu
Application to Multispectral Image Smoothing......Page p0536.djvu
Conclusion......Page p0538.djvu
Introduction......Page p0541.djvu
Related Work......Page p0542.djvu
Weak Surface Measurements......Page p0543.djvu
Improving the Crease Detection......Page p0545.djvu
Weighted Linear Approximation......Page p0547.djvu
Dewarping and Output......Page p0548.djvu
Results......Page p0549.djvu
Conclusion and Further Work......Page p0551.djvu
Introduction......Page p0553.djvu
Requirements for a Segmentation Environment......Page p0555.djvu
The Model......Page p0556.djvu
Updating and Feature Extraction Functions......Page p0559.djvu
An Example of Segmentation Algorithm......Page p0561.djvu
Conclusion......Page p0563.djvu
Author Index......Page p0565.djvu