7.2.3.1 Digital Geometry -- Lines, Curves and Contours

Mason, R.M.[Robert M.],
The Digital Approximation of Contours,
JACM(3), No. 4, October 1956, pp. 355-359. BibRef 5610
And: Remarks: JACM(4), No. 4, October 1957, pp. 524-529. BibRef

Brons, R.,
Linguistic Methods for the Description of a Straight Line on a Grid,
CGIP(3), No. 1, March 1974, pp. 48-62.
Elsevier DOI Strings representing straight lines. BibRef 7403

Kim, C.E.[Chul E.],
On Cellular Straight Line Segments,
CGIP(18), No. 4, April 1982, pp. 369-381.
Elsevier DOI Digitize curves consistent with digitizing regions. BibRef 8204

Rosenfeld, A., Kim, C.E.,
How a Digital Computer Can Tell Whether a Line is Straight,
AMM(89), 1982, pp. 230-235. BibRef 8200

Kim, C.E.,
Three-Dimensional Line Segments,
PAMI(5), No. 2, March 1983, pp. 231-234. BibRef 8303

Broder, A., Rosenfeld, A.,
A Note on Collinearity Merit,
PR(13), No. 3, 1981, pp. 237-239. Not on the web site. BibRef 8100

Bongiovanni, G., Luccio, F., Zorat, A.,
The Discrete Equation of the Straight Line,
TC(24), 1975, pp. 310-313. BibRef 7500

Stout, Q.F.,
Drawing Straight Lines with a Pyramid Cellular Automaton,
IPL(15), 1982, pp. 233-237. BibRef 8200

Hung, S.H.Y.,
On the Straightness of Digital Arcs,
PAMI(7), No. 2, March 1985, pp. 203-215. BibRef 8503

Minoh, M., Sakai, T.,
Mesh-Oriented Line Drawings Tehory (MOLD Theory),
PAMI(8), No. 2, March 1986, pp. 210-221. BibRef 8603

Dorst, L., Smeulders, A.W.M.,
Discrete Representation of Straight Lines,
PAMI(6), No. 4, July 1984, pp. 450-463. Different straight lines that when digitized give the same (chain code) representation. BibRef 8407

Dorst, L., Duin, R.P.W.,
Spirograph Theory: A Framework for Calculations on Digitized Straight Lines,
PAMI(6), No. 5, September 1984, pp. 632-639. Effects of closely spaced lines. BibRef 8409

Dorst, L., Smeulders, W.M.,
Best Linear Unbiased Estimators for Properties of Digitized Straight Lines,
PAMI(8), No. 2, March 1986, pp. 276-282. BibRef 8603
And: Correction: PAMI(8), No. 5, September 1986, pp. 676. BibRef

Dorst, L.[Leo], Smeulders, A.W.M.[Arnold W.M.],
Length Estimators for Digitized Contours,
CVGIP(40), No. 3, December 1987, pp. 311-333.
Elsevier DOI How to determine the continuous length from a discrete contour. BibRef 8712

van Lierop, M.L.P., van Overveld, C.W.A.M., and van de Wetering, H.M.M.,
Line Rasterization Algorithms That Satisfy the Subset Line Property,
CVGIP(41), No. 2, February 1988, pp. 210-228.
Elsevier DOI Generate raster line segments BibRef 8802

Berenstein, C.A., Lavine, D.,
On the Number of Digital Straight Line Segments,
PAMI(10), No. 6, November 1988, pp. 880-887.
IEEE DOI BibRef 8811

Maes, M.[Maurice],
Digitization of Straight Line Segments Closeness and Convexity,
CVGIP(52), No. 2, November 1990, pp. 297-305.
Elsevier DOI BibRef 9011

Lindenbaum, M., Koplowitz, J.,
A New Parameterization of Digital Straight Lines,
PAMI(13), No. 8, August 1991, pp. 847-852.
IEEE DOI BibRef 9108

O'Gorman, L.,
Subpixel Precision of Straight-Edged Shapes for Registration And Measurement,
PAMI(18), No. 7, July 1996, pp. 746-751.
IEEE DOI 9608
BibRef

Kishimoto, K.,
Characterizing Digital Convexity and Straightness in Terms of Length and Total Absolute Curvature,
CVIU(63), No. 2, March 1996, pp. 326-333.
DOI Link BibRef 9603

Chattopadhyay, S., Das, P.P.,
Estimation of the Original Length of a Straight Line Segment from Its Digitization in Three Dimensions,
PR(25), No. 8, August 1992, pp. 787-798.
Elsevier DOI Properties of continuous curve vs. digitized contour. BibRef 9208

Imiya, A.,
A Metric For Spatial Lines,
PRL(17), No. 12, October 25 1996, pp. 1265-1269. 9612
BibRef

Hu, Z.Y., Ma, S.D.,
Uniform Line Parameterization,
PRL(17), No. 5, May 1 1996, pp. 503-507. 9606
BibRef

Hu, Z., Ma, S.D.,
The Three Conditions of a Good Line Parameterization,
PRL(16), 1995, pp. 385-388. BibRef 9500

Melter, R.A., Stojmenovic, I., Zunic, J.,
A New Characterization of Digital Lines by Least Square Fits,
PRL(14), 1993, pp. 83-88.
See also Parametrization of Digital Planes by Least-Squares Fits and Generalizations, A. BibRef 9300

Chattopadhyay, S., Das, P.P.,
A New Method of Analysis for Discrete Straight Lines,
PRL(12), 1991, pp. 747-755. BibRef 9100

Amarunnishad, T.M., Das, P.P.,
Estimation of Length for Digitized Straight Lines in Three Dimensions,
PRL(11), 1990, pp. 207-213. BibRef 9000

Beckers, A.L.D., Smeulders, A.W.M.,
The Probability of a Random Straight Line in Two and Three Dimensions,
PRL(11), 1990, pp. 233-240. BibRef 9000

Ronse, C.[Christian],
A Simple Proof of Rosenfeld's Characterization of Digital Straight Line Segments,
PRL(3), 1985, pp. 323-326.
See also Digital Straight Line Segments. BibRef 8500

Inselberg, A.[Alfred], Dimsdale, B.[Bernard],
Multidimensional Lines I: Representation,
SIAM_JAM(54), No. 2, 1994, pp. 559-577. Representation for computations. BibRef 9400

Inselberg, A.[Alfred], Dimsdale, B.[Bernard],
Multidimensional Lines II: Proximity and Applications,
SIAM_JAM(54), No. 2, 1994, pp. 578-596. BibRef 9400

Inselberg, A.[Alfred],
The plane with parallel coordinates,
VC(1), 1985, pp. 69-91.
Springer DOI BibRef 8500

Inselberg, A.[Alfred], Chatterjee, A.[Avijit], Dimsdale, B.[Bernard],
System using parallel coordinates for automated line detection in noisy images,
US_Patent5,631,982, May 20, 1997
WWW Link. BibRef 9705

Kovalevsky, V.A.[Vladimir A.],
A New Concept for Digital Geometry,
MDSG94(37)
See also Axiomatic Digital Topology. BibRef 9400

Kovalevsky, V.A.[Vladimir A.],
New Definition and Fast Recognition of Digital Straight Segments and Arcs,
ICPR90(II: 31-34).
IEEE DOI 9208
BibRef

Marchand-Maillet, S., Sharaiha, Y.M.,
Discrete Convexity, Straightness, and the 16-Neighborhood,
CVIU(66), No. 3, June 1997, pp. 316-329.
DOI Link 9706
BibRef

Congalton, R.G.,
Exploring and Evaluating the Consequences of Vector-to-Raster and Raster-to-Vector Conversion,
PhEngRS(63), No. 4, April 1997, pp. 425-434. 9704
BibRef

Gross, A.D., Latecki, L.J.,
A Realistic Digitization Model of Straight-Lines,
CVIU(67), No. 2, August 1997, pp. 131-142.
DOI Link 9708
BibRef
Earlier:
Modelling Digital Straight Lines,
ICPR96(II: 156-160).
IEEE DOI 9608
(Univ. of Hamburg, D)
See also Digitizations Preserving Topological and Differential Geometric-Properties. BibRef

Gross, A.D.[Ari D.], Latecki, L.J.[Longin J.],
Digitizations Preserving Topological and Differential Geometric-Properties,
CVIU(62), No. 3, November 1995, pp. 370-381.
DOI Link BibRef 9511
Earlier:
Digital Geometric Invariance and Shape Representation,
SCV95(121-126).
IEEE DOI BibRef
Earlier:
Toward Non-Parametric Digital Shape Representation and Recovery,
ORCV94(313-325).
Springer DOI 9412
Graduate Center and Queens College CUNY. U. of Hamburg. Studies the issue of what features are preserved with digitization. What digitizations preserve topological properties.
See also Modelling Digital Straight Lines. BibRef

Latecki, L.J.[Longin J.], Gross, A.D.[Ari D.],
Digitization Constraints That Preserve Topology and Geometry,
SCV95(127-132).
IEEE DOI U. of Hamburg. Graduate Center and Queens College CUNY. Camera constraints to preserve the properties. BibRef 9500

Latecki, L.J., Conrad, C., Gross, A.D.,
Preserving Topology by a Digitization Process,
JMIV(8), No. 2, March 1998, pp. 131-159.
DOI Link 9803
BibRef

Thürmer, G.[Grit],
Closed curves in n-dimensional discrete space,
GM(65), No. 1-3, May 2003, pp. 43-60.
Elsevier DOI 0309
BibRef

Buzer, L.[Lilian],
A linear incremental algorithm for naive and standard digital lines and planes recognition,
GM(65), No. 1-3, May 2003, pp. 61-76.
Elsevier DOI 0309
Incremental.
See also Linear Algorithm for Segmentation of Digital Curves, A. BibRef

Buzer, L.[Lilian],
A simple algorithm for digital line recognition in the general case,
PR(40), No. 6, June 2007, pp. 1675-1684.
Elsevier DOI 0704
BibRef
Earlier:
Digital Line Recognition, Convex Hull, Thickness, a Unified and Logarithmic Technique,
IWCIA06(189-198).
Springer DOI 0606
Digital line; Incremental recognition; Convex hull; Thickness; Implementation
See also Optimal Consensus Set for Digital Line and Plane Fitting. BibRef

Kenmochi, Y.[Yukiko], Buzer, L.[Lilian], Talbot, H.[Hugues],
Efficiently Computing Optimal Consensus of Digital Line Fitting,
ICPR10(1064-1067).
IEEE DOI 1008

See also Optimal Consensus Set for Digital Line and Plane Fitting. BibRef

Mokbel, M.F.[Mohamed F.], Aref, W.G.[Walid G.], Kamel, I.[Ibrahim],
Analysis of Multi-Dimensional Space-Filling Curves,
GeoInfo(7), No. 3, September 2003, pp. 179-209.
DOI Link 0309
BibRef

Cicerone, S.[Serafino], Clementini, E.[Eliseo],
Efficient Estimation of Qualitative Topological Relations based on the Weighted Walkthroughs Model,
GeoInfo(7), No. 3, September 2003, pp. 211-227.
DOI Link 0309
BibRef

Coeurjolly, D.[David], Klette, R.[Reinhard],
A Comparative Evaluation of Length Estimators of Digital Curves,
PAMI(26), No. 2, February 2004, pp. 252-258.
IEEE Abstract. 0402
BibRef
Earlier:
A comparative evaluation of length estimators,
ICPR02(IV: 330-334).
IEEE DOI 0211
Evaluate a number of methods, propose a gradient-based method thatc ombines one method with polygonization method.
See also Linear Algorithm for Segmentation of Digital Curves, A.
See also Discrete Representation of Straight Lines.
See also New Definition and Fast Recognition of Digital Straight Segments and Arcs. (best initial result),
See also Theory of Nonuniformly Digitized Binary Pictures, A.
See also Minimum-Length Polygons in Approximation Sausages.
See also Measurement of the Lengths of Digitized Curved Lines.
See also Distance Transformations in Digital Images. BibRef

Uscka-Wehlou, H.[Hanna],
Run-hierarchical structure of digital lines with irrational slopes in terms of continued fractions and the Gauss map,
PR(42), No. 10, October 2009, pp. 2247-2254.
Elsevier DOI 0906
BibRef
Earlier:
Continued Fractions and Digital Lines with Irrational Slopes,
DGCI08(xx-yy).
Springer DOI 0804
Digital geometry; Digital line; Irrational slope; Continued fraction; Quadratic surd; Gauss map BibRef

Pottmann, H.[Helmut], Wallner, J.[Johannes],
Computational Line Geometry,
Springer2001, ISBN: 978-3-642-04017-7
WWW Link. Buy this book: Computational Line Geometry (Mathematics and Visualization) 1003
BibRef

Chen, N.[Nan],
Influence of conversion on the location of points and lines: The change of location entropy and the probability of a vector point inside the converted grid point,
PandRS(137), 2018, pp. 84-96.
Elsevier DOI 1802
Conversion, Probability theory, Entropy, Grid data model, Vector data model BibRef

Baudrier, É.[Étienne], Mazo, L.[Loïc],
Combinatorics of the Gauss Digitization Under Translation in 2D,
JMIV(61), No. 2, February 2019, pp. 224-236.
Springer DOI 1902
BibRef
Earlier: A2, A1:
Study on the Digitization Dual Combinatorics and Convex Case,
DGCI17(363-374).
Springer DOI 1711
BibRef

Mazo, L.[Loïc], Baudrier, É.[Étienne],
About Multigrid Convergence of Some Length Estimators,
DGCI14(214-225).
Springer DOI 1410
Curve length. BibRef

Chi, G.Y.[Guo-Yi], Loi, K.[Keng_Liang], Lasang, P.[Pongsak],
An Efficient Method to Find a Triangle with the Least Sum of Distances from Its Vertices to the Covered Point,
CVS17(626-639).
Springer DOI 1711
BibRef

Cardoso, J.[João], Miraldo, P.[Pedro], Araujo, H.[Helder],
Plücker correction problem: Analysis and improvements in efficiency,
ICPR16(2795-2800)
IEEE DOI 1705
A given six dimensional vector represents a 3D straight line in Plücker coordinates. Cameras, Linear programming, Matrix decomposition, Optimization, Robot kinematics, Three-dimensional, displays BibRef

Provot, L.[Laurent], Gérard, Y.[Yan],
Estimation of the Derivatives of a Digital Function with a Convergent Bounded Error,
DGCI11(284-295).
Springer DOI 1104
BibRef

Monteil, T.[Thierry],
Freeman Digitization and Tangent Word Based Estimators,
DGCI14(176-189).
Springer DOI 1410
BibRef

Monteil, T.[Thierry],
Another Definition for Digital Tangents,
DGCI11(95-103).
Springer DOI 1104
BibRef

Berthé, V.[Valérie], Labbé, S.[Sébastien],
An Arithmetic and Combinatorial Approach to Three-Dimensional Discrete Lines,
DGCI11(47-58).
Springer DOI 1104
Generating line segments in 3D BibRef

Roussillon, T.[Tristan], Lachaud, J.O.[Jacques-Olivier],
Delaunay Properties of Digital Straight Segments,
DGCI11(308-319).
Springer DOI 1104

See also What Does Digital Straightness Tell about Digital Convexity?. BibRef

Richard, A.[Aurélie], Largeteau-Skapin, G.[Gaëlle], Rodríguez, M.[Marc], Andres, E.[Eric], Fuchs, L.[Laurent], Ouattara, J.S.D.[Jean-Serge Dimitri],
Properties and Applications of the Simplified Generalized Perpendicular Bisector,
DGCI11(296-307).
Springer DOI 1104
BibRef

Said, M.[Mouhammad], Lachaud, J.O.[Jacques-Olivier],
Computing the Characteristics of a SubSegment of a Digital Straight Line in Logarithmic Time,
DGCI11(320-332).
Springer DOI 1104
BibRef

Kumaran, T.,
On Determining Slope and Derivative of Curve Components in a Binary Image,
WSSIP09(1-4).
IEEE DOI 0906
BibRef

Pavlopoulou, C.[Christina], Yu, S.X.[Stella X.],
A Unifying View of Contour Length Bias Correction,
ISVC09(I: 906-913).
Springer DOI 0911
BibRef

Brlek, S.[Srecko], Koskas, M.[Michel], Provençal, X.[Xavier],
A Linear Time and Space Algorithm for Detecting Path Intersection,
DGCI09(397-408).
Springer DOI 0909
BibRef

Daurat, A.[Alain], Tajine, M.[Mohamed], Zouaoui, M.[Mahdi],
Patterns in Discretized Parabolas and Length Estimation,
DGCI09(373-384).
Springer DOI 0909
BibRef

Gatellier, G., Labrouzy, A., Mourrain, B., Técourt, J.P.,
Computing the topology of three-dimensional algebraic curves,
INRIARR-5194, 2004.
HTML Version. BibRef 0400

Beder, C.[Christian],
Fast Statistically Geometric Reasoning About Uncertain Line Segments in 2D- and 3D-Space,
DAGM04(375-382).
Springer DOI 0505
BibRef

Toh, V.[Vivian], Glasbey, C.A.[Chris A.], Gray, A.J.[Alison J.],
A Comparison of Digital Length Estimators for Image Features,
SCIA03(961-968).
Springer DOI 0310
BibRef

Kozera, R.[Ryszard],
Cumulative Chord Piecewise-Quartics for Length and Curve Estimation,
CAIP03(697-705).
Springer DOI 0311
BibRef

Kozera, R.[Ryszard], Noakes, L.[Lyle], Rasinski, M.[Mariusz],
Length Estimation for the Adjusted Exponential Parameterization,
ICCVG12(139-147).
Springer DOI 1210
BibRef

Kozera, R.[Ryszard], Noakes, L.[Lyle], Szmielew, P.[Piotr],
Length Estimation for Exponential Parameterization and epsilon-Uniform Samplings,
PSIVTWS13(33-46).
Springer DOI 1402
BibRef

Kozera, R.[Ryszard], Noakes, L.[Lyle], Klette, R.[Reinhard],
External versus Internal Parameterizations for Lengths of Curves with Nonuniform Samplings,
WTRCV02(413-427). 0204
BibRef
Earlier: A2, A1, A3:
Length Estimation for Curves with Non-Uniform Sampling,
CAIP01(518 ff.).
Springer DOI 0210
BibRef

August, J.[Jonas], Zucker, S.W.[Steven W.],
A Markov Process Using Curvature for Filtering Curve Images,
EMMCVPR01(497-512).
Springer DOI 0205
BibRef

Povazan, I.[Ivo],
The Structure of Digital Straight Line Segments and Euclid's Algorithm,
TR1998.
WWW Link. A definition of Digital Straight Line Segments (DSLS) without using the equation of the Euclidean straight line (y=kx + q). BibRef 9800

Hu, Z., Destine, J.,
Performance Comparison of Line Parametrizations,
ICPR92(III:335-338).
IEEE DOI BibRef 9200

Lindenbaum, M., Koplowitz, J., Bruckstein, A.M.,
On the Number of Digital Straight Lines on an NxN Grid,
CVPR88(610-615).
IEEE DOI BibRef 8800

Roberts, K.S.,
A new representation for a line,
CVPR88(635-640).
IEEE DOI 0403
BibRef

Chapter on 2-D Feature Analysis, Extraction and Representations, Shape, Skeletons, Texture continues in
Triangular, Hexagonal Grids, Geometry, Computations .