6.4.2.1 Piece-Wise Linear Representations from Curves

Wald, A.,
Fitting of Straight Lines if Both Variables are Subject to Error,
AMS(11), 1940, pp. 284-300. BibRef 4000

Madansky, A.,
The Fitting of Straight Lines when Both Variables are Subject to Error,
ASAJ(54), 1959, pp. 173-205. BibRef 5900

Williams, C.M.,
An Efficient Algorithm for the Piecewise Linear Approximation of Planar Curves,
CGIP(8), No. 2, October 1978, pp. 286-293.
WWW Version. BibRef 7810

Williams, C.M.,
Bounded Straight-Line Approximation of Digitized Planar Curves and Lines,
CGIP(16), No. 4, August 1981, pp. 370-381.
WWW Version. BibRef 8108

Cederberg, R.L.T.,
A New Method for Vector Generation,
CGIP(9), No. 2, February 1979, pp. 183-195.
WWW Version. BibRef 7902

Kropatsch, W.G., and Tockner, H.,
Detecting the Straightness of Digital Curves in O(n) Steps,
CVGIP(45), No. 1, January 1989, pp. 1-21.
WWW Version. BibRef 8901
And: Erratum: CVGIP(56), No. 2, September 1992, p. 269.
WWW Version. BibRef

Gritzali, F., Papakonstantinou, G.,
A Fast Piecewise Linear Approximation Algorithm,
SP(5), 1983, pp. 221-227. BibRef 8300

Dhome, M., Rives, G., Richetin, M.,
Sequential Piecewise-Linear Segmentation of Binary Contours,
PRL(2), 1983, pp. 101-107. BibRef 8300

Wu, L.D.,
A Piecewise Linear Approximation Based on a Statistical Model,
PAMI(6), No. 1, January 1984, pp. 41-45. BibRef 8401

Anderson, T.A., Kim, C.E.,
Representation of Digital Line Segments and Their Preimages,
CVGIP(30), No. 3, June 1985, pp. 279-288.
WWW Version. BibRef 8506

Rives, G., Dhome, M., La Preste, J.T., Richetin, M.,
Detection of Patterns in Images from Piecewise Linear Contours,
PRL(3), 1985, pp. 99-104. BibRef 8500

Dobkin, D.P., Levy, S.V.F., Thurston, W.P., Wilks, A.R.,
Contour Tracing by Piecewise Linear Approximations,
TOG(9), No. 4, October 1990, pp. 389-423. BibRef 9010

Dunham, J.G.,
Optimum Uniform Piecewise Linear Approximation of Planar Curves,
PAMI(8), No. 1, January 1986, pp. 67-75. Minimum number of segments within uniform error and fixed end points. References to a lot of other methods. BibRef 8601

Phillips, T.Y., Rosenfeld, A.,
An Isodata Algorithm for Straight Line Fitting,
PRL(7), 1988, pp. 291-297. BibRef 8800

Rosenfeld, A., Sher, A.C.,
Direction-Weighted Line Fitting to Edge Data,
PRL(5), 1987, pp. 289-292. BibRef 8700

Boldt, M., Weiss, R., and Riseman, E.M.,
Token-Based Extraction of Straight Lines,
SMC(19), No. 6, Nov/Dec 1989, pp. 1581-1594. BibRef 8911
Earlier: A1, A2:
Geometric Grouping Applied to Straight Lines,
CVPR86(489-495). Apply hierarchial hueristics to the grouping of events into straight lines. Global structure from local. BibRef

Weiss, R., Hanson, A.R., and Riseman, E.M.,
Geometric Grouping of Straight Lines,
DARPA85(443-449). BibRef 8500

Weiss, I.,
Line Fitting in a Noisy Image,
PAMI(11), No. 3, March 1989, pp. 325-329.
IEEE Abstract. IEEE Top Reference.
WWW Version. BibRef 8903
Earlier:
Straight Line Fitting in a Noisy Image,
CVPR88(647-652).
IEEE Abstract. IEEE Top Reference. BibRef

Netanyahu, N.S., Weiss, I.,
Analytic Outlier Removal in Line Fitting,
ICPR94(B:406-408).
IEEE DOI Link BibRef 9400

Kamgar-Parsi, B.[Behzad], Kamgar-Parsi, B.[Behrooz], Netanyahu, N.S.,
A Nonparametric Method for Fitting a Straight Line to a Noisy Image,
PAMI(11), No. 9, September 1989, pp. 998-1001.
IEEE Abstract. IEEE Top Reference.
WWW Version. BibRef 8909

Venkateswar, V., and Chellappa, R.,
Extraction of Straight Lines in Aerial Images,
PAMI(14), No. 11, November 1992, pp. 1111-1114.
IEEE Abstract. IEEE Top Reference.
WWW Version. Related to the aerial image paper in applications. Turn the edge image into a linked edgel image with local operations. BibRef 9211

Pham, S.,
Digital Straight Segments,
CVGIP(36), No. 1, October 1986, pp. 10-30.
WWW Version. Some theory on where a digital straight segment may really be and what it all means. BibRef 8610

Fahn, C.S., Wang, J.F., and Lee, J.Y.[Jau-Yien],
An Adaptive Reduction Procedure for the Piecewise Linear Approximation of Digitized Curves,
PAMI(11), No. 9, September 1989, pp. 967-973.
IEEE Abstract. IEEE Top Reference.
WWW Version. BibRef 8909

Aoyama, H., and Kawagoe, M.,
A Piecewise Linear Approximation Method Preserving Visual Feature Points of Original Figures,
GMIP(53), No. 5, 1991, pp. 435-446. BibRef 9100

Lindenbaum, M., and Bruckstein, A.M.,
On Recursive, O(N) Partitioning of a Digitized Curve into Digital Straight Segments,
PAMI(15), No. 9, September 1993, pp. 949-953.
IEEE Abstract. IEEE Top Reference.
WWW Version. BibRef 9309

Nelson, R.C.,
Finding Line Segments by Stick Growing,
PAMI(16), No. 5, May 1994, pp. 519-523.
IEEE Abstract. IEEE Top Reference.
WWW Version. BibRef 9405

Strackee, J.,
The Slope of a Straight-Line: A Phony Estimator,
PAMI(18), No. 10, October 1996, pp. 1051-1052.
IEEE Abstract. IEEE Top Reference.
WWW Version. 9611
Addresses part of the Werman-Geyzel paper above. BibRef

Werman, M.,
The Slope of a Straight-Line: A Phony Estimator - Remarks,
PAMI(18), No. 10, October 1996, pp. 1052.
IEEE Abstract. IEEE Top Reference.
WWW Version. 9611
BibRef

Breuel, T.M.,
Finding Lines under Bounded Error,
PR(29), No. 1, January 1996, pp. 167-178.
WWW Version. BibRef 9601

Yin, P.Y.,
Algorithms for Straight Line Fitting Using K-Means,
PRL(19), No. 1, January 1998, pp. 31-41. 9807
BibRef

Pittman, J.[Jennifer], Murthy, C.A.,
Fitting Optimal Piecewise Linear Functions Using Genetic Algorithms,
PAMI(22), No. 7, July 2000, pp. 701-718.
IEEE Abstract. IEEE Top Reference.
WWW Version. 0008
Fitting ordinary data, but would apply to image curves. BibRef

Kégl, B.[Balazs], Krzyzak, A.[Adam], Linder, T.[Tamas], Zeger, K.[Kenneth],
Learning and Design of Principal Curves,
PAMI(22), No. 3, March 2000, pp. 281-297.
IEEE Abstract. IEEE Top Reference.
WWW Version. 0005
Fitting curves to scattered data. With some applications. BibRef

Netanyahu, N.S.[Nathan S.], Weiss, I.[Isaac],
Analytic line fitting in the presence of uniform random noise,
PR(34), No. 3, March 2001, pp. 703-710.
WWW Version. 0101
BibRef

Verbeek, J.J., Vlassis, N., Kröse, B.,
A k-segments algorithm for finding principal curves,
PRL(23), No. 8, June 2002, pp. 1009-1017.
HTML Version. 0204
BibRef

Hu, W.C.[Wu-Chih],
Multiprimitive segmentation based on meaningful breakpoints for fitting digital planar curves with line segments and conic arcs,
IVC(23), No. 9, 1 September 2005, pp. 783-789.
WWW Version. 0508
BibRef

Wang, H.N.[Hao-Nan], Lee, T.C.M.[Thomas C.M.],
Automatic parameter selection for a k-segments algorithm for computing principal curves,
PRL(27), No. 10, 15 July 2006, pp. 1142-1150.
WWW Version. 0606
BibRef
Earlier: A2, A1:
On a K-Segments Algorithm for Computing Principal Curves,
Southwest06(183-187).
IEEE DOI Link 0603
Curvilinear feature extraction; k-segments algorithm; Minimum description length principle; Principal curves; Self-consistency; Unsupervised learning BibRef

Lachaud, J.O.[Jacques-Olivier], Vialard, A.[Anne], de Vieilleville, F.[Francois],
Fast, accurate and convergent tangent estimation on digital contours,
IVC(25), No. 10, 1 October 2007, pp. 1572-1587.
WWW Version. 0709
Multigrid convergence; Digital straight segment; Tangent estimator; Maximal segments BibRef

Nguyen, H.G., Kerautret, B., Desbarats, P., Lachaud, J.O.,
Discrete Contour Extraction from Reference Curvature Function,
ISVC08(II: 1176-1185).
Springer DOI Link 0812
BibRef

de Vieilleville, F.[Francois], Lachaud, J.O.[Jacques-Olivier],
Comparison and improvement of tangent estimators on digital curves,
PR(42), No. 8, August 2009, pp. 1693-1707.
Elsevier DOI Link
WWW Version. 0904
Digital straight segments; Tangent estimator; Adaptive tangent estimator; Multi-grid convergence BibRef

Latecki, L.J.[Longin Jan], Sobel, M.[Marc], Lakaemper, R.[Rolf],
Piecewise Linear Models with Guaranteed Closeness to the Data,
PAMI(31), No. 8, August 2009, pp. 1525-1531.
IEEE DOI Link 0906
No constraints on data order or number of lines. BibRef

Salmon, J.P., Debled-Rennesson, I., Wendling, L.,
A new method to detect arcs and segments from curvature profiles,
ICPR06(III: 387-390).
WWW Version. 0609
See also Linear Algorithm for Segmentation of Digital Curves, A. BibRef

Zhang, H.[Hui], Yong, J.H.[Jun-Hai], Paul, J.C.[Jean-Claude],
Adaptive Geometry Compression Based on 4-Point Interpolatory Subdivision Schemes,
IWICPAS06(425-434).
Springer DOI Link 0608
Compression of curves. BibRef

Asano, T.[Tetsuo], Kawamura, Y.[Yasuyuki], Klette, R.[Reinhard], Obokata, K.[Koji],
Minimum-Length Polygons in Approximation Sausages,
VF01(103 ff.).
HTML Version. 0209
Approximation for digital curves. BibRef

Horst, J., and Beichl, I.,
A Simple Algorithm for Efficient Piecewise Linear Approximation of Space Curves,
ICIP97(II: 744-747).
IEEE DOI Link BibRef 9700

Schmid, G., Robles, L.A.[L. Altamirano], Eckstein, W.,
Automatic segmentation of boundaries in line segments and circular arcs,
CAIP95(556-561).
Springer DOI Link 9509
BibRef

Yan, J.[Jiafeng], Qing, B.C.C.[Ban Cen Cao], Agui, T., Nagao, T.,
The use of complex transform for extraction circular arcs and straight lines in engineering drawings,
ICPR92(III:290-293).
IEEE DOI Link 9208
BibRef

Abdelmalek, N.N.,
Piecewise Linear L(1) Approximation Of Plane Curves,
ICPR84(105-108). BibRef 8400

Chapter on Edge Detection and Analysis, Lines, Segments, Curves, Corners, Hough Transform continues in
Polygonal Representations from Curves .