Piece-Wise Linear Representations from Curves

Chapter Contents (Back)
Piecewise Linear. 0103

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.[Charles M.],
An Efficient Algorithm for the Piecewise Linear Approximation of Planar Curves,
CGIP(8), No. 2, October 1978, pp. 286-293.
Elsevier DOI BibRef 7810

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

Cederberg, R.L.T.[Roger L.T.],
A New Method for Vector Generation,
CGIP(9), No. 2, February 1979, pp. 183-195.
Elsevier DOI BibRef 7902

Kropatsch, W.G., Tockner, H.,
Detecting the Straightness of Digital Curves in O(n) Steps,
CVGIP(45), No. 1, January 1989, pp. 1-21.
Elsevier DOI BibRef 8901
And: Erratum: CVGIP(56), No. 2, September 1992, p. 269.
Elsevier DOI 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.[Timothy A.], Kim, C.E.[Chul E.],
Representation of Digital Line Segments and Their Preimages,
CVGIP(30), No. 3, June 1985, pp. 279-288.
Elsevier DOI BibRef 8506

Rives, G., Dhome, M., Lapreste, 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.[Azriel],
An Isodata Algorithm for Straight Line Fitting,
PRL(7), 1988, pp. 291-297. BibRef 8800

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

Boldt, M., Weiss, R., 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., 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 DOI BibRef 8903
Straight Line Fitting in a Noisy Image,

Netanyahu, N.S., Weiss, I.,
Analytic Outlier Removal in Line Fitting,
IEEE DOI 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 DOI BibRef 8909

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

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

Fahn, C.S., Wang, J.F., 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 DOI BibRef 8909

Aoyama, H., 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., 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 DOI BibRef 9309

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

Strackee, J.,
The Slope of a Straight-Line: A Phony Estimator,
PAMI(18), No. 10, October 1996, pp. 1051-1052.
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.

Breuel, T.M.[Thomas M.],
Finding Lines under Bounded Error,
PR(29), No. 1, January 1996, pp. 167-178.
Elsevier DOI BibRef 9601

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

Pittman, J.[Jennifer], Murthy, C.A.,
Fitting Optimal Piecewise Linear Functions Using Genetic Algorithms,
PAMI(22), No. 7, July 2000, pp. 701-718.
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.
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.
Elsevier DOI 0101

Verbeek, J.J., Vlassis, N., Kröse, B.J.A.,
A k-segments algorithm for finding principal curves,
PRL(23), No. 8, June 2002, pp. 1009-1017.
Elsevier DOI 0204
Further analysis:
See also Automatic parameter selection for a k-segments algorithm for computing principal curves. 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.
Elsevier DOI 0508

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.
Elsevier DOI 0606
Earlier: A2, A1:
On a K-Segments Algorithm for Computing Principal Curves,
Curvilinear feature extraction; k-segments algorithm; Minimum description length principle; Principal curves; Self-consistency; Unsupervised learning Extension of:
See also k-segments algorithm for finding principal curves, A. 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.
Elsevier DOI 0709
Multigrid convergence; Digital straight segment; Tangent estimator; Maximal segments BibRef

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

See also Curvature estimation along noisy digital contours by approximate global optimization. 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 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.
No constraints on data order or number of lines. BibRef

Nguyen, T.P.[Thanh Phuong], Debled-Rennesson, I.[Isabelle],
A discrete geometry approach for dominant point detection,
PR(44), No. 1, January 2011, pp. 32-44.
Elsevier DOI 1003
Circularity Measuring in Linear Time,
Fast and robust dominant points detection on digital curves,
Curvature and Torsion Estimators for 3D Curves,
ISVC08(I: 688-699).
Springer DOI 0812
Curvature Estimation in Noisy Curves,
Springer DOI 0708
Dominant point; Corner detection; Polygonal approximation; Discrete line
See also Circular Arc Reconstruction of Digital Contours with Chosen Hausdorff Error.
See also Arc Segmentation in Linear Time. BibRef

Salmon, J.P., Debled-Rennesson, I., Wendling, L.,
A new method to detect arcs and segments from curvature profiles,
ICPR06(III: 387-390).

See also Linear Algorithm for Segmentation of Digital Curves, A. BibRef

Lampert, T.A.[Thomas A.], O'Keefe, S.E.M.[Simon E.M.],
A detailed investigation into low-level feature detection in spectrogram images,
PR(44), No. 9, September 2011, pp. 2076-2092.
Elsevier DOI 1106
Spectrogram; Low-level feature detection; Periodic time series; Remote sensing; Line detection
See also active contour algorithm for spectrogram track detection, An. BibRef

Lampert, T.A.[Thomas A.], Pears, N.E.[Nick E.], O'Keefe, S.E.M.[Simon E. M.],
A Multi-scale Piecewise-Linear Feature Detector for Spectrogram Tracks,

Žunic, J.[Joviša], Rosin, P.L.[Paul L.],
Measuring linearity of open planar curve segments,
IVC(29), No. 12, November 2011, pp. 873-879.
Elsevier DOI 1112
Shape; Curves; Linearity measure; Image processing BibRef

Koutroumbas, K.D.,
Piecewise Linear Curve Approximation Using Graph Theory and Geometrical Concepts,
IP(21), No. 9, September 2012, pp. 3877-3887.

Rosin, P.L.[Paul L.], Pantovic, J.[Jovanka], Žunic, J.[Joviša],
Measuring Linearity of Connected Configurations of a Finite Number of 2D and 3D Curves,
JMIV(53), No. 1, September 2015, pp. 1-11.
WWW Link. 1505
Measuring Linearity of Closed Curves and Connected Compound Curves,
Springer DOI 1304

Rosin, P.L.[Paul L.], Pantovic, J.[Jovanka], Žunic, J.[Joviša],
Measuring linearity of curves in 2D and 3D,
PR(49), No. 1, 2016, pp. 65-78.
Elsevier DOI 1511
Shape BibRef

Kirov, S.[Slav], Slepcev, D.[Dejan],
Multiple Penalized Principal Curves: Analysis and Computation,
JMIV(59), No. 2, October 2017, pp. 234-256.
WWW Link. 1709

Bibi, K.[Khalida], Akram, G.[Ghazala], Rehan, K.[Kashif],
Shape Preserving Properties with Constraints on the Tension Parameter of Binary Three-Point Approximating Subdivision Scheme,
IJIG(20), No. 1 2020, pp. 2050005.
DOI Link 2002

Baudrier, É.[Étienne], Mazo, L.[Loďc],
Curve Digitization Variability,
WWW Link. 1606

Petkovic, T.[Tomislav], Loncaric, S.[Sven],
Using Gradient Orientation to Improve Least Squares Line Fitting,
Computers BibRef

Alkalai, M.[Mohamed], Sorge, V.[Volker],
A Histogram-Based Approach to Mathematical Line Segmentation,
Springer DOI 1311

Sivignon, I.[Isabelle],
Walking in the Farey Fan to Compute the Characteristics of a Discrete Straight Line Subsegment,
Springer DOI 1304

Ma, W.Y.[Wei-Yin], Zhang, R.J.[Ren-Jiang],
Efficient Piecewise Linear Approximation of Bézier Curves with Improved Sharp Error Bound,
Springer DOI 0607

Zhang, H.[Hui], Yong, J.H.[Jun-Hai], Paul, J.C.[Jean-Claude],
Adaptive Geometry Compression Based on 4-Point Interpolatory Subdivision Schemes,
Springer DOI 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.).
Springer DOI 0209
Approximation for digital curves. BibRef

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

Schmid, G., Robles, L.A.[L. Altamirano], Eckstein, W.,
Automatic segmentation of boundaries in line segments and circular arcs,
Springer DOI 9509

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,

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 of Curves .

Last update:Jul 13, 2024 at 15:27:21