*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 Link.
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 Link.
BibRef
**8108**

*Cederberg, R.L.T.*,

**A New Method for Vector Generation**,

*CGIP(9)*, No. 2, February 1979, pp. 183-195.

WWW Link.
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 Link.
BibRef
**8901**

And:
Erratum:
*CVGIP(56)*, No. 2, September 1992, p. 269.

WWW Link.
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 Link.
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.*,

**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 DOI
BibRef
**8903**

Earlier:

**Straight Line Fitting in a Noisy Image**,

*CVPR88*(647-652).

IEEE DOI
BibRef

*Netanyahu, N.S.*,
*Weiss, I.*,

**Analytic Outlier Removal in Line Fitting**,

*ICPR94*(B:406-408).

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.*, and
*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.*,

**Digital Straight Segments**,

*CVGIP(36)*, No. 1, October 1986, pp. 10-30.

WWW Link. 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 DOI
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 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.

IEEE DOI
**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 DOI
**9611**

BibRef

*Breuel, T.M.*,

**Finding Lines under Bounded Error**,

*PR(29)*, No. 1, January 1996, pp. 167-178.

WWW Link.
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 DOI
**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 DOI
**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 Link.
**0101**

BibRef

*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**

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 Link.
**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 Link.
**0606**

BibRef

Earlier: A2, A1:

**On a K-Segments Algorithm for Computing Principal Curves**,

*Southwest06*(183-187).

IEEE DOI
**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 Link.
**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.

IEEE DOI
**0906**

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**

BibRef

Earlier:

**Circularity Measuring in Linear Time**,

*ICPR10*(2098-2101).

IEEE DOI
**1008**

BibRef

Earlier:

**Fast and robust dominant points detection on digital curves**,

*ICIP09*(953-956).

IEEE DOI
**0911**

BibRef

Earlier:

**Curvature and Torsion Estimators for 3D Curves**,

*ISVC08*(I: 688-699).

Springer DOI
**0812**

BibRef

Earlier:

**Curvature Estimation in Noisy Curves**,

*CAIP07*(474-481).

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).

IEEE DOI
**0609**

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**,

*AVSBS09*(330-335).

IEEE DOI
**0909**

BibRef

*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.

IEEE DOI
**1208**

BibRef

*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**

BibRef

Earlier:

**Measuring Linearity of Closed Curves and Connected Compound Curves**,

*ACCV12*(III:310-321).

Springer DOI
**1304**

BibRef

*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**

BibRef

WWW Link.

BibRef

*Petkovic, T.[Tomislav]*,
*Loncaric, S.[Sven]*,

**Using Gradient Orientation to Improve Least Squares Line Fitting**,

*CRV14*(226-231)

IEEE DOI
**1406**

Computers
BibRef

*Alkalai, M.[Mohamed]*,
*Sorge, V.[Volker]*,

**A Histogram-Based Approach to Mathematical Line Segmentation**,

*CIARP13*(I:447-455).

Springer DOI
**1311**

BibRef

*Sivignon, I.[Isabelle]*,

**Walking in the Farey Fan to Compute the Characteristics of a Discrete
Straight Line Subsegment**,

*DGCI13*(23-34).

Springer DOI
**1304**

BibRef

*Ma, W.Y.[Wei-Yin]*,
*Zhang, R.J.[Ren-Jiang]*,

**Efficient Piecewise Linear Approximation of Bézier Curves with Improved
Sharp Error Bound**,

*GMP06*(157-174).

Springer DOI
**0607**

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
**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.*, and
*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**,

*CAIP95*(556-561).

Springer DOI
**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
**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 of Curves .

Last update:Nov 18, 2017 at 20:56:18