6.4.4 General Systems for Lines and Curves

Chaikin, G.,
An Algorithm For High Speed Curve Generation,
CGIP(3), No. 4, December 1974, pp. 346-349.
WWW Version. BibRef 7412

Riesenfeld, R.F.,
On Chaikin's algorithm,
CGIP(4), No. 3, September 1975, pp. 304-310.
WWW Version. 0501 See also Algorithm For High Speed Curve Generation, An. BibRef

Shlien, S.[Seymour], Allard, P.[Paul],
A FIR filtering approach for the generation of smooth curves on a graphics terminal,
CGIP(17), No. 3, November 1981, pp. 269-280.
WWW Version. 0501 BibRef

Ramer, U., Ballard, D.H.,
Strip Trees: A Hierarchical Representation for Curves,
CACM(24), No. 5, May 1981, pp. 310-321. BibRef 8105
And: Correction: CACM(25), No. 3, March 1982, pp. 213. The strip is a rectangle that contains the curve in the given straight line section. This allows for more efficient intersection and membership tests since strips can be tested first. BibRef

Ballard, D.H.,
Strip Trees: A Hierarchical Representation for Map Features,
PRIP79(278-285). BibRef 7900
And: DARPA79(121-133). BibRef

Stockman, G.C., and Kanal, L.N.,
Problem Reduction Representation for the Linguistic Analysis of Waveforms,
PAMI(5), No. 3, May 1983, pp. 287-298. BibRef 8305

Kanatani, K.,
Errors of the Incremental Method for Curves,
CVGIP(26), No. 1, April 1984, pp. 130-133.
WWW Version. Output of curves. BibRef 8404

Kanatani, K.[Kenichi],
Cramer-Rao Lower Bounds for Curve Fitting,
GMIP(60), No. 2, March 1998, pp. 93-99. BibRef 9803

Hoffman, D.D., and Richards, W.A.,
Parts of Recognition,
Cognition(18), 1985, pp. 65-96. BibRef 8500
And: RCV87(227-242). BibRef
And: MIT AI Memo-732, December 1983. A discussion of how humans partition curves and shapes and a proposal that it will work for object recognition. BibRef

Singh, M., Seyranian, G., and Hoffman, D.D.,
Parsing silhouettes: The short-cut rule,
PandP(61), 1999, pp. 636-660. BibRef 9900

Safaee-Rad, R., Tchoukanov, I., Smith, K.C., Benhabib, B.,
Constraints on Quadratic-Curved Features under Perspective Projection,
IVC(10), No. 8, October 1992, pp. 532-548.
WWW Version. BibRef 9210

Safaee-Rad, R., Tchoukanov, I., Benhabib, B., Smith, K.C.,
Accurate Parameter Estimation of Quadratic Curves from Grey-Level Images,
CVGIP(54), No. 2, September 1991, pp. 259-274.
WWW Version. BibRef 9109

Safaee-Rad, R., Smith, K.C., Banhabib, B.,
Accurate estimation of elliptical shape parameters from a grey-level image,
ICPR90(II: 20-26).
IEEE DOI may work or IEEE-CS DOI may work. 9208 BibRef

Kiryati, N.[Nahum], Bruckstein, A.M.[Alfred M.],
What's in a Set of Points?,
PAMI(14), No. 4, April 1992, pp. 496-500.
IEEE Abstract. IEEE Top Reference.
WWW Version. BibRef 9204
Earlier: Robust90(xx). Fitting a line to a set of points. BibRef

Reumann, K., and Witkam, A.P.,
Optimizing Curve Segmentation in Computer Graphics,
Intl. Computer SymposiumNew York, 1974, pp. 467-472. Early strip fitting system for line segment detection. BibRef 7400

Leung, M.K., and Yang, Y.H.,
Dynamic Strip Algorithm in Curve Fitting,
CVGIP(51), No. 2, August 1990, pp. 146-165.
WWW Version. Fit a strip to the points adjusting the direction to contain the most points. BibRef 9008

Leung, M.K., Yang, Y.H.,
Dynamic Two-Strip Algorithm in Curve Fitting,
PR(23), No. 1-2, 1990, pp. 69-79.
WWW Version. BibRef 9000

Horn, B.K.P., and Weldon, Jr., E.J.,
Filtering Closed Curves,
PAMI(8), No. 5, September 1986, pp. 665-668. BibRef 8609
Earlier: CVPR85(478-484). (MIT) Represent as radius of curvature vs. tangent direction. Derives various processing techniques, adding curves, and smoothing. BibRef

Tsai, W.H.[Wen-Hsiang],
Moment-preserving thresolding: A new approach,
CVGIP(29), No. 3, 1985, pp. 377-393.
WWW Version. 0501 BibRef

Chen, L.H., Tsai, W.H.,
Moment-Preserving Curve Detection,
SMC(18), 1988, pp. 148-158. BibRef 8800

Chen, L.H., Tsai, W.H.,
Moment-Preserving Line Detection,
PR(21), No. 1, 1988, pp. 45-53.
WWW Version. BibRef 8800

Walters, D.,
Selection of Image Primitives for General-Purpose Visual Processing,
CVGIP(37), No. 2, February 1987, pp. 261-298.
WWW Version. BibRef 8702

Walters, D.,
Selection and Use of Image Features for Segmentation of Boundary Images,
CVPR86(319-324). BibRef 8600

Chen, D.S.,
A Data-Driven Intermediate Level Feature Extraction Algorithm,
PAMI(11), No. 7, July 1989, pp. 749-758.
IEEE Abstract. IEEE Top Reference.
WWW Version. Fit curves to edge data without linking, etc. BibRef 8907

Gunther, O., and Wong, E.,
The Arc Tree: An Approximation Scheme to Represent Arbitrary Curved Shapes,
CVGIP(51), No. 3, September 1990, pp. 313-337.
WWW Version. The curve is broken in half at each level of the tree, not at any interest point. BibRef 9009

Wang, L.[Li], Pavlidis, T.[Theo],
Detection of Curved and Straight Segments from Gray-Scale Topography,
CVGIP(58), No. 3, November 1993, pp. 352-365.
WWW Version. BibRef 9311

Liang, P.[Ping], Lee, J.F.[Jeng-Feng], and Wang, Y.F.[Yuan-Fang],
Orientation-based Unique Representation for Planar Curves and Shapes,
VC(8), 1992, pp. 191-199. BibRef 9200

Tsai, D.M., Chen, M.F.,
Curve-Fitting Approach for Tangent Angle and Curvature Measurements,
PR(27), No. 5, May 1994, pp. 699-711.
WWW Version. BibRef 9405

Lam, L.T.S., Lam, W.C.Y., Leung, D.N.K.,
A Knowledge-Based Boundary Convergence Algorithm for Line Detection,
PRL(15), No. 4, April 1994, pp. 383-392. BibRef 9404

Werman, M., Geyzel, Z.,
Fitting a Second Degree Curve in the Presence of Error,
PAMI(17), No. 2, February 1995, pp. 207-211.
IEEE Abstract. IEEE Top Reference.
WWW Version. BibRef 9502

Dori, D., Haralick, R.M.,
A Pattern-Recognition Approach to the Detection of Complex Edges,
PRL(16), No. 5, May 1995, pp. 517-529. BibRef 9505

Nishida, H.,
Curve Description Based on Directional Features and Quasi-Convexity Concavity,
PR(28), No. 7, July 1995, pp. 1045-1051.
WWW Version. BibRef 9507

Viero, T., Jeulin, D.,
Morphological Extraction of Line Networks from Noisy Low-Contrast Images,
JVCIR(6), No. 4, December 1995, pp. 335-347. BibRef 9512

Wu, K.N., Levine, M.D.,
2D Shape Segmentation: A New Approach,
PRL(17), No. 2, February 8 1996, pp. 133-140. Related 3d: See also 3D Part Segmentation: A New Physics-Based Approach. BibRef 9602

Zhu, Q.M.[Qiu-Ming],
Efficient Evaluations of Edge-Connectivity and Width Uniformity,
IVC(14), No. 1, February 1996, pp. 21-34.
WWW Version. 9608 Evaluation, Edges. Edges, Evaluation. Connectivity. Similar to See also Edge Evaluation using Local Edge Coherence. BibRef

Zhu, Q.M., Payne, M., Riordan, V.,
Edge Linking by a Directional Potential Function (DPF),
IVC(14), No. 1, February 1996, pp. 59-70.
WWW Version. 9608 BibRef

Babaguchi, N., Aibara, T.,
Curvedness of a Line Picture,
PR(20), No. 3, 1987, pp. 273-280.
WWW Version. BibRef 8700

Zunic, J.,
A Coding Scheme for Certain Sets of Digital Curves,
PRL(16), 1995, pp. 97-104. BibRef 9500

Hsu, J.C., Hwang, S.Y.,
A Machine Learning Approach for Acquiring Descriptive Classification Rules of Shape Contours,
PR(30), No. 2, February 1997, pp. 245-252.
WWW Version. 9704 BibRef

Kocic, L.M., Milovanovic, G.V.,
Shape-Preserving Approximations by Polynomials and Splines,
CompMathApp(33), No. 11, June 1997, pp. 59-97. 9708 BibRef

Kudo, M.[Mineichi], Toyama, J.[Jun], Shimbo, M.[Masaru],
Multidimensional curve classification using passing-through regions,
PRL(20), No. 11-13, November 1999, pp. 1103-1111. 0001 BibRef

Redding, N.J.[Nicholas J.],
Implicit Polynomials, Orthogonal Distance Regression, and the Closest Point on a Curve,
PAMI(22), No. 2, February 2000, pp. 191-199.
IEEE Abstract. IEEE Top Reference.
WWW Version. 0003Fitting a curve to the data. BibRef

Blane, M.M.[Michael M.], Lei, Z.B.[Zhi-Bin], Civi, H.[Hakan], Cooper, D.B.[David B.],
The 3L Algorithm for Fitting Implicit Polynomial Curves and Surfaces to Data,
PAMI(22), No. 3, March 2000, pp. 298-313.
IEEE Abstract. IEEE Top Reference.
WWW Version. 0005Fit polynomial shape models to data. BibRef

Horng, J.H.[Ji-Hwei], Li, J.T.[Johnny T.],
A dynamic programming approach for fitting digital planar curves with line segments and circular arcs,
PRL(22), No. 2, February 2001, pp. 183-197. 0101 BibRef

Horng, J.H.[Ji-Hwei],
Improving fitting quality of polygonal approximation by using the dynamic programming technique,
PRL(23), No. 14, December 2002, pp. 1657-1673.
HTML Version. 0208 BibRef

Pei, S.C., Horng, J.H.,
Fitting digital Curve Using Circular Arcs,
PR(28), No. 1, January 1995, pp. 107-116.
WWW Version. See also Circular-Arc Detection Based on Hough Transform. BibRef 9501

Pei, S.C., Horng, J.H.,
Optimum Approximation of Digital Planar Curves Using Circular Arcs,
PR(29), No. 3, March 1996, pp. 383-388.
WWW Version. BibRef 9603

Horng, J.H.[Ji-Hwei], Li, J.T.[Johnny T.],
An automatic and efficient dynamic programming algorithm for polygonal approximation of digital curves,
PRL(23), No. 1-3, January 2002, pp. 171-182.
HTML Version. 0201 BibRef

Horng, J.H.[Ji-Hwei],
An adaptive smoothing approach for fitting digital planar curves with line segments and circular arcs,
PRL(24), No. 1-3, January 2003, pp. 565-577.
HTML Version. 0211 BibRef

Streekstra, G.J., van den Boomgaard, R.[Rein], Smeulders, A.W.M.,
Scale Dependency of Image Derivatives for Feature Measurement in Curvilinear Structures,
IJCV(42), No. 3, May-June 2001, pp. 177-189.
WWW Version. 0108 BibRef

Streekstra, G.J., van den Boomgaard, R.[Rein], Smeulders, A.W.M.,
Scale Dependent Differential Geometry for the Measurement of Center Line and Diameter in 3D Curvilinear Structures,
ECCV00(I: 856-870).
WWW Version. 0003 BibRef

Streekstra, G.J., Smeulders, A.W.M., van den Boomgaard, R.,
Tracing of Curvilinear Structures in 3D Images with Single Scale Diameter Measurement,
ScaleSpace99(501-506). BibRef 9900

Geusebroek, J.M.[Jan-Mark], Smeulders, A.W.M.[Arnold W.M.], Geerts, H.[Hugo],
A Minimum Cost Approach for Segmenting Networks of Lines,
IJCV(43), No. 2, July 2001, pp. 99-111.
WWW Version. 0108 BibRef

Tang, Y.Y.[Yuan Y.], Yang, F.[Feng], Liu, J.M.[Ji-Ming],
Basic Processes of Chinese Character Based on Cubic B-Spline Wavelet Transform,
PAMI(23), No. 12, December 2001, pp. 1443-1448.
IEEE Abstract. IEEE Top Reference.
WWW Version. 0112For character compression, type descriptions, etc. Describe contour as b-spline, use wavelet to get control points for different resolutions. BibRef

Huo, X., Chen, J.,
JBEAM: Multiscale Curve Coding via Beamlets,
IP(14), No. 11, November 2005, pp. 1665-1677.
IEEE DOI may work or IEEE-CS DOI may work. 0510 BibRef

Piegl, L.A.[Les A.], Ma, W.Y.[Wei-Yin], Tiller, W.[Wayne],
An alternative method of curve interpolation,
VC(21), No. 1-2, February 2005, pp. 104-117.
WWW Version. 0502 BibRef

Ganguly, P.[Pankaj],
Modified Arc tree based hierarchical representation of digital curve,
PRL(27), No. 6, 15 April 2006, pp. 529-535.
WWW Version. Digital curve; Hierarchical representation; Arc tree; Split points; ISE 0604 BibRef

Guo, F.[Fenghua], Zhang, C.M.[Cai-Ming],
A New Method for Approximating Optimal Parameterization of Polynomial Curves,
ISVC06(II: 98-105).
WWW Version. 0611 BibRef

Toutant, J.L.,
Characterization of the Closest Discrete Approximation of a Line in the 3-Dimensional Space,
ISVC06(I: 618-627).
WWW Version. 0611Line fitting. BibRef

Baloch, S.H., Krim, H., Mio, W., Srivastava, A.,
3D Curve Interpolation and Object Reconstruction,
ICIP05(II: 982-985).
IEEE DOI may work or IEEE-CS DOI may work. 0512 BibRef

Angelopoulou, A.[Anastassia], Psarrou, A.[Alexandra], Rodríguez, J.G.[José García], Revett, K.[Kenneth],
Automatic Landmarking of 2D Medical Shapes Using the Growing Neural Gas Network,
CVBIA05(210-219).
WWW Version. 0601 BibRef

van Ginkel, M.[Michael], Kraaijveld, M.A., van Vliet, L.J.[Lucas J.], Reding, E.P., Verbeek, P.W., Lammers, H.J.,
Robust Curve Detection Using a Radon Transform in Orientation Space,
SCIA03(125-132).
WWW Version. 0310 BibRef

Mokhtari, M., Bergevin, R.,
Generic multi-scale segmentation and curve approximation method,
ScaleSpace01(xx-yy). 0106 BibRef

Shah, J.,
Segmentation of shapes,
ScaleSpace01(xx-yy). 0106 BibRef

Goshtasby, A.,
Multiple-Scale Segmentation and Representation of Solid Plane Shapes,
CVPR86(351-356). Piecewise approximation using splines and different resolutions. BibRef 8600

Sporring, J., and Arps, R.,
Representing Contours as Sequence of One Dimensional Functions,
ACCV00(xx-yy). Minimum Description Length, Moving Frame
Postscript Version. 0001 BibRef

Beyer, G.,
Representation and Wavelet Transformation of Relief-Related Space Curves,
ISPRSGIS99(49-54). BibRef 9900

Mahmoodi, S., Sharif, B.S., and Chester, E.,
Contour Detection Using Multi-Scale Active Shape Models,
ICIP97(II: 708-711).
IEEE DOI may work or IEEE-CS DOI may work. BibRef 9700

Vosselman, G., Haralick, R.M.,
Performance Analysis of Line and Circle Fitting in Digital Images,
PERF96(XX-YY).
HTML Version. BibRef 9600

Ran, X.N.[Xiao-Nong], Farvardin, N.,
On planar curve representation,
ICIP94(I: 676-680).
IEEE DOI may work or IEEE-CS DOI may work. 9411 BibRef

Li, B.C.[Bing-Cheng], Ma, S.D.[Song De],
Moment difference method for the parameter estimation of a quadratic curve,
ICPR94(A:169-173).
IEEE DOI may work or IEEE-CS DOI may work. 9410 BibRef

Deren, D., Marcus, R., Werman, M., and Peleg, S.,
Segmentation by Minimum Length Encoding,
ICPR90(I: 681-683).
IEEE DOI may work or IEEE-CS DOI may work. Line segment generation of curves (or waveforms). BibRef 9000

Saund, E.,
Labeling of Curvilinear Structure Across Scales by Token Grouping,
CVPR92(257-263).
IEEE Abstract. IEEE Top Reference. BibRef 9200

Sheinvald, J., Dom, B., Niblack, W., Banerjee, S.,
Detecting parameterized curve segments using MDL and the Hough transform,
CVPR92(547-552).
IEEE Abstract. IEEE Top Reference. 0403 BibRef

Han, J.H.,
Detection of Convex and Concave Discontinuous Points in a Plane Curve,
ICCV90(71-74).
IEEE DOI may work or IEEE-CS DOI may work. BibRef 9000

O'Gorman, L.,
Curvilinear Feature Detection from Curvature Estimation,
ICPR88(II: 1116-1119).
IEEE DOI may work or IEEE-CS DOI may work. 8811 BibRef
And:
An Analysis of Feature Detectability from Curvature Estimation,
CVPR88(235-240).
IEEE Abstract. IEEE Top Reference. BibRef

Liao, Y.Z.,
A Two-Stage Method of Fitting Conic Arcs and Straight Line Segments to Digitized Contours,
PRIP81(237-239). BibRef 8100

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