6.1.7 Laplacian, Gaussian Filters for Edges and Zero Crossings

Logan, Jr., B.F.,
Information in the Zero Crossings of Bandpass Signals,
Bell System Tech.(56), No. 4, April 1977, pp. 487-510. BibRef 7704

Marr, D., and Hildreth, E.C.,
Theory of Edge Detection,
RoyalP(B-207), 1980, pp. 187-217. BibRef 8000
And: MIT AI Memo-518, April 1979. Edges, History. The zero crossing Gaussian filter edge detector paper. BibRef

Hildreth, E.C.[Ellen C.],
The Detection of Intensity Changes by Computer and Biological Vision Systems,
CVGIP(22), No. 1, April 1983, pp. 1-27.
WWW Version. The Marr Hildreth operator implementation and some examples. Compared in: See also Some Defects in Finite-Difference Edge Finders. and Compared in: See also Edge Detection and Linear Feature Extraction Using a 2-D Random Field Model. BibRef 8304

Hildreth, E.C.[Ellen C.],
Implementation of a Theory of Edge Detection,
MIT AI-TR-579, April 1980.
WWW Version. BibRef 8004

Hildreth, E.C.[Ellen C.],
Edge Detection,
MIT AI Memo-858, September 1985. BibRef 8509

Alparslan, E.,
Component-Wise Edge Detection by Laplacian Operator Masks,
SP(2), 1980, pp. 179-183. BibRef 8000

Woods, R.E., and Gonzalez, R.C.,
Sampling Considerations for Multilevel Crossing Analysis,
PAMI(4), No. 2, March 1982, pp. 117-123. BibRef 8203

Lunscher, W.H.H.J.[Wolfram H.H.J.], and Beddoes, M.P.[Michael P.],
Optimal Edge Detector Design I: Parameter Selection and Noise Effects,
PAMI(8), No. 2, March 1986, pp. 164-177. BibRef 8603
Optimal Edge Detector Design II: Coefficient Quantization,
PAMI(8), No. 2, March 1986, pp. 178-187. BibRef
And:
Optimal Edge Detector Evaluation,
SMC(16), 1986, pp. 304-312. Repeat of much of the prior discussion of Gaussian edge detection (what kind of optimality is there) with more analysis. A paper study, with synthetic data but does it help? BibRef

Chen, J.S., Huertas, A., and Medioni, G.G.,
Fast Convolution with Laplacian-of-Gaussian Masks,
PAMI(9), No. 4, July 1987, pp. 584-590. BibRef 8707 USC Computer Vision BibRef
Earlier:
Very Fast Convolution with Laplacian-of-Gaussian Masks,
CVPR86(293-298). See also the comments and reply given below (Sotak). Study the properties of the filter and it can be very fast - reduced image size is a major part. BibRef

Chen, J.S.,
Accurate Edge Detection for Multiple Scale Processing,
Ph.D.Thesis (EE), October 1989. BibRef 8910 USC_IRISTR-256. Scale Space. Adaptive Smoothing. Thesis of his edge and adaptive smoothing work. BibRef

Sotak, Jr., G.E., and Boyer, K.L.,
Comments on 'Fast Convolution with Laplacian-of-Gaussian Masks,
PAMI(11), No. 12, December 1989, pp. 1329-1332.
IEEE Abstract. IEEE Top Reference.
WWW Version. BibRef 8912
And:
Authors' Reply,
PAMI(11), No. 12, December 1989, pp. 1332. BibRef

Sotak, Jr., G.E., and Boyer, K.L.,
The Laplacian-of-Gaussian Kernal: A Formal Analysis and Design for Fast Accurate Convolution and Full Frame Operation,
CVGIP(48), No. 2, November 1989, pp. 147-189. BibRef 8911

Haralick, R.M.,
Digital Step Edges from Zero-Crossings of Second Directional Derivatives,
PAMI(6), No. 1, January 1984, pp. 58-68. BibRef 8401
And: RCV87(216-226). BibRef
And: Reply to Comments: PAMI(7), No. 1, January 1985, pp. 127-129. BibRef
Earlier:
Zero-Crossing of Second Directional Derivative Edge Operator,
SPIE(xx), Robot Vision, 1982. Facet Model. The comparison is based on an inaccurate implementation of the See also Theory of Edge Detection. algorithm based on incomplete details in their paper. This paper caused some controversy. A facet model application to edges paper. See also The Facet Model for Descriptions. BibRef

Haralick, R.M.,
The Digital Edge,
PRIP81(285-291). BibRef 8100

Grimson, W.E.L., Hildreth, E.C.,
Comments On 'Digital Step Edges from Zero Crossings of Second Directional Derivatives',
PAMI(7), No. 1, January 1985, pp. 121-127. BibRef 8501

Grimson, W.E.L.,
To have your edge and fill-in too: A commentary,
BBS(6), No. 4, 1983, pp. 666-667. BibRef 8300

van Vliet, L.J., Young, I.T., Beckers, G.L.,
A Nonlinear Laplace Operator As Edge Detector In Noisy Images,
CVGIP(45), No. 2, February 1989, pp. 167-195.
WWW Version. BibRef 8902

Clark, J.J.,
Authenticating Edges Produced by Zero-Crossing Algorithms,
PAMI(11), No. 1, January 1989, pp. 43-57.
IEEE Abstract. IEEE Top Reference.
WWW Version. Analysis of See also Theory of Edge Detection. to improve detection. See correction in next entry. BibRef 8901

Piech, M.A.,
Decomposing the Laplacian,
PAMI(12), No. 8, August 1990, pp. 830-831.
IEEE Abstract. IEEE Top Reference.
WWW Version. Correction to the Clark paper above. BibRef 9008

Chen, M.H., Lee, D., and Pavlidis, T.,
Residual Analysis for Feature Detection,
PAMI(13), No. 1, January 1991, pp. 30-40.
IEEE Abstract. IEEE Top Reference.
WWW Version. BibRef 9101

Basu, M.,
Gaussian Derivative Model For Edge Enhancement,
PR(27), No. 11, November 1994, pp. 1451-1461.
WWW Version. BibRef 9411

Lee, D., Wasilkowski, G.W., Mehrotra, R.,
An Optimal Zero-Crossing-Based Discontinuity Detector,
IP(2), No. 2, 1993, pp. 265-268.
IEEE Top Reference. See also Computational Approach to Zero-Crossing-Based Two-Dimensional Edge-Detection. BibRef 9300

Mehrotra, R., Zhan, S.M.,
Computational Approach to Zero-Crossing-Based Two-Dimensional Edge-Detection,
GMIP(58), No. 1, January 1996, pp. 1-17. See also Zero-Crossing-Based Optimal 3-Dimensional Edge Detector, A. BibRef 9601

Lee, D., Wasilkowski, G.W., Mehrotra, R.,
A New Zero-Crossing-Based Discontinuity Detector,
IP(2), No. 2, April 1993, pp. 265-268.
WWW Version. BibRef 9304

Zhan, S.M., Mehrotra, R.,
A Zero-Crossing-Based Optimal 3-Dimensional Edge Detector,
CVGIP(59), No. 2, March 1994, pp. 242-253.
WWW Version. See also Computational Approach to Zero-Crossing-Based Two-Dimensional Edge-Detection. BibRef 9403

Koplowitz, J., Greco, V.,
On the Edge Location Error for Local Maximum and Zero-Crossing Edge Detectors,
PAMI(16), No. 12, December 1994, pp. 1207-1212.
IEEE Abstract. IEEE Top Reference.
WWW Version. BibRef 9412

Qian, R.J.[Richard J.], and Huang, T.S.[Thomas S.],
Optimal Edge Detection in Images,
AIU96(94-112). BibRef 9600
And:
Optimal Edge-Detection in Two-Dimensional Images,
IP(5), No. 7, July 1996, pp. 1215-1220.
WWW Version. 9607 BibRef
Earlier: ARPA94(II:1581-1588). BibRef
And:
A Two-Dimensional Edge Detection Scheme for General Visual Processing,
ICPR94(A:595-598).
WWW Version. BibRef

Lei, G.,
Level Crossing Curvature and the Laplacian,
IVC(6), No. 3, August 1988, pp. 185-188.
WWW Version. BibRef 8808

Tamura, S., Okamoto, Y., Yanashima, K.,
Zero-Crossing Interval Correction in Tracing Eye-Fundus Blood Vessels,
PR(21), No. 3, 1988, pp. 227-233.
WWW Version. BibRef 8800

Lewis, A.[Aaron], Albeck, Y.[Yehuda], Lange, Z.[Zvi], Benchowski, J.[Julia], and Weizman, G.[Gavril],
Optical Computation with Negative Light Intensity with a Plastic Bacteriorhodopsin Film,
Science(275), No. 5305, 7 March 1997, pp. 1462-1464. An application of optical computing representing nevative values to compute a difference of Gaussian edge detector. BibRef 9703

Kennedy, L.M., Basu, M.,
Gaussian Derivative Operator for Authentic Edge Detection and Accurate Edge Localization,
PRAI(13), No. 3, May 1999, pp. 367. BibRef 9905

Kimmel, R., Bruckstein, A.M.,
Regularized Laplacian Zero Crossings as Optimal Edge Integrators,
IJCV(53), No. 3, July-August 2003, pp. 225-243.
WWW Version. 0304 BibRef

Tabbone, S.A., Alonso, L., Ziou, D.,
Behavior of the Laplacian of Gaussian Extrema,
JMIV(23), No. 1, July 2005, pp. 107-128.
WWW Version. 0505 BibRef

Tabbone, S.A., and Ziou, D.,
Subpixel Positioning of Edges for First and Second Order Operators,
ICPR92(III:655-658).
WWW Version. BibRef 9200

Tabbone, S.A., and Ziou, D.,
On the Behavior of the Laplacian of Gaussian for Junction Models,
2nd Annual Joint Conference on Information SciencesNorth Carolina, 1995. pp. 304-307. Corner Detection BibRef 9500

Tabbone, S.A.[Salvatore A.],
Cooperation between edges and junctions for edge grouping,
ICIP94(I: 954-957).
WWW Version. 9411 BibRef

Tabbone, S.A.,
Detecting Junctions Using Properties of the Laplacian of Gaussian Detector,
ICPR94(A:52-56).
WWW Version. BibRef 9400

Wang, X.[Xin],
Laplacian Operator-Based Edge Detectors,
PAMI(29), No. 5, May 2007, pp. 886-890.
WWW Version. 0704deal with noise sensitivity of Laplacian operators. BibRef

Xu, Z.,
A Further Study on Error Probabilities of Laplacian-Gaussian Edge Detection,
ICPR86(601-603). BibRef 8600

Eklundh, J.O., Elfving, T., Nyberg, S.,
Edge Detection using the Marr-Hildrith Operator with Different Sizes,
ICPR82(1109-1112). BibRef 8200

Chapter on Detection and Analysis of Edges, Lines, Curves, Corners, Hough Transform continues in
Gaussian Filters, General .