*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 Link. 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 Link.
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_IRIS*TR-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 DOI
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.

WWW Link.
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 Link.
BibRef
**8902**

*Clark, J.J.*,

**Authenticating Edges Produced by Zero-Crossing Algorithms**,

*PAMI(11)*, No. 1, January 1989, pp. 43-57.

IEEE DOI 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 DOI 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 DOI
BibRef
**9101**

*Basu, M.*,

**Gaussian Derivative Model For Edge Enhancement**,

*PR(27)*, No. 11, November 1994, pp. 1451-1461.

WWW Link.
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.

IEEE DOI
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 Link.
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 DOI
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.

IEEE DOI
**9607**

BibRef

Earlier:
*ARPA94*(II:1581-1588).
BibRef

And:

**A Two-Dimensional Edge Detection Scheme for General Visual Processing**,

*ICPR94*(A:595-598).

IEEE DOI
BibRef

*Lei, G.*,

**Level Crossing Curvature and the Laplacian**,

*IVC(6)*, No. 3, August 1988, pp. 185-188.

WWW Link.
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 Link.
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**

*Hashimoto, M.[Manabu]*,
*Sumi, K.[Kazuhiko]*,

**Image processing device for processing grey level images**,

*US_Patent*5,625,717, Apr 29, 1997

WWW Link.
BibRef
**9704**

*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.

DOI Link
**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.

Springer DOI
**0505**

BibRef

*Tabbone, S.A.*, and
*Ziou, D.*,

**Subpixel Positioning of Edges for First and Second Order Operators**,

*ICPR92*(III:655-658).

IEEE DOI
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 Sciences*North 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).

IEEE DOI
**9411**

BibRef

*Tabbone, S.A.*,

**Detecting Junctions Using Properties of the
Laplacian of Gaussian Detector**,

*ICPR94*(A:52-56).

IEEE DOI
BibRef
**9400**

*Wang, X.[Xin]*,

**Laplacian Operator-Based Edge Detectors**,

*PAMI(29)*, No. 5, May 2007, pp. 886-890.

IEEE DOI
**0704**

deal with noise sensitivity of Laplacian operators.
BibRef

*Li, S.G.[Shi-Gang]*,
*Funaki, H.[Hiroya]*,

**Discrete Spherical Laplacian Operator**,

*IEICE(E99-D)*, No. 6, June 2016, pp. 1716-1719.

WWW Link.
**1606**

BibRef

IEEE DOI

BibRef

*Pap, L.[Laurence]*,
*Zou, J.J.[Ju Jia]*,

**Sub-pixel edge detection for photogrammetry using Laplace difference of
Gaussian and 4th order ENO interpolation**,

*ICIP10*(2841-2844).

IEEE DOI
**1009**

BibRef

*van Vliet, L.J.[Lucas J.]*,
*Young, I.[Ian]*,
*Verbeek, P.W.[Piet W.]*,

**Recursive Gaussian Derivative Filters**,

*ICPR98*(Vol I: 509-514).

IEEE DOI
**9808**

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 Edge Detection and Analysis, Lines, Segments, Curves, Corners, Hough Transform continues in

Gaussian Filters, General .

Last update:Sep 18, 2017 at 11:34:11