loading...
 This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Scaling Theorems for Zero-Crossings
January 1990 (vol. 12 no. 1)
pp. 46-54
ASCII Text
x 
 
L. Wu, Z. Xie, "Scaling Theorems for Zero-Crossings," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 12, no. 1, pp. 46-54, January, 1990.
 
 
BibTex
x
 
@article{ 10.1109/34.41383,
author = {L. Wu and Z. Xie},
title = {Scaling Theorems for Zero-Crossings},
journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence},
volume = {12},
number = {1},
issn = {0162-8828},
year = {1990},
pages = {46-54},
doi = {http://doi.ieeecomputersociety.org/10.1109/34.41383},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Pattern Analysis and Machine Intelligence
TI - Scaling Theorems for Zero-Crossings
IS - 1
SN - 0162-8828
SP46
EP54
EPD - 46-54
A1 - L. Wu,
A1 - Z. Xie,
PY - 1990
KW - pattern recognition; scaling theorems; zero-crossings; polynomial functions; smoothness conditions; pattern recognition; polynomials
VL - 12
JA - IEEE Transactions on Pattern Analysis and Machine Intelligence
ER -
 

Two scaling theorems are given. Instead of delta functions, polynomial functions are used as input. The advantages are twofold: the smoothness conditions on kernels are not required, so that kernels of the form e/sup -k mod X mod / can be included; the proofs are based on calculus completely and so can be more easily understood.

[1] A. Rosenfeld and M. Thurston, "Edge and curve detection for visual scene analysis,"IEEE Trans. Comput., vol. C-20, pp. 562-569, 1971.
[2] D. Marr,Vision. San Francisco, CA: Freeman, 1982.
[3] D. Marr and E. Hildreth, "Theory of edge detection,"Proc. Roy. Soc. London, vol. B207, pp. 187-217, 1980.
[4] A. P. Witkin, "Scale-space filtering, " inProc. IJCAI-8, 1983.
[5] A. Yuille and T. Poggio, "Scaling theorems for zero crossings,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, no. 1, pp. 15-25, 1986.
[6] J. Babaud, A. P. Witkin, M. Baudin, and R. O. Duda, "Uniqueness of the Gaussian kernel for scale-space filtering,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, pp. 26-33, Jan. 1986.

Index Terms:
pattern recognition; scaling theorems; zero-crossings; polynomial functions; smoothness conditions; pattern recognition; polynomials
Citation:
L. Wu, Z. Xie, "Scaling Theorems for Zero-Crossings," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 12, no. 1, pp. 46-54, Jan. 1990, doi:10.1109/34.41383
Usage of this product signifies your acceptance of the Terms of Use.