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Density Functional
Gradient Estimate
Kernel Function
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The estimation of the gradient of a density function, with applications in pattern recognition
The estimation of the gradient of a density function, with applications in pattern recognition,10.1109/TIT.1975.1055330,IEEE Transactions on Informati
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The estimation of the gradient of a density function, with applications in pattern recognition
(
Citations: 578
)
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KEINOSUKE FUKUNAGA
,
LARRY D. HOSTETLER
Nonparametric
density gradient
estimation using a generalized kernel approach is investigated. Conditions on the kernel functions are derived to guarantee asymptotic unbiasedness, consistency, and
uniform consistency
of the estimates. The results are generalized to obtain a simple mcan-shift estimate that can be extended in ak-nearest-neighbor approach. Applications of gradient estimation to
pattern recognition
are presented using clustering and intrinsic dimensionality problems, with the ultimate goal of providing further understanding of these problems in terms of density gradients.
Journal:
IEEE Transactions on Information Theory - TIT
, vol. 21, no. 1, pp. 32-40, 1975
DOI:
10.1109/TIT.1975.1055330
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Citation Context
(371)
...Mean-shift [
9
, 3, 4] is arguably the best known of the mode-seeking algorithms.,Mean shift, as rst introduced in [
9
] and later formalized in [3], is arguably the best known among the mode-seeking algorithms, and many others have later contributed to theoretical aspects hereof...
Bo Thiesson
,
et al.
Fast Variational Mode-Seeking
...In the now classic paper
6
Fukunaga and Hostetler estimated such density using statistical kernel estimators – presently the main method of nonparametric estimation...
Piotr Kulczycki
,
et al.
The Complete Gradient Clustering Algorithm: properties in practical ap...
...Our non-parametric approach is reminiscent of the well known and understood mean-shift (
Fukunaga and Hostetler 1975
) mode seeking algorithm...
Jason M. Saragih
,
et al.
Deformable Model Fitting by Regularized Landmark Mean-Shift
...While our goal is similar to that of Rother et al., we use the simple approach of Dale et al. [15] that is based on the mean-shift framework [
32
]...
Micah K. Johnson
,
et al.
CG2Real: Improving the Realism of Computer Generated Images Using a La...
...Those planes that do not satisfy this constraint are removed in step 6. In step 7, we cluster the hypothesis planes through mean-shift [
7
] to remove duplicated planes...
Tianfan Xue
,
et al.
Symmetric piecewise planar object reconstruction from a single image
References
(9)
Remarks on Some Nonparametric Estimates of a Density Function
(
Citations: 723
)
Murray Rosenblatt
Journal:
The Annals of Mathematical Statistics
, vol. 27, no. 1956, pp. 832-837, 1956
On Estimation of a Probability Density Function and Mode
(
Citations: 2340
)
Emanuel Parzen
Journal:
The Annals of Mathematical Statistics
, vol. 33, no. 1962, pp. 1065-1076, 1962
Estimation of a multivariate density
(
Citations: 220
)
Theophilos Cacoullos
Journal:
Annals of The Institute of Statistical Mathematics - ANN INST STATIST MATH
, vol. 18, no. 1, pp. 179-189, 1966
On Non-Parametric Estimates of Density Functions and Regression Curves
(
Citations: 107
)
É. A. Nadaraya
Journal:
Theory of Probability and Its Applications - THEOR PROBAB APPL-ENGL TR
, vol. 10, no. 1, 1965
On Strong Consistency of Density Estimates
(
Citations: 43
)
J. Van Ryzin
Journal:
The Annals of Mathematical Statistics
, vol. 40, no. 1969, pp. 1765-1772, 1969
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Citations
(578)
Fast Variational Mode-Seeking
(
Citations: 1
)
Bo Thiesson
,
Jingu Kim
Published in 2012.
The Complete Gradient Clustering Algorithm: properties in practical applications
Piotr Kulczycki
,
Malgorzata Charytanowicz
,
Piotr A. Kowalski
,
Szymon Lukasik
Journal:
Journal of Applied Statistics - J APPL STAT
, vol. ahead-of-p, no. ahead-of-p, pp. 1-14, 2012
Image segmentation from scale and rotation invariant texture features from the double dyadic dual-tree complex wavelet transform
(
Citations: 1
)
Edward H. S. Lo
,
Mark R. Pickering
,
Michael R. Frater
,
John F. Arnold
Journal:
Image and Vision Computing - IVC
, vol. 29, no. 1, pp. 15-28, 2011
Deformable Model Fitting by Regularized Landmark Mean-Shift
(
Citations: 1
)
Jason M. Saragih
,
Simon Lucey
,
Jeffrey F. Cohn
Journal:
International Journal of Computer Vision - IJCV
, vol. 91, no. 2, pp. 200-215, 2011
CG2Real: Improving the Realism of Computer Generated Images Using a Large Collection of Photographs
(
Citations: 1
)
Micah K. Johnson
,
Kevin Dale
,
Shai Avidan
,
Hanspeter Pfister
,
William T. Freeman
,
Wojciech Matusik
Journal:
IEEE Transactions on Visualization and Computer Graphics - TVCG
, vol. 17, no. 9, pp. 1273-1285, 2011