LNCS 3024 Transformation Invariant Embedding
for Image Analysis 1st edition by Ali Ghodsi,
Jiaytian Huang, Dale Schuurmans ISBN 3540219811
978-3540219811 pdf download
https://ebookball.com/product/lncs-3024-transformation-invariant-
embedding-for-image-analysis-1st-edition-by-ali-ghodsi-jiaytian-
huang-dale-schuurmans-isbn-3540219811-978-3540219811-14006/
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LNCS 3024 Multiphase Dynamic Labeling for Variational Recognition-
Driven Image Segmentation 1st edition by Daniel Cremers, Nir Sochen,
Christoph Schnorr ISBN 3540219811 978-3540219811
https://ebookball.com/product/lncs-3024-multiphase-dynamic-
labeling-for-variational-recognition-driven-image-
segmentation-1st-edition-by-daniel-cremers-nir-sochen-christoph-
schnorr-isbn-3540219811-978-3540219811-11458/
LNCS 3024 Seamless Image Stitching in the Gradient Domain 1st edition
by Anat Levin, Assaf Zormet, Shrmuel Peleg, Yair Weiss ISBN 3540219811
978-3540219811
https://ebookball.com/product/lncs-3024-seamless-image-stitching-
in-the-gradient-domain-1st-edition-by-anat-levin-assaf-zormet-
shrmuel-peleg-yair-weiss-isbn-3540219811-978-3540219811-13856/
LNCS 3024 Reliable Fiducial Detection in Natural Scenes 1st edition by
David Claus, Andrew Fitzgiblon ISBN 3540219811 978-3540219811
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detection-in-natural-scenes-1st-edition-by-david-claus-andrew-
fitzgiblon-isbn-3540219811-978-3540219811-11374/
LNCS 3024 Tracking People with a Sparse Network of Bearing Sensors 1st
edition by Rahimi, Dunagan, Darrell ISBN 3540219811 978-3540219811
https://ebookball.com/product/lncs-3024-tracking-people-with-a-
sparse-network-of-bearing-sensors-1st-edition-by-rahimi-dunagan-
darrell-isbn-3540219811-978-3540219811-14496/
,LNCS 3024 Morphological Operations on Matrix Valued Images 1st
edition by Bernhard Burgeth, Martin Welk, Christian Feddern, Joachim
Weickert ISBN 3540219811 978-3540219811
https://ebookball.com/product/lncs-3024-morphological-operations-
on-matrix-valued-images-1st-edition-by-bernhard-burgeth-martin-
welk-christian-feddern-joachim-weickert-
isbn-3540219811-978-3540219811-13114/
LNCS 3024 Fusion of Infrared and Visible Images for Face Recognition
1st edition by Aglika Gyaourova George Bebis and Ioannis Pavlidis
ISBN 3540219811 Â 978-3540219811
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visible-images-for-face-recognition-1st-edition-by-aglika-
gyaourova-george-bebis-and-ioannis-pavlidis-
isbn-3540219811-978-3540219811-14236/
LNCS 3024 - Light Field Appearance Manifolds 1st edition by Chris
Mario Chiristoudias, Louis Philippe Morency and Trevor Darrell ISBN
3540219811 Â 978-3540219811
https://ebookball.com/product/lncs-3024-light-field-appearance-
manifolds-1st-edition-by-chris-mario-chiristoudias-louis-
philippe-morency-and-trevor-darrell-
isbn-3540219811-978-3540219811-11920/
LNCS 3024 Stereovision Based Head Tracking Using Color and Ellipse
Fitting in a Particle Filter 1st edition by Bogdan Kwolek ISBN
3540219811 978-3540219811
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tracking-using-color-and-ellipse-fitting-in-a-particle-
filter-1st-edition-by-bogdan-kwolek-
isbn-3540219811-978-3540219811-12932/
LNCS 3024 On the Significance of Real World Conditions for Material
Classification 1st edition by Eric Hayman, Barbara Caputo, Mario
Fritz, Jan Olof Eklundh ISBN 3540219811 978-3540219811
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real-world-conditions-for-material-classification-1st-edition-by-
eric-hayman-barbara-caputo-mario-fritz-jan-olof-eklundh-
isbn-3540219811-978-3540219811-10640/
, Transformation-Invariant Embedding for Image
Analysis
Ali Ghodsi1 , Jiayuan Huang1 , and Dale Schuurmans2
1
School of Computer Science
University of Waterloo
{aghodsib,j9huang}@cs.uwaterloo.ca
2
Department of Computing Science
University of Alberta
Abstract. Dimensionality reduction is an essential aspect of visual pro-
cessing. Traditionally, linear dimensionality reduction techniques such as
principle components analysis have been used to find low dimensional
linear subspaces in visual data. However, sub-manifolds in natural data
are rarely linear, and consequently many recent techniques have been de-
veloped for discovering non-linear manifolds. Prominent among these are
Local Linear Embedding and Isomap. Unfortunately, such techniques cur-
rently use a naive appearance model that judges image similarity based
solely on Euclidean distance. In visual data, Euclidean distances rarely
correspond to a meaningful perceptual difference between nearby images.
In this paper, we attempt to improve the quality of manifold inference
techniques for visual data by modeling local neighborhoods in terms of
natural transformations between images—for example, by allowing im-
age operations that extend simple differences and linear combinations.
We introduce the idea of modeling local tangent spaces of the manifold
in terms of these richer transformations. Given a local tangent space
representation, we then embed data in a lower dimensional coordinate
system while preserving reconstruction weights. This leads to improved
manifold discovery in natural image sets.
1 Introduction
Recently there has been renewed interest in manifold recovery techniques moti-
vated by the development of efficient algorithms for finding non-linear manifolds
in high dimensional data. Isomap [1] and Local Linear Embedding (LLE) [2] are
two approaches that have been particularly influential. Historically, two main
ideas for discovering low dimensional manifolds in high dimensional data have
been to find a mapping from the original space to a lower dimensional space
that: (1) preserves pairwise distances (i.e. multidimensional scaling [3]); or (2)
preserves mutual linear reconstruction ability (i.e. principle components analysis
[4]). In each case, globally optimal solutions are linear manifolds. Interestingly,
the more recent methods for manifold discovery, Isomap and LLE, are based on
T. Pajdla and J. Matas (Eds.): ECCV 2004, LNCS 3024, pp. 519–530, 2004.
c Springer-Verlag Berlin Heidelberg 2004
for Image Analysis 1st edition by Ali Ghodsi,
Jiaytian Huang, Dale Schuurmans ISBN 3540219811
978-3540219811 pdf download
https://ebookball.com/product/lncs-3024-transformation-invariant-
embedding-for-image-analysis-1st-edition-by-ali-ghodsi-jiaytian-
huang-dale-schuurmans-isbn-3540219811-978-3540219811-14006/
Explore and download more ebooks or textbooks
at ebookball.com
, Get Your Digital Files Instantly: PDF, ePub, MOBI and More
Quick Digital Downloads: PDF, ePub, MOBI and Other Formats
LNCS 3024 Multiphase Dynamic Labeling for Variational Recognition-
Driven Image Segmentation 1st edition by Daniel Cremers, Nir Sochen,
Christoph Schnorr ISBN 3540219811 978-3540219811
https://ebookball.com/product/lncs-3024-multiphase-dynamic-
labeling-for-variational-recognition-driven-image-
segmentation-1st-edition-by-daniel-cremers-nir-sochen-christoph-
schnorr-isbn-3540219811-978-3540219811-11458/
LNCS 3024 Seamless Image Stitching in the Gradient Domain 1st edition
by Anat Levin, Assaf Zormet, Shrmuel Peleg, Yair Weiss ISBN 3540219811
978-3540219811
https://ebookball.com/product/lncs-3024-seamless-image-stitching-
in-the-gradient-domain-1st-edition-by-anat-levin-assaf-zormet-
shrmuel-peleg-yair-weiss-isbn-3540219811-978-3540219811-13856/
LNCS 3024 Reliable Fiducial Detection in Natural Scenes 1st edition by
David Claus, Andrew Fitzgiblon ISBN 3540219811 978-3540219811
https://ebookball.com/product/lncs-3024-reliable-fiducial-
detection-in-natural-scenes-1st-edition-by-david-claus-andrew-
fitzgiblon-isbn-3540219811-978-3540219811-11374/
LNCS 3024 Tracking People with a Sparse Network of Bearing Sensors 1st
edition by Rahimi, Dunagan, Darrell ISBN 3540219811 978-3540219811
https://ebookball.com/product/lncs-3024-tracking-people-with-a-
sparse-network-of-bearing-sensors-1st-edition-by-rahimi-dunagan-
darrell-isbn-3540219811-978-3540219811-14496/
,LNCS 3024 Morphological Operations on Matrix Valued Images 1st
edition by Bernhard Burgeth, Martin Welk, Christian Feddern, Joachim
Weickert ISBN 3540219811 978-3540219811
https://ebookball.com/product/lncs-3024-morphological-operations-
on-matrix-valued-images-1st-edition-by-bernhard-burgeth-martin-
welk-christian-feddern-joachim-weickert-
isbn-3540219811-978-3540219811-13114/
LNCS 3024 Fusion of Infrared and Visible Images for Face Recognition
1st edition by Aglika Gyaourova George Bebis and Ioannis Pavlidis
ISBN 3540219811 Â 978-3540219811
https://ebookball.com/product/lncs-3024-fusion-of-infrared-and-
visible-images-for-face-recognition-1st-edition-by-aglika-
gyaourova-george-bebis-and-ioannis-pavlidis-
isbn-3540219811-978-3540219811-14236/
LNCS 3024 - Light Field Appearance Manifolds 1st edition by Chris
Mario Chiristoudias, Louis Philippe Morency and Trevor Darrell ISBN
3540219811 Â 978-3540219811
https://ebookball.com/product/lncs-3024-light-field-appearance-
manifolds-1st-edition-by-chris-mario-chiristoudias-louis-
philippe-morency-and-trevor-darrell-
isbn-3540219811-978-3540219811-11920/
LNCS 3024 Stereovision Based Head Tracking Using Color and Ellipse
Fitting in a Particle Filter 1st edition by Bogdan Kwolek ISBN
3540219811 978-3540219811
https://ebookball.com/product/lncs-3024-stereovision-based-head-
tracking-using-color-and-ellipse-fitting-in-a-particle-
filter-1st-edition-by-bogdan-kwolek-
isbn-3540219811-978-3540219811-12932/
LNCS 3024 On the Significance of Real World Conditions for Material
Classification 1st edition by Eric Hayman, Barbara Caputo, Mario
Fritz, Jan Olof Eklundh ISBN 3540219811 978-3540219811
https://ebookball.com/product/lncs-3024-on-the-significance-of-
real-world-conditions-for-material-classification-1st-edition-by-
eric-hayman-barbara-caputo-mario-fritz-jan-olof-eklundh-
isbn-3540219811-978-3540219811-10640/
, Transformation-Invariant Embedding for Image
Analysis
Ali Ghodsi1 , Jiayuan Huang1 , and Dale Schuurmans2
1
School of Computer Science
University of Waterloo
{aghodsib,j9huang}@cs.uwaterloo.ca
2
Department of Computing Science
University of Alberta
Abstract. Dimensionality reduction is an essential aspect of visual pro-
cessing. Traditionally, linear dimensionality reduction techniques such as
principle components analysis have been used to find low dimensional
linear subspaces in visual data. However, sub-manifolds in natural data
are rarely linear, and consequently many recent techniques have been de-
veloped for discovering non-linear manifolds. Prominent among these are
Local Linear Embedding and Isomap. Unfortunately, such techniques cur-
rently use a naive appearance model that judges image similarity based
solely on Euclidean distance. In visual data, Euclidean distances rarely
correspond to a meaningful perceptual difference between nearby images.
In this paper, we attempt to improve the quality of manifold inference
techniques for visual data by modeling local neighborhoods in terms of
natural transformations between images—for example, by allowing im-
age operations that extend simple differences and linear combinations.
We introduce the idea of modeling local tangent spaces of the manifold
in terms of these richer transformations. Given a local tangent space
representation, we then embed data in a lower dimensional coordinate
system while preserving reconstruction weights. This leads to improved
manifold discovery in natural image sets.
1 Introduction
Recently there has been renewed interest in manifold recovery techniques moti-
vated by the development of efficient algorithms for finding non-linear manifolds
in high dimensional data. Isomap [1] and Local Linear Embedding (LLE) [2] are
two approaches that have been particularly influential. Historically, two main
ideas for discovering low dimensional manifolds in high dimensional data have
been to find a mapping from the original space to a lower dimensional space
that: (1) preserves pairwise distances (i.e. multidimensional scaling [3]); or (2)
preserves mutual linear reconstruction ability (i.e. principle components analysis
[4]). In each case, globally optimal solutions are linear manifolds. Interestingly,
the more recent methods for manifold discovery, Isomap and LLE, are based on
T. Pajdla and J. Matas (Eds.): ECCV 2004, LNCS 3024, pp. 519–530, 2004.
c Springer-Verlag Berlin Heidelberg 2004
