organizing a spectral image database by using self-organizing maps research seminar 7.10.2005 oili...
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Organizing a spectral image database by using Self-Organizing Maps
Research Seminar 7.10.2005Oili Kohonen
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Motivation?
Image retrieval from conventional databases since 1990's ... many efficient techniques have been developed
However, efficient techniques for querying images from spectral image database does not exist.
Due to the high amount of data in the case of spectral images, the efficient techniques will be needed.
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Spectral imaging?
Metameric imaging: cheap and practical way to achieve a color match.
Spectral imaging: needed to achieve a color match for all observers across the changes in the illumination.
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Principle of SOM:
The Self-Organizing Map (SOM) algorithm:
Is an unsupervised learning algorithm.
Defines mapping from high-dimensional data into lower-dimensional data.
SOM:
Consists of arranged units (or neurons), which are represented by weight vectors.
Units are connected to each other by neighborhood relation.
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Principle of SOM:
SOM Algorithm:
beginInitialize the SOMfor i = 1 : number of epochs
take input vector x randomly from the training data;find the BMU for x;update the weight vectors of the map;decrease the learning rate & neighborhood
function;end;
end;
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Principle of SOM: finding the BMU
Mathematically the BMU is defined for input data vector, x, as follows:
Euclidean distance is a typically used distance measure.
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Principle of SOM: updating the weight vectors
Learning rate: product of learning rate parameter & neighborhood function:
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Principle of SOM: neighborhood function
Neighborhood function
h(t) has to fullfill the following two requirements:
It has to be symmetric about the maximum point (BMU).
It's amplitude has to decrease monotonically with an increasing distance from BMU.
Gaussian function is a typical choice for h(t)
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Principle of SOM: Lattice structure
Lattice structures: hexagonal & rectangular
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Searching Technique: Constructing histogram database
Train SOM
Find BMU for each pixel in an image
Generate BMU-histogram & normalize it by the number of pixels in an image
Repeat steps 2 & 3 for all images in a spectral image database
Save histogram database with the information of SOM-map
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Searching Technique: making a search
Choose an image and generate its histogram.
Calculate the distances between the generated histogram and the existing histogram database.
Order images by these distances.
The results of the search are shown to user as RGB-images
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Searching techniques:
One-dimensional SOM:
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Searching techniques:
Two-dimensional histogram-trained SOM
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Distance Calculations:
H1 & H2 are the compared histograms
L1 & L2 are the indices of max. values|
H3=(H1+H2)/2
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Experiments:
One-dimensional SOM for unweighted images
One-dimensional SOM for images weighted by HVS-function
Two-dimensional SOM
From histogram data
From spectral data
Human Visual Sensitivity-function
(Unweighted images)
(Unweighted and weighted images)
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The Used Database:
106 images: 61 components, spectral range from 400 nm to 700 nm at 5 nm interval.
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Training of the SOMs:
10 000 spectra were selected randomly from each image.
2 000 000 & 4 000 000 epochs in ordering & fine tuning phases, respectively.
Unit sizes: 50 – chosen empirically 49 – to have comparable results with 1D-SOM 14*14 map in the case of histogram-trained SOM
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Results: 1d-SOM, Unweighted images
Pure data Multiplied data
The distance measure: Euclidean distance
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Results: 1D, Unweighted images
Energy
K-L
Peak
DPD
JD
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Results: 1D, Weighted images
Energy
K-L
Peak
DPD
JD
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Conclusions I:
The “structure” of the database is different for weighted and unweighted images.
The “best” results were got by using euclidean distance and Jeffrey divergence.
Importance of normalization?? * Better results with Euclidean distance & DPD * Worse results with Jeffrey divergence
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Results: 2D, Unweighted spectral data
Euclidean
Energy
K-L
Peak
DPD
JD
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Results: 2D, Weighted spectral data
Euclidean
Energy
K-L
Peak
DPD
JD
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Conclusions II:
In the case of two-dimensional SOM better results are achieved by using non-weighted images.
When the weighted images are used, the use of 1D- SOM seems to be more reasonable.
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Results: histogram-trained 2D-SOM
Euclidean
Energy
K-L
Peak
DPD
JD
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Connections between images and histograms:
non-weighted
weighted
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Past, Present & Future:
Past: What you have seen so far...
Present: Texture features in addition to color features
Future: Testing the effect of different metrics in ordering and fine-tuning phases (during the training of SOM)
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Questions:
?Thank you for not asking any... =)
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