Diffusion Distance for Histogram
Comparison, CVPR06.
Haibin Ling, Kazunori Okada
Group Meeting
Presented by Wyman
3/14/2006
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Introduction
• This paper proposed:
– A new dissimilarity measure between
histogram-based descriptors called diffusion
distance (SIFT, GLOH, Shape Context, Spin Image)
• It performs better in both accuracy and efficiency
than other distance measures in shape matching
and interest point matching
• It may be useful to other histogram comparison
problems
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Background
• Given one image of an object, how do we find all
of its remaining images in a database?
Difficulties:
• Shapes look
similar, but are
articulated
Solutions:
• Use histogrambased shape
descriptor, such as
Shape context
Articulated shape database
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Background – Shape Context
PAMI 2002
Key idea: Represent an image in terms of descriptors at certain
locations that describe the edges relative to those locations
Shape context of a point is the histogram of the relative
positions of all other points in the image.
Use bins that are uniform in log-polar space to emphasize closeby, local structure.
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Background – Shape Context
• Original method use the chi-square test statistic
to compare two histograms:
Bin-to-bin distances between
histograms/descriptors
Some problems arose due to this distance metric!
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Background – Shape Context
• Problems:
– Sensitive to quantization effects
– Sensitive to distortion problems due to deformation, illumination
change and noise
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Background – Shape Context
• Solutions:
– Use cross-bin distance metric such as the
Earth Mover’s Distance (EMD)
• It allows bins at different locations to be partially
matched
• It solves quantization effect
• Very slow!
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Modeling Histogram Difference with a
Heat Diffusion Process
• First consider 1D distributions h1(x) and h2(x)
• Their difference d(x) = h1(x) - h2(x)
• Bin-by-bin distance can be obtained by putting a metric
(e.g. L2 norm) on d(x), but we do not do so!
• Treat the difference as an initial value (at time t = 0) of an
isolated temperature field T(x,t), i.e.
T(x,0) = d(x)
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Heat Diffusion Equation
As time goes by, d(x) vanishes everywhere!
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The distance
• A distance between the histograms is defined as:
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Example
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Example
• From the result, we see that K are monotonically
increasing with delta, thus K measures the degree of
deformation between two histograms
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Better than EMD
EMD
EMD = minimal amount of work that
needs to be done to transform one
distribution into the other
The same for both differences!
Diffusion Dist.
Smaller distance for d12
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Diffusion distance
• Now consider 2D histograms
Interpretation:
Summing the value in each layer of difference’s pyramid
(with exponentially decreasing size)
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Experiment 1
• Shape Matching with Shape Context
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Experiment 2
• Image Feature Matching
– SIFT and Spin Image are
also histogram-based
descriptors
– SIFT and Spin Image are
originally designed to use
L2 norm as the distance
metric
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Experiment 2
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Experiment 2
• Running time is low!
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Q&A
Thank you!
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