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Segmentation using vector-attribute filters: methodology andapplication to dermatological imaging
Benoît Naegel1,2, Nicolas Passat3, Nicolas Boch4, Michel Kocher1
1EIG-HES, Geneva School of Engineering, Geneva, Switzerland2LORIA, UMR 7503, Vandœuvre-lès-Nancy, France
3LSIIT, UMR 7005 CNRS/ULP, Strasbourg 1 University, France4Digital Imaging Unit, Department of Radiology, Geneva University Hospital, Switzerland
ISMM’07Rio de Janeiro
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Outline
Purpose
Vector-attribute filters
Application to dermatological imaging
Results
Conclusion
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Outline
Purpose
Vector-attribute filters
Application to dermatological imaging
Results
Conclusion
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Introduction
Purpose of this work
I To retrieve in a grey-level image all “objects” that belong to a specificclass.
Class of objects
Object detection
Image
Filtered image containing only objects of interest
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Introduction
Vector-attribute filters
I Introduced recently (Urbach et al., ISMM’05).I Connected operators allowing to remove in a grey-level image all
“objects” that are similar enough to a given shape.
Motivation of this work
I Demonstrate the efficiency and usefulness of vector-attribute filters forobject detection purpose.
I Vector-attribute filters have been seldom used in real applications.I Design an interactive application devoted to dermatological imaging.
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Introduction
Application
I Retrieve in dermatological digital photographs all moles similar to aspecific set.
Class of moles (learning set)
Mole detection usingvector-attr ibute f i l ter
Vectorial attr ibutes
Input image
Filtered image
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Outline
Purpose
Vector-attribute filters
Application to dermatological imaging
Results
Conclusion
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Grey-level vector attribute filters
Principle
Image peaks are the connectedcomponents of the threshold sets :
Xt(F ) = {p | F (p) ≥ t}
PSfrag replacements
F
p
tPp,t(F )
P↑p,t(F )
V
EV
To each peak, attach a vectorcontaining real-valued attributes :
v = (v1, v2, . . . , vn)
PSfrag replacements
F
p
tPp,t(F )
P↑p,t(F )
V
E
Keep only peaks which satisfy a gi-ven criterion :
T (v) = trueIn order to design non-flat attributes,consider the peak and all the su-perior connected components (thelobe).
PSfrag replacements
F
p
tPp,t(F )
P↑p,t(F )V
E
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Grey-level vector attribute filters
Function decomposition
A function can be decomposed into its peak and lobe components.PSfrag replacements
F
p
tPp,t(F )
P↑p,t(F )
V
EV
Function F .
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Grey-level vector attribute filters
Function decomposition
A function can be decomposed into its peak and lobe components.
PSfrag replacements
F
p
tPp,t(F )
P↑p,t(F )
V
E
Peak function Pp,t(F ) containing p at level t .
Pp,t(F )(x) =
t if x ∈ γp(Xt(F )),⊥ otherwise.
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Grey-level vector attribute filters
Function decomposition
A function can be decomposed into its peak and lobe components.
PSfrag replacements
F
p
tPp,t(F )
P↑p,t(F )V
E
Lobe function P↑p,t(F ) containing p at level t .
P↑p,t(F )(x) =
F (x) if x ∈ γp(Xt(F )),⊥ otherwise.
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Grey-level vector attribute filters
Valuation function
I τ : V E → RN
I Attach a vector of values to a lobe function.I Using lobe functions enables to use non-flat attributes (i.e. height,
volume,...).
Criterion
I T : RN → {true, false}I Accept or reject a vector according to some defined strategy.I Can be defined with respect to some learning set.
Grey-level vector-attribute filter
I φ(F ) =W{Pp,t(F ) | T (τ(P↑
p,t(F ))) = true}
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Grey-level vector attribute filters
Valuation function
I τ : V E → RN
I Attach a vector of values to a lobe function.I Using lobe functions enables to use non-flat attributes (i.e. height,
volume,...).
Criterion
I T : RN → {true, false}I Accept or reject a vector according to some defined strategy.I Can be defined with respect to some learning set.
Grey-level vector-attribute filter
I φ(F ) =W{Pp,t(F ) | T (τ(P↑
p,t(F ))) = true}
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Grey-level vector attribute filters
Valuation function
I τ : V E → RN
I Attach a vector of values to a lobe function.I Using lobe functions enables to use non-flat attributes (i.e. height,
volume,...).
Criterion
I T : RN → {true, false}I Accept or reject a vector according to some defined strategy.I Can be defined with respect to some learning set.
Grey-level vector-attribute filter
I φ(F ) =W{Pp,t(F ) | T (τ(P↑
p,t(F ))) = true}
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Grey-level vector-attribute filters
Vector-attribute filter
Grey-level image
Function F
E
T
E
T
E
T
E
T
E
T
E
T
. . .
Valuation
Valuation
Valuation
Valuation
Valuation
Criterion
Criterion
Criterion
Criterion
Criterion
Filtered image
E
T
Lobe decomposition
Supremum of peak functions
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Grey-level vector-attribute filters
Implementation
Efficient implementation using the image component-tree. Efficientalgorithms :
I Salembier (recursive flooding)I Najman (Tarjan’s union-find))
T
E
T
EOriginal tree Filtered tree using direct decision
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Outline
Purpose
Vector-attribute filters
Application to dermatological imaging
Results
Conclusion
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Application to dermatological imaging
Computer-aided diagnosis for dermatologist
I Total Body Photography.
I Images acquired at different times.I Purpose : early detection of suspicious lesions.
I Detection and cartography ofmoles.
I Moles follow-up in the dif-ferent images.
I Alert associated to eachmole evolution.
I Mole segmentation : first step of a mole mapping application.
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Application to dermatological imagingInteractive segmentation application
DermatologistManual delineationof moles of interest
Learning set
Detection of similarmoles
Input image
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Application to dermatological imagingLearning set construction
Compute the image component-tree.
E
T
For each manually delineated mole : findthe corresponding node in the component-tree.
E
T
Compute the vector-attribute vi
(area, contrast , compacity)
E
Tareacontrastcompacity
Object class defined by :I Mean vector rI Covariance matrix Σ
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Application to dermatological imaging
Mole detection
Compute the component-tree of thesaturation image.
E
T
I Filter the component-tree using valuation function :
τ = (area, contrast , compacity)
I Criterion used :
Tr,ε(v) = dM(r, v) < ε
I dM is the Mahalanobis distance (using the covariance matrix of thelearning set).
I ε is a parameter that can be set in real-time thanks to thecomponent-tree implementation.
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Outline
Purpose
Vector-attribute filters
Application to dermatological imaging
Results
Conclusion
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Results
Manually delineated moles Segmentation result for ε = 3
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Results
Manually delineated moles Segmentation result for ε = 3
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Results
Computation time
I Images size : 4288× 2848 (12 Mp).I Component-tree computation : 8 s.I Detection time : 0.1 s.I Once the tree is computed, ε can be updated in real-time.
Other methods
I For comparison, computation time obtained with template-matchingmethods (grey-level hit-or-miss transform) : 2 mns.
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Outline
Purpose
Vector-attribute filters
Application to dermatological imaging
Results
Conclusion
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Conclusion
Vector-attribute filters
I Enable detection of an object directly in a grey-level image : nobinarization is needed.
I Very efficient due to the component-tree implementation.
Dermatological application
I Design of an interactive application for mole detection and segmentation.I Attribute parameters are retrieved from the learning set.I Allows real-time interaction with the segmentation parameter ε.I Using vector-attribute filters imposes some condition on the result (i.e.,
each flat zone meets a given criterion).
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Conclusion
Future works
I Use more descriptive attributes (geometric or shape attributes).I Use more complex non-flat attributes (texture distribution on a
peak/node),...I Extension to classification tasks involving multiple classes.I Application to other domains (indexation...).
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Properties
Grey-level vector-attribute filters
I Not increasing.I Anti-extensive.I Not idempotent if the peaks instead of the lobes are used for the
reconstruction (as h-reconstruction, volumic filters,...).I Not morphological filters.I Connected-operators (act only by merging flat-zones).
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Dermatological application
Input image
I The filtering is performed on the saturation image.I Use of the saturation image enables to discriminate moles from skin.
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Dermatological application
Attributes
I Area : area of the node.I Contrast (or height) : distance between the node and the leaf.I Compacity :(4π ∗ area)/(perimeter 2).
E
T
Area
Contrast
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Component-tree
Filtering strategy
T
E
T
E
T
E
Original Max decision Min decisionT
E
T
E
Direct decision Subtractive decision