Document 6520178

Context
Fractal Dimension and Lacunarity
of Psoriatic Lesions
„
– Application – measurement of the
efficiency of cosmetic and dermatological
treatment
– A Colour Approach –
„
M. Ivanovici, N. Richard, H. Decean
Skin analysis and characterization
New fractal analysis tools for colour
images
EHB 2009
Why Fractal Analysis?
„
Mihai Ivanovici
2
Fractals and Human Skin
Fractals are everywhere in nature
„
Skin – fractal pattern
(colour and texture)
– Thin ditches that intersect
– Characteristic rhomboidal
network
– Pores and hair of different
size, thickness and density
50x
EHB 2009
Mihai Ivanovici
3
Fractal dimension (FD)
„
„
Mihai Ivanovici
4
Lacunarity (Л)
Captures the complexity of a fractal object
Shows how much space is occupied by the
fractal
1D Random Fractals
EHB 2009
„
„
„
2D Random Fractals
A massmass-distribution function
Shows how the space is occupied
Discriminates between objects with the
same fractal dimension
Stochastic fractals with the
same fractal dimension, but
with different lacunarity
FD = 1.05
EHB 2009
FD = 1.45
FD = 2.1
Mihai Ivanovici
FD = 2.5
5
EHB 2009
Mihai Ivanovici
6
1
The Box-Counting FD
„
„
Our Approach
For different boxbox-sizes (δ
(δ), count how many
boxes (N(δ
(N(δ)) are needed to cover the object
FD = the slope of the regression line through
the points <log(δ
<log(δ),),-log(N
log(N(δ))>
))>
δ1 = 3
N(δ1) = 48
δ2 = 5
N(δ2) = 19
EHB 2009
δ1 = 3
δ2 Mihai
= 5Ivanovici
δ3 = 7
δ3 = 7
N(δ3) = 8
7
Experimental Results
„
„
„
A colour extension of the Voss
probabilistic (box(box-counting like) approach
We consider the colour image a 5D object
(pixel’
(pixel’s spatial coordinates + colour)
colour)
We use hyperhyper-cubes (5D boxes) in the
(x,y,R,G,B)
x,y,R,G,B) space
EHB 2009
Mihai Ivanovici
8
Experimental Results
„
a
FD = 3.16
c
FD = 3.64
e
FD = 3.88
b
FD = 3.33
d
FD = 3.78
f
FD = 3.99
„
(b) more lacunar
than (a)
(d) >>> (c)
„ (e) >>> (f) !!!
Largest zoom factor
EHB 2009
Mihai Ivanovici
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EHB 2009
Mihai Ivanovici
10
Conclusions
„
Fractal dimension and lacunarity
– appropriate to characterize skin (lesions)
– capable to reflect the relative degree of
severity of the psoriatic lesions
„
Lacunarity – inversed behaviour
(interpretation) for images with the
largest zoom factor
EHB 2009
Mihai Ivanovici
11
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