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 9 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 2