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Multi-bands image analysis using local fractal dimension Aura Conci and Eldman O. Nunes IC - UFF

Multi-bands image analysis using local fractal dimension Aura Conci and Eldman O. Nunes IC - UFF. Introduction. Use of fractals and image multiespectral bands to characterize texture. C onsidering inter-relation among bands the image FD є [ 0 , number of bands + 2] .

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Multi-bands image analysis using local fractal dimension Aura Conci and Eldman O. Nunes IC - UFF

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  1. Multi-bands image analysis using local fractal dimensionAura Conci and Eldman O. NunesIC - UFF

  2. Introduction • Use of fractals and image multiespectral bands to characterize texture. • Considering inter-relation among bands the image FDє [ 0 , number of bands + 2] . • Improve the possibilies of usual false color segmentations (assigning satellite bands to RGB color). It is not now limited to 3 band.

  3. Eletromagnetic Spectrum :it is possible to measure waves in a strip that varies in frequency of 1 to 1024 Hz, or lengths with interval of values between 10-10m and 10+10m (micrometers).

  4. The color sensations noticed by humans are combination of the intensities received by 3 types ofcells cones. • Combination of the 3 primary colors produces the others • In the video: R=700 nm, G = 546,1 nm, B=435,1 nm.

  5. Digital images Monocromatic : one color channel or one band. • binary image: each pixel only 0 or 1 values. • intensity level (grey level): each pixel one value from 0 to 255.

  6. Multiband images: n band value for each pixel. • examples: • color images • sattelite images • medical images

  7. color images each pixel 3 values ( from 0 to 255 ) 3 bands: Red - Green -Blue.

  8. Satellite Images

  9. Band 1 Band 2 Band 3 Band 4 Band 5 Band 6 Band 7 example : a LandSat-7 image is a collection of 7 images of same scene

  10. Multiespectral false color : l , m, n Bands to Red, Greenand Blue. Band 4 (R), 5 (G), 3 (B) Band 4 (R), 3 (G), 2 (B)

  11. Textures Texture is characterized by the repetition of a model on an area. Textons : size, format, color and orientation of the elements. Textons can be repeated in an exact way or with small variations on a same theme. Texture 1 Texture 2

  12. FractalGeometry • self similar sets • fractal dimensions and measures used to classify textures

  13. FD for binary image • Box Counting Theorem - 2D images. • For a set A, Nn(A) = number of boxes of side 1/2n which interser the setA: DF = lim n log Nn (A) / log 2n

  14. n Nn (A) 2n log Nn (A) log 2n 1 4 2 1,386 0,693 2 12 4 2,484 1,386 3 36 8 3,583 2,079 4 108 16 4,682 2,772 5 324 32 5,780 3,465 6 972 64 6,879 4,158

  15. gray level images • Box Counting Theorem extension for 3-dimensional object: third coordinate represents the intensity of the pixel. • DF between 2 e 3.

  16. Blanket Dimension - Blanket Covering Method The space is subdivided in cubes of sides SxSxS ’. Nn(A) denotes the number of cubes intercept a blanket covering the image: Nn =  nn (i,j) On each grid (i,j),nn (i,j) = int ( ( max – min ) / s’ ) + 1

  17. for multi-bands image • a color R GB image is a subset of the pentadimensional space : N5). Each pixel is defined by: (x, y, r, g, b) • FD of this images: values from 2 to 5.

  18. Generalizing: d-cube • points (0D), segments (1D), squares (2D), cubes (3D) and • for a n-dimensional : n-cube (nD) • But what is d-cubos , and how many d-cubes appear in a divison of Nd space?

  19. Sweep representation : • n-cube as translational swepps of (n-1) cube

  20. Generalizing: d-Cube Counting - DCC: • the experimental determination of the fractal dimension of images with multiple channels will imply in the recursive division of the N space in d-cubes of size r followed by the contagem of the numbers of d-cubes that intercept the image.

  21. monochrome images: the space N3 is divided by 3-cubos of size 1/2n, and the number of 3-cubos that intercept the image it is counted. • color images: the space N5is divided by 5-cubos of the same size 1/2n, and the number of 5-cubos that intercept the image is counted. • satellite images: the space Nd is divided by d-cubes of size 1/2n and the number of d-cubes that intercept the image is counted.

  22. number of 1-cubes: Nn 1-cubos = 2 1x n, where n is the number of divisions. • number of 2-cubes: Nn 2-cubos = 2 2x n, where n is the number of divisions. • number of 3-cubos: Nn 3-cubos = 2 3x n, where n is the number of divisions. • Generalizing, the number of identical d-cube: Nn d-cubes = 2 d x n, where d is the space dimension and n it is the number of divisions. Then FD of d-dimensional images can be obtained by: DFn = log (Nn,d-cubo) /log (2n )

  23. Results and Conclusions • binary images • gray scale • colored images • satellite images

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