1 / 28

Multi-bands Image Analysis with Local Fractal Dimension

This study explores the use of local fractal dimension to analyze multi-bands images and characterize textures. It allows for improved false color segmentations and is not limited to 3 bands.

trishar
Download Presentation

Multi-bands Image Analysis with Local Fractal Dimension

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related