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Calculating Fractal Dimension from Vector Images

Calculating Fractal Dimension from Vector Images. Kelly Ran. What Is A Fractal?. Fractal Dimension. Lines: D=1 Squares: D=2 Fractals: Non-integer D Calculated using multiple methods Box-counting dimension. Fractal Dimension Applications. Texture classification Protein molecule analysis

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Calculating Fractal Dimension from Vector Images

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  1. Calculating Fractal Dimension from Vector Images Kelly Ran

  2. What Is A Fractal?

  3. Fractal Dimension • Lines: D=1 • Squares: D=2 • Fractals: Non-integer D • Calculated using multiple methods • Box-counting dimension

  4. Fractal Dimension Applications • Texture classification • Protein molecule analysis • Plant growth analysis • Model: plants, particle motion

  5. Vector Graphics • Raster graphics: pixel-by-pixel • Research applications calculate D from raster graphics • Vector graphics: Objects like paths and shapes • Scalable Vector Graphics (SVG) based on XML • Paths

  6. Goals • Is it possible to calculate fractal dimension from vector images? • Goals: • Calculate D from SVG images • Show calculations on a display screen • Compare raster v. vector • Time? Accuracy?

  7. Procedures • Create SVG files • Inskcape Software Sierpinski Triangle, 3 iterations Sierpinski Triangle, 6 iterations

  8. Procedures • Processing language • Import SVG • Array of objects • D calculation: size N of grid, number s of grids • Hash table: N is key, s is value

  9. Testing • Line, square • Fractals with known fractal dimensions

  10. 3rd quarter development • Inkscape SVGs • Processing code

  11. To Be Done • Improve upon program • Gather more data • Implement raster method

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