calculating fractal dimension from vector images kelly ran
TRANSCRIPT
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Calculating Fractal Dimension from Vector Images
Kelly Ran
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What Is A Fractal?
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Fractal Dimension
• Lines: D=1• Squares: D=2• Fractals: Non-integer D• Calculated using multiple methods• Box-counting dimension
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Fractal Dimension Applications• Texture classification• Protein molecule analysis• Plant growth analysis• Model: plants, particle motion
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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
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SVG
• <?xml version="1.0" standalone="no"?>• <desc>Example rect01 - rectangle with sharp
corners</desc>• <rect x="1" y="1" width="1198" height="398"• fill="none" stroke="blue" stroke-
width="2"/>• </svg>
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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?
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Procedures
• Create SVG files• Inskcape Software
Sierpinski Triangle, 3 iterations
Sierpinski Triangle, 6 iterations
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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
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Testing
• Line, square• Fractals with known fractal dimensions
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To Be Done
• Improve upon program• Gather more data• Implement raster method• Linear regression function: linear algebra least
squares method