Presentation on theme: "FRACTAL DIMENSION OF BIOFILM IMAGES"— Presentation transcript:
1FRACTAL DIMENSION OF BIOFILM IMAGES Presented by Zhou JiMajor advisor: Dr. Giri Narasimhan
2Outline Introduction Fractal dimension of pixel-based images Biofilm researchFractals and fractal dimensionFractal dimension of pixel-based imagesGeneration of standard images with known fractal dimensionNumerical results and conclusion
31. Introduction What is biofilm? What interests biologist? A thin layer of bacteria.What interests biologist?The structure and how they grow.What does this project want to do?Quantify the pictures of them.
51. Introduction What is fractal? What is fractal dimension? Special geometrical figure that is not whole number-dimensional, like lines, surfaces or solidsWhat is fractal dimension?Measurement of where it is in betweenHow does this project use the concept?Calculate fractal dimension from pixel image
6Properties of fractal Self-similarity Irregularity Fractal dimension In each tiny piece we observe the form of the entire shape.IrregularityThere are no smooth boundary. Length or area cannot be determined.Fractal dimensionIt has not dimension of whole number.
9Calculating fractal dimension From Richardson’s plotLog-log plot of log L vs. log L: length, : intervalFormula: D = 1 - slopeKoch curveGenerationFormula: D = log N/log(1/r)Koch snowflake N=4, r=1/3, D =