Presentation is loading. Please wait.

Presentation is loading. Please wait.


Similar presentations

Presentation on theme: "FRACTAL DIMENSION OF BIOFILM IMAGES"— Presentation transcript:

Presented by Zhou Ji Major advisor: Dr. Giri Narasimhan

2 Outline Introduction Fractal dimension of pixel-based images
Biofilm research Fractals and fractal dimension Fractal dimension of pixel-based images Generation of standard images with known fractal dimension Numerical results and conclusion

3 1. 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.


5 1. Introduction What is fractal? What is fractal dimension?
Special geometrical figure that is not whole number-dimensional, like lines, surfaces or solids What is fractal dimension? Measurement of where it is in between How does this project use the concept? Calculate fractal dimension from pixel image

6 Properties of fractal Self-similarity Irregularity Fractal dimension
In each tiny piece we observe the form of the entire shape. Irregularity There are no smooth boundary. Length or area cannot be determined. Fractal dimension It has not dimension of whole number.

7 Julia Set

8 Richardson’s plot

9 Calculating fractal dimension
From Richardson’s plot Log-log plot of log L vs. log  L: length,  : interval Formula: D = 1 - slope Koch curve Generation Formula: D = log N/log(1/r) Koch snowflake N=4, r=1/3, D =

10 Generation of Koch snowflake

11 2. Fractal dimension of pixel-based images
What is special? Detection of objects. Lower limit of scale - pixel. Boundary described with pixels - width. BIP (by Qichang Li et al) Preprocessing Algorithms

12 binarize

13 Small objects deleted

14 Small holes filled

15 Boundaries found

16 Dilation method Log-log plot: area ~ dilation count D = 2 - slope

17 EMD(Euclidean Distance Map) method
Log-log plot: area ~ threshold level D = 2 - slope

18 Mass radius method Log-log plot: average area in a circle~ radius
D = slope

19 3. Generating standard images
Purpose Test and validate algorithms or their implementations like BIP Features Known fractal dimension Diverse appearance Based on Koch curve

20 3. Generating standard images
Snowflake/Random curves Single shape/Group quadratic Koch island

21 D= , n=3

22 D= , n=5

23 Random curve, D= , n=3

24 Group of single snowflake, D=1.26816, n=4

25 Group of random curves, D=1.26816, n=4

26 D= , n=3

27 D= , n=3

28 Quadratic Koch Island, D=1.5

29 4. Results Biofilm images Standard images – discussion of algorithm

30 Result of biofilm images







37 Summary Powerful tools (BIP & KochGen) developed
Comparison of Algorithms More correlations of fractal dimension in biofilm images are still to be found.

38 Demonstration KochGen BIP Biofilm3 Julia

39 Thank you! Questions?

40 1. Fractals and Fractal Dimension
What is in common in these three pictures? Fractal fern Sierpinski’s triangle Koch snowflake

41 Types of fractals Iteration function system (random)
Iteration function system (deterministic) L-system Julia set Mandelbrot set Heron Map

42 Application of fractals
Simulation and model Kidney, skeletal structure, nervous system landscape, plant Stock market, internet traffic Music Image compression Others Biofilm research



45 Original image fractal compressed


Similar presentations

Ads by Google