1. VOLUMETRIC SEGMENTATION USING GENETIC ALGORITHM
“Genetic Algorithms are good at taking large, potentially huge search spaces and navigating them, looking for optimal combinations of things, solutions you might not otherwise find in a lifetime.”
-DAVID PRABAHARJ
RAVI SANKAR.R
SARAVANAN.M

2. ABSTRACT
To improve its performance (Speed, Stability), a genetic algorithm-based active model method is proposed and applied to segment the lateral ventricles from magnetic resonance

3. PROCESS Input. (Brain image) Segmentation. Tumor classification.
Tumor surface coordination.
Back projection.
Optimization.
Getting the output

4. Image segmentation
The process of segmenting image into meaningful groups of connected
pixels is called segmentation
􀁑 The difficulty in representing the word “meaningful” in low level image
feature space makes segmentation one of the hardest computer vision
Problems
􀁑 An example

5. Approaches to segmentation
Edge detection
‘Biological systems are sensitive to color and
texture edges
‘ Detect and identify collections of edges that
“outline” an object or are likely to be part of
the outline of a single object
Region detection
‘ Identify (possibly multiple) partitions of the
image into uniform regions

6. Image segmentation by clustering pixels
Grouping together pixels that have similar properties such as color,
texture, motion, etc
Each pixels can be treated as a data point in the feature space
Some clustering algorithms:
Divisive clustering – the entire dataset is considered as a cluster, and then
clusters are recursively split to yield good clustering
Agglomerative clustering – each data point is considered as a
cluster, then clusters are recursively merged to yield good clustering
K-means clustering
Grouping the dataset into K clusters that minimize some objective
function

7. Hierarchical segmentation
Original image segmented image

8. Active contour model-snake

9. THE WAVELET BASED ACTIVE CONTOUR MODEL

10. THE WAVELET BASED ACTIVE CONTOUR MODEL

11. THE WAVELET BASED ACTIVE CONTOUR MODEL

12. Snake movement

13. Snake movement

14. Snake movement

15. Snake movement

16. Snake movement

17. Snake movement

18. Snake movement

19. Snake movement

20. Snake movement

21. Snake movement
Active contour model

22. Applications of Snakes
2D Image Segmentation: Medical Imaging Segmentation
3D Image Segmentation: Volume Image segmentation. Either segment 2d images and then using active contour models and then connect them. Or 3D snakes are used for extracting 3D objects.
Matching: Consist of two different tasks Labeling and Registration. Labeling is the matching process between regions in the image and a-priori models. Registration is the matching process between two volumes in different 3D images.
Stereo.
Motion, Tracking: 3D deformable models have been used for measuring the dynamic behavior of the heart.

23. Problem Formulation Optimization Framework
Energy function (Objective):
Internal Energy:
Tension
Stiffness or rigidity
: Weight that controls snake’s tension
: Weight that controls snake’s stifness

24. Problem Formulation Internal Energy:
Where the gradient of an image is defined as:

25. Problem Formulation Optimization Criterion:
Euler Langrage equation continuous case:
Where the vector u is:

26. Problem Formulation Optimization Criterion:
Euler Langrage equation continuous case:
Where the vector u is:

27. Problem Formulation Discretization:
Euler Langrage equation discrete case:

28. Problem Formulation X coordinate of each snake pixels i:
Y coordinate of each snake pixels i:

29. Problem Formulation In a Matrix form: Where: Gradient Method:
Optimization Scheme:

30. Calculus of Variations
min
Taylor Series Expansion:

31. Calculus of Variations

32. Calculus of Variation
Since
and

33. Calculus of Variation
Since we know that:

34. Calculus of Variation
Euler Langrage equation continuous case:

35. Segmentation
The snake will try to align itself with lightest or darkest nearby contours:
The snake will be attracted to contours with large image gradients
Minimization of snake by scale blurring continuation
1. When snake is far away from a contour increase blurring.
2. When snake is close to the contour we reduce blurring.

36. Termination functional

38. Conclusions
The minimization of the energy function is too sensitive to the initial seed of the snake. This means that if the initial radius of the snake is small then boundary of the object will not be efficiently captured.
The importance weights of the internal and external forces, in the energy objective function affect snake performance. There is a fine tuning process that is required such that the results to be acceptable.
The number of pixels that snake contains plays a critical role in the minimization process. If the number of pixels is small the snake will
not be able to capture the boundaries of the regions of our interest.

39. Back projection
After getting the active contour model getting the Z-coordination using FFT algorithm.
Then finding the depth of the Z coordination using back projection technique.

40. VOLUMETRIC REPRESENTATION, DIRECT MEASUREMENTS
An object is placed in some Reference co ordination system and it’s volume is subdivided into small volume element called voxal it is usual for representation of voxal based volumetric model is the 3D occupancy grid which is implemented as a 3D Boolean array. Each voxal is indexed by x,y,z co-ordination
In the voxal based volumetric model the patch are applied by a surface fusion process& getting the reconstructed 3D model .

41. VOLUMETRIC REPRESENTATION, DIRECT MEASUREMENTS
Voxelization in 3D (a) continuous surface (b) voxelized image consisting of cubes of the same size.

42. VOLUMETRIC REPRESENTATION, DIRECT MEASUREMENTS
After rendering the proposed model is to be generating and an accurate and robust anatomic descriptor for complex objects in the human brain.
Then the 3D model is optimized by the genetic algorithm.

43. GENETIC ALGORITHM Cross over Mutation Selection
Random recombination of two distinct solution to form novel solution.
Mutation
Random perturbation of a candidate solution.
Selection
Replication of successful solutions, which “survive” and “reproduce”

44. The Evolutionary Cycle

45. GENETIC OPERATERS EVALUATION
The evaluation procedure measures the fitness of each individual solution in the population and assigns to it a score.
SELECTION
The selection procedure randomly selects individuals of the current population for development of the next generation.
CROSSOVER
The crossover procedure takes two selected individuals and combines them about a crossover point thereby creating two new individuals.
MUTATION
The mutation procedure randomly modifies the genes of an individual subject to a small mutation factor, introducing further randomness into the population.

46. Permutation representation: TSP example
Problem:
Given n cities
Find a complete tour with minimal length
Encoding:
Label the cities 1, 2, … , n
One complete tour is one permutation (e.g. for n =4 [1,2,3,4], [3,4,2,1] are OK)
Search space is BIG:
for 30 cities there are 30!  1032 possible tours

47. TSP Example: 30 Cities

48. Solution i (Distance = 941)

49. Solution j(Distance = 800)

50. Solution k(Distance = 652)

51. Best Solution (Distance = 420)

52. FUTURE EXTENTION

53. Parallel Genetic Algorithms
Parallel self evolution of several isolated subpopulations
Periodic exchange-migration-of the best individuals between subpopulations.
Different migration strategies and different strategies of subpopulations self-evolution produce different instantiations for parallel genetic algorithm
More natural, and more successful in the optimization than classical genetic algorithm.

54. BASIC ALGORITHM Define the Problem input:
Solution encoding
Genetic operator
GA parameters
Generate initial population of candidate solutions.
Partition it to several subpopulations
Decide migration strategy for share individuals between the subpopulation.
While termination condition not met do
For each subpopulation:
Self-evolve (parallel) subpopulation with GA
Share individuals between neighboring subpopulation.
(receive the best, replace the worst)
End for
End while

55. MIGRATION STRATEGIE ISLAND MODEL STEPPER STORN MODEL

56. ISLAND MODEL STEPER STORN MODEL
Send best individual to any other individual
All subpopulations are neighbors.
Better model of nature
High communication over head
Share best individual to any subpopulations with it’s two neighbors.
Close chain neighborhood structure
Reduced communication overhead

57. output
BEFORE OPTIMISATION AFTER OPTIMISATION

58. Some GA Application Types

59. REFERANCE
Volumetric segmentation of Brain Image Using Parallel Genetic Algorithms
(yong fan,Tianzi Jiang,IEEE,and David j.Enans)
Genetic algorithm Archive
Genetic programming note book:
.com
BOOK: Image processing analysis and Machine Vision (Milan sonka,Vaclav hlavac,Roger Boyle)

60. Conclusions
‘Genetic algorithms are rich - rich in application across a large and growing number of disciplines.’