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Mixed-Integer Evolution Strategies and their Application to Medical Image Analysis. Jeroen Eggermont Rui Li & Michael Emmerich. Background. Student Computer Science, Leiden University Master Thesis: “Rule-extraction and Learning in the BP-SOM Architecture” PhD Student, Leiden University

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mixed integer evolution strategies and their application to medical image analysis

Mixed-Integer Evolution Strategies and their Application to Medical Image Analysis

Jeroen Eggermont

Rui Li

&

Michael Emmerich

background
Background
  • Student Computer Science, Leiden University
    • Master Thesis: “Rule-extraction and Learning in the BP-SOM Architecture”
  • PhD Student, Leiden University
    • PhD Thesis: “Data Mining using Genetic Programming: Classification and Symbolic Regression”
  • Postdoc, Division of Image Processing, LUMC
    • NWO-Savage Project

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

overview
Overview
  • LKEB / Division of Image Processing
  • Atherosclerosis
  • NWO-Savage Project
  • Mixed-Integer Evolution Strategies
  • MIES Extensions
    • Fitness Based Partitioning
    • RBFN
    • Niching

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

lkeb division of image processing
LKEB / Division of Image Processing
  • Research entity of the Department of Radiology of the LUMC
  • The mission is directed towards the research, implementation and validation of automated segmentation, quantification and visualization approaches for structures in medical images
  • The objective results of these approaches serve to support the clinical decision making processes and the outcomes of clinical research studies

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

lkeb division of image processing1
LKEB / Division of Image Processing
  • Core competence
  • Translation of medical imaging problems into clinically applicable technical solutions
  • Development of scientifically innovative automated analysis methods for medical images
  • Development of “physician friendly” user interfaces and visualization tools
  • Extensive clinical validation, beta testing and scientific publication

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

slide6

Research

Development

  • Hospitals
  • Research institutes

Application

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

lkeb image modalities
LKEB: Image Modalities
  • Röntgen (X-ray)
  • Echocardiography
  • IntraVasculaire UltraSound (IVUS)
  • Magnetic Resonance Imaging (MRI)
  • Computer Tomography (CT)

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

lkeb topics
LKEB: Topics
  • Cardiovascular (heart & bloodvessels)
  • Lungs (cpod, emphysema)
  • Orthopedics
  • Neurology (brains, Alzheimer disease)

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

overview1
Overview
  • LKEB
  • Atherosclerosis
  • NWO-Savage Project
  • Mixed-Integer Evolution Strategies
  • MIES Extensions
    • Fitness Based Partitioning
    • RBFN
    • Niching

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

atherosclerosis
Atherosclerosis

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

atherosclerosis cta analysis
Atherosclerosis: CTA Analysis

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

atherosclerosis cta analysis1
Atherosclerosis: CTA Analysis

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

cta detecting narrowings

Lumen

Calcified plaque

CTA: Detecting Narrowings

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

overview2
Overview
  • LKEB
  • Atherosclerosis
  • NWO-Savage Project
  • Mixed-Integer Evolution Strategies
  • MIES Extensions
    • Fitness Based Partitioning
    • RBFN
    • Niching

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

savage project

?

Savage Project

Feature

Detector

Images

parameter setting

Result

So you set the first value to 0.1 the second to 42 …

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

savage project1
Savage Project
  • How to find the optimal parameter setting ?
    • Trial and Error ?
    • Educated guess ?
    • Experience ?

 How to optimize a new algorithm ?

Solution: Optimize parameters automatically

How ?  EvolutionaryAlgorithms

Self-Adaptive Vision Agents using Genetic Evolution

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

overview3
Overview
  • LKEB
  • Atherosclerosis
  • NWO-Savage Project
  • Mixed-Integer Evolution Strategies
  • MIES Extensions
    • Fitness Based Partitioning
    • RBFN
    • Niching

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

evolution strategies quick overview
Evolution Strategies: quick overview*
  • Developed: Germany in the 1970’s
  • Early names: I. Rechenberg, H.-P. Schwefel
  • Typically applied to:
    • numerical optimisation
  • Attributed features:
    • fast
    • good optimizer for real-valued optimisation
    • relatively much theory
  • Special:
    • self-adaptation of (mutation) parameters standard

*A.E. Eiben and J.E. Smith, Introduction to Evolutionary Computing, Springer, 2003, ISBN 3-540-40184-9

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

evolution strategies technical summary
Evolution Strategies: technical summary*

*A.E. Eiben and J.E. Smith, Introduction to Evolutionary Computing, Springer, 2003, ISBN 3-540-40184-9

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

mixed integer evolution strategies
Mixed-Integer Evolution Strategies

Why Mixed-Integer Evolution Strategies ?:

Image segmentation algorithms have parameters of different types:

  • Ordinal Discrete {red, green, blue}, {true, false}
  • Continuous { 3.14, 6.28 }
  • Integer { 3,18, 42 }

 Mixed-Integer Evolution Strategies have Self-Adaptive Mutation operators for each type

 MIES outperformsstandard ES on Mixed-Integer Problems

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

mixed integer evolution strategies1
Mixed-Integer Evolution Strategies

Courtesy of Gunther Rudolph

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

mixed integer evolution strategies2
Mixed-Integer Evolution Strategies

CTA Lumen

Detector

Images

parameter solution

Expert contours

optimal parameter solution

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

mixed integer evolution strategies3
Mixed-Integer Evolution Strategies

Fitness Function

for each image I:

  • resample expert contour E and solution contour C every 2 degrees (180 points per contour)
  • compute average Euclidean distance between corresponding points

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

mixed integer evolution strategies4
Mixed-Integer Evolution Strategies

Experiments

  • 9 CTA data sets ( 59-82 images each)
  • 10 random seeds
  • (4+28)-MIES (4 parents, 28 offspring)
  • 50 generations
  • Comparison to the default parameter settings currently used

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

mixed integer evolution strategies5
Mixed-Integer Evolution Strategies

Conclusion:

 MIES works and converges to solutions which are better than the default parameter settings.

THERE IS NOT ONE OPTIMAL SOLUTION FOR ALL IMAGES !

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

overview4
Overview
  • LKEB
  • Atherosclerosis
  • NWO-Savage Project
  • Mixed-Integer Evolution Strategies
  • MIES Extensions
    • Fitness Based Partitioning
    • RBFN
    • Niching

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

fitness based partitioning
Fitness Based Partitioning

Goal:We want to find optimal parameter settings for all images.

  • First Idea: Cluster images according to their image segmentation context
  • Problem:
    • We don’t know the number of image segmentation contexts
    • We have no natural distance measure that indicates which images require similar parameter solutions
  • Second Idea: Co-evolve parameter solutions and image clusters
  • Problem:
    • This requires a large number of fitness evaluations  Image segmentation is very time consuming

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

fitness based partitioning1
Fitness Based Partitioning

Group images together that require similar parameter settings for image segmentation

Find optimal parameter settings for these groups

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

fitness based partitioning2

?

?

?

Fitness Based Partitioning

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

fitness based partitioning3

assign images to partitions

CTA Lumen Detector

CTA Lumen Detector

MI-ES 1

MI-ES 2

best solution

best solution

CTA Lumen Detector

CTA Lumen Detector

Fitness Based Partitioning

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

fitness based partitioning artificial problems
Fitness Based Partitioning: Artificial Problems

Uniform distribution

Gaussian distribution

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

fitness based partitioning test results
Fitness Based Partitioning: Test Results
  • T = number of MI-ES generations.
  • Types of Errors: - a sample put on wrong island, or - combined & split partitions

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

fitness based partitioning potential problem
Fitness Based Partitioning: Potential Problem

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

fitness based partitioning potential problem 2
Fitness Based Partitioning: Potential Problem 2

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

fitness based partitioning empty partitions
Fitness Based Partitioning: Empty Partitions

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

fitness based partitioning4
Fitness Based Partitioning

What to when a partition becomes empty ?

  • destroy MI-ES population
  • clone population of the MI-ES algorithm of the largest partition
  • divide images of largest partition

CTA Lumen Detector

CTA Lumen Detector

MI-ES 1

MI-ES 2

MI-ES 1’

best solution

best solution

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

fitness based partitioning5
Fitness Based Partitioning
  • Divide images over K partitions
  • Initialize a MIES algorithm for each partition
  • for T iterations do
    • Apply a MIES to each partition for G generations
    • Select the best MIES solution for each partition
    • Test the best MIES solution of each partition on all problem instances
    • Re-assign images to the partition with the best solution
    • Split partitions if needed

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

fitness based partitioning6
Fitness Based Partitioning

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

fitness based partitioning experiments
Fitness Based Partitioning: Experiments
  • 9 CTA Data sets
  • 10 random seeds
  • (4+28)-MIES algorithm (4 parents, 28 offspring)
  • each MIES algorithm is run for 5 generations at a time
  • images are reassigned 10 times

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

fitness based partitioning results 2 partitions
Fitness Based Partitioning: Results 2-partitions

expert contour

evolved solution contour

best solution MIES 1

best solution MIES 2

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

fitness based partitioning results
Fitness Based Partitioning: Results

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

fitness based partitioning results1
Fitness Based Partitioning: Results

overall fitness results

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

fitness based partitioning conclusions
Fitness Based Partitioning: Conclusions
  • F.B.P. results in parameter settings which lead to better CTA lumen segmentations
  • Performance assessment:
    • High reliability: Groups of images usually assigned to the same partition
    • ….however there remains some sensitivity to the random seed used.

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

overview5
Overview
  • LKEB
  • Atherosclerosis
  • NWO-Savage Project
  • Mixed-Integer Evolution Strategies
  • MIES Extensions
    • Fitness Based Partitioning
    • RBFN
    • Niching

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

mies rbfn time expensive evaluations
MIES+RBFN: Time expensive evaluations

CTA Lumen

Detector

Images

parameter solution

Expert contours

optimal parameter solution

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

mies rbfn
MIES+RBFN
  • What if we could predict

quality of a parameter solution

  • How ?
    • Neural Networks (RBFN)
  • Image processing is time consuming
  • Every potential parameter solutions must be evaluated

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

mies rbfn train nn
MIES+RBFN: Train NN

CTA Lumen

Detector

Images

parameter solution

Expert contours

optimal parameter solution

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

mies rbfn1
MIES+RBFN

CTA Lumen

Detector

Images

parameter solution

optimal parameter solution

Expert contours

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

mies rbfn2
MIES+RBFN

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

mies rbfn3
MIES+RBFN

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

mies rbfn4
MIES+RBFN

Conclusions:

  • Less fitness evaluations required
  • …but training RBFN takes time

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

overview6
Overview
  • LKEB
  • Atherosclerosis
  • NWO-Savage Project
  • Mixed-Integer Evolution Strategies
  • MIES Extensions
    • Fitness Based Partitioning
    • RBFN
    • Niching

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

mi es niching evolutionary algorithms

select parents

parents

recombination

mutation

offspring

select offspring

MI-ES+Niching: Evolutionary Algorithms

decrease diversity

population of solutions

increase diversity

decrease diversity

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

mi es niching
MI-ES+Niching
  • EA’s have the tendency to converge to a single global solution
    • Diversity loss

 all parameter solutions look the same after some time

  • Niching was designed to counteract loss of diversity in EA’s

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

mi es niching fitness landscapes
MI-ES+Niching: Fitness Landscapes

slightly more difficult problem landscape

simple problem landscape

difficult problem landscape

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

mi es niching example

Speed (mph)

Dogs

Antelopes

Horses

cats

Feature Y

Feature X

MI-ES+Niching: Example

Find the fastest land animal ?

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

mi es niching example niching

Speed (mph)

Dogs

Antelopes

Horses

cats

Feature Y

Feature X

MI-ES+Niching: Example - Niching

Find the 4 fastest species ?

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

mi es niching finding multiple optima
MI-ES+Niching: Finding multiple optima

Find multiple optima by maintaining diversity

  • Dynamically identify various niches in the fitness landscape
  • Classify parameter solutions into those niches
  • restrict “mating” to the niches

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

mies niching finding multiple optima
MIES+Niching: Finding multiple optima
  • sphere size indicates niche radius
  • niche radius decreases over time
  • distance between niches increases over time

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

es niching examples courtesy of ofer m shir
ES+Niching: Examples (courtesy of Ofer M. Shir)

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

mies niching
MIES+Niching

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

mies niching1
MIES+Niching

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

mies niching2
MIES+Niching

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

mies niching3
MIES+Niching

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

mies niching4
MIES+Niching

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

mies niching5
MIES+Niching

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

mi es niching conclusions
MI-ES+Niching: Conclusions

Results on artificial landscapes with 1 global optimum:

  • Niching increases the chance of finding the global optimum
  • On simple landscapes (problems) it is slightly slower

Future Work:

  • Tests are needed on problems with multiple optima
  • More tests are needed in general to understand niche-forming in MI-ES

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

the end
The End

Mixed-Integer Evolution Strategies and their application to Medical Image Analysis

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