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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 Medical Image Analysis

  • 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 Medical Image Analysis

  • 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 Medical Image Analysis

  • 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 Medical Image Analysis

  • 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


Research Medical Image Analysis

Development

  • Hospitals

  • Research institutes

Application

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


Lkeb image modalities
LKEB: Image Modalities Medical Image Analysis

  • 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 Medical Image Analysis

  • Cardiovascular (heart & bloodvessels)

  • Lungs (cpod, emphysema)

  • Orthopedics

  • Neurology (brains, Alzheimer disease)

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


Overview1
Overview Medical Image Analysis

  • 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 Medical Image Analysis

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


Atherosclerosis cta analysis
Atherosclerosis: CTA Analysis Medical Image Analysis

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


Atherosclerosis cta analysis1
Atherosclerosis: CTA Analysis Medical Image Analysis

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


Cta detecting narrowings

Lumen Medical Image Analysis

Calcified plaque

CTA: Detecting Narrowings

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


Overview2
Overview Medical Image Analysis

  • 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

? Medical Image Analysis

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 Medical Image Analysis

  • 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 Medical Image Analysis

  • 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* Medical Image Analysis

  • 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* Medical Image Analysis

*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 Medical Image Analysis

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 Medical Image Analysis

Courtesy of Gunther Rudolph

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


Mixed integer evolution strategies2
Mixed-Integer Evolution Strategies Medical Image Analysis

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 Medical Image Analysis

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 Medical Image Analysis

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 Medical Image Analysis

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 Medical Image Analysis

  • 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 Medical Image Analysis

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 Medical Image Analysis

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

? Medical Image Analysis

?

?

Fitness Based Partitioning

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


Fitness based partitioning3

assign images to partitions Medical Image Analysis

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 Medical Image Analysis

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 Medical Image Analysis

  • 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 Medical Image Analysis

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


Fitness based partitioning potential problem 2
Fitness Based Partitioning: Potential Problem 2 Medical Image Analysis

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


Fitness based partitioning empty partitions
Fitness Based Partitioning: Empty Partitions Medical Image Analysis

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


Fitness based partitioning4
Fitness Based Partitioning Medical Image Analysis

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 Medical Image Analysis

  • 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 Medical Image Analysis

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


Fitness based partitioning experiments
Fitness Based Partitioning: Experiments Medical Image Analysis

  • 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: Medical Image AnalysisResults 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 Medical Image Analysis

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


Fitness based partitioning results1
Fitness Based Partitioning: Results Medical Image Analysis

overall fitness results

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


Fitness based partitioning conclusions
Fitness Based Partitioning: Conclusions Medical Image Analysis

  • 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 Medical Image Analysis

  • 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 Medical Image Analysis

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 Medical Image Analysis

  • 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 Medical Image Analysis

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 Medical Image Analysis

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 Medical Image Analysis

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


Mies rbfn3
MIES+RBFN Medical Image Analysis

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


Mies rbfn4
MIES+RBFN Medical Image Analysis

Conclusions:

  • Less fitness evaluations required

  • …but training RBFN takes time

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


Overview6
Overview Medical Image Analysis

  • 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 Medical Image Analysis

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 Medical Image Analysis

  • 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 Medical Image Analysis

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) Medical Image Analysis

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) Medical Image Analysis

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 Medical Image Analysis

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 Medical Image Analysis

  • 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 Medical Image Analysis(courtesy of Ofer M. Shir)

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


Mies niching
MIES+Niching Medical Image Analysis

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


Mies niching1
MIES+Niching Medical Image Analysis

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


Mies niching2
MIES+Niching Medical Image Analysis

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


Mies niching3
MIES+Niching Medical Image Analysis

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


Mies niching4
MIES+Niching Medical Image Analysis

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


Mies niching5
MIES+Niching Medical Image Analysis

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


Mi es niching conclusions
MI-ES+Niching: Conclusions Medical Image Analysis

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 Medical Image Analysis

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


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