An introduction to Computational Anatomy St´ephanieAllassonni`ere Facult´ede m´edecine,Universit´eParis Descartes September 2018 St´ephanieAllassonni`ere (Descartes) Computational Anatomy September 2018 1 / 82 Goals Mathematical tools Databases Deformable Template framework Introduction Outline 1. Introduction to Computational Anatomy 2. Registration technics 3. Statistical analysis of the deformations 4. Bayesian Modelling for template estimation St´ephanieAllassonni`ere (Descartes) Computational Anatomy September 2018 2 / 82 Introduction Outline 1. Introduction to Computational Anatomy Goals Mathematical tools Databases Deformable Template framework 2. Registration technics 3. Statistical analysis of the deformations 4. Bayesian Modelling for template estimation St´ephanieAllassonni`ere (Descartes) Computational Anatomy September 2018 2 / 82 Establish \normal" variability Classify pathologies from structural deviations Model organ development across time Build prior knowledge to simulate new anatomies, segment areas or organs in new patient, predict from the shape of an organ the evolution of a disease (through clinical variables for example) Estimate representative organs within groups (anatomical invariants) Analysis of populations : Classification / Discrimination : Learn the temporal evolution (growth, evolution of a disease) : Segmentation, prediction, help therapy : Introduction to CA Goals To design mathematical methods and algorithms to model and analyse the anatomy Characterise anatomical shapes : St´ephanieAllassonni`ere (Descartes) Computational Anatomy September 2018 3 / 82 Establish \normal" variability Classify pathologies from structural deviations Model organ development across time Build prior knowledge to simulate new anatomies, segment areas or organs in new patient, predict from the shape of an organ the evolution of a disease (through clinical variables for example) Analysis of populations : Classification / Discrimination : Learn the temporal evolution (growth, evolution of a disease) : Segmentation, prediction, help therapy : Introduction to CA Goals To design mathematical methods and algorithms to model and analyse the anatomy Characterise anatomical shapes : Estimate representative organs within groups (anatomical invariants) St´ephanieAllassonni`ere (Descartes) Computational Anatomy September 2018 3 / 82 Classify pathologies from structural deviations Model organ development across time Build prior knowledge to simulate new anatomies, segment areas or organs in new patient, predict from the shape of an organ the evolution of a disease (through clinical variables for example) Establish \normal" variability Classification / Discrimination : Learn the temporal evolution (growth, evolution of a disease) : Segmentation, prediction, help therapy : Introduction to CA Goals To design mathematical methods and algorithms to model and analyse the anatomy Characterise anatomical shapes : Estimate representative organs within groups (anatomical invariants) Analysis of populations : St´ephanieAllassonni`ere (Descartes) Computational Anatomy September 2018 3 / 82 Classify pathologies from structural deviations Model organ development across time Build prior knowledge to simulate new anatomies, segment areas or organs in new patient, predict from the shape of an organ the evolution of a disease (through clinical variables for example) Classification / Discrimination : Learn the temporal evolution (growth, evolution of a disease) : Segmentation, prediction, help therapy : Introduction to CA Goals To design mathematical methods and algorithms to model and analyse the anatomy Characterise anatomical shapes : Estimate representative organs within groups (anatomical invariants) Analysis of populations : Establish \normal" variability St´ephanieAllassonni`ere (Descartes) Computational Anatomy September 2018 3 / 82 Model organ development across time Build prior knowledge to simulate new anatomies, segment areas or organs in new patient, predict from the shape of an organ the evolution of a disease (through clinical variables for example) Classify pathologies from structural deviations Learn the temporal evolution (growth, evolution of a disease) : Segmentation, prediction, help therapy : Introduction to CA Goals To design mathematical methods and algorithms to model and analyse the anatomy Characterise anatomical shapes : Estimate representative organs within groups (anatomical invariants) Analysis of populations : Establish \normal" variability Classification / Discrimination : St´ephanieAllassonni`ere (Descartes) Computational Anatomy September 2018 3 / 82 Model organ development across time Build prior knowledge to simulate new anatomies, segment areas or organs in new patient, predict from the shape of an organ the evolution of a disease (through clinical variables for example) Learn the temporal evolution (growth, evolution of a disease) : Segmentation, prediction, help therapy : Introduction to CA Goals To design mathematical methods and algorithms to model and analyse the anatomy Characterise anatomical shapes : Estimate representative organs within groups (anatomical invariants) Analysis of populations : Establish \normal" variability Classification / Discrimination : Classify pathologies from structural deviations St´ephanieAllassonni`ere (Descartes) Computational Anatomy September 2018 3 / 82 Build prior knowledge to simulate new anatomies, segment areas or organs in new patient, predict from the shape of an organ the evolution of a disease (through clinical variables for example) Model organ development across time Segmentation, prediction, help therapy : Introduction to CA Goals To design mathematical methods and algorithms to model and analyse the anatomy Characterise anatomical shapes : Estimate representative organs within groups (anatomical invariants) Analysis of populations : Establish \normal" variability Classification / Discrimination : Classify pathologies from structural deviations Learn the temporal evolution (growth, evolution of a disease) : St´ephanieAllassonni`ere (Descartes) Computational Anatomy September 2018 3 / 82 Build prior knowledge to simulate new anatomies, segment areas or organs in new patient, predict from the shape of an organ the evolution of a disease (through clinical variables for example) Segmentation, prediction, help therapy : Introduction to CA Goals To design mathematical methods and algorithms to model and analyse the anatomy Characterise anatomical shapes : Estimate representative organs within groups (anatomical invariants) Analysis of populations : Establish \normal" variability Classification / Discrimination : Classify pathologies from structural deviations Learn the temporal evolution (growth, evolution of a disease) : Model organ development across time St´ephanieAllassonni`ere (Descartes) Computational Anatomy September 2018 3 / 82 Build prior knowledge to simulate new anatomies, segment areas or organs in new patient, predict from the shape of an organ the evolution of a disease (through clinical variables for example) Introduction to CA Goals To design mathematical methods and algorithms to model and analyse the anatomy Characterise anatomical shapes : Estimate representative organs within groups (anatomical invariants) Analysis of populations : Establish \normal" variability Classification / Discrimination : Classify pathologies from structural deviations Learn the temporal evolution (growth, evolution of a disease) : Model organ development across time Segmentation, prediction, help therapy: St´ephanieAllassonni`ere (Descartes) Computational Anatomy September 2018 3 / 82 Introduction to CA Goals To design mathematical methods and algorithms to model and analyse the anatomy Characterise anatomical shapes : Estimate representative organs within groups (anatomical invariants) Analysis of populations : Establish \normal" variability Classification / Discrimination : Classify pathologies from structural deviations Learn the temporal evolution (growth, evolution of a disease) : Model organ development across time Segmentation, prediction, help therapy: Build prior knowledge to simulate new anatomies, segment areas or organs in new patient, predict from the shape of an organ the evolution of a disease (through clinical variables for example) St´ephanieAllassonni`ere (Descartes) Computational Anatomy September 2018 3 / 82 Geometry Statistical Modelling and differential geometry Statistical analysis Statistical learning Functional analysis Etc... Introduction to CA Mathematical tools Characterise anatomical shapes : Analysis of populations : Classification / Discrimination : Learn the temporal evolution (growth, evolution of a disease) : Segmentation, prediction, help therapy : St´ephanieAllassonni`ere (Descartes) Computational Anatomy September 2018 4 / 82 Statistical Modelling and differential geometry Statistical analysis Statistical learning Functional analysis Etc... Introduction to CA Mathematical tools Characterise anatomical shapes : Geometry Analysis of populations : Classification / Discrimination : Learn the temporal evolution (growth, evolution of a disease) : Segmentation, prediction, help therapy : St´ephanieAllassonni`ere (Descartes) Computational Anatomy September 2018 4 / 82 Statistical analysis Statistical learning Functional analysis Etc... Introduction to CA Mathematical tools Characterise anatomical shapes : Geometry Analysis of populations : Statistical Modelling and differential geometry Classification / Discrimination : Learn the temporal evolution