masterarbeit/arbeit/ma.md

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How to read this Thesis

As a guide through the nomenclature used in the formulas we prepend this chapter.

Unless otherwise noted the following holds:

• lowercase letters x,y,z
  refer to real variables and represent a point in 3D-Space.
• lowercase letters u,v,w
  refer to real variables between 0 and 1 used as coefficients in a 3D B-Spline grid.
• other lowercase letters
  refer to other scalar (real) variables.
• lowercase bold letters (e.g. \vec{x},\vec{y})
  refer to 3D coordinates
• uppercase BOLD letters (e.g. D, M)
  refer to Matrices

Introduction

In this Master Thesis we try to extend a previously proposed concept of predicting the evolvability of \acf{FFD} given a Deformation-Matrix\cite{anrichterEvol}. In the original publication the author used random sampled points weighted with \acf{RBF} to deform the mesh and defined three different criteria that can be calculated prior to using an evolutional optimisation algorithm to asses the quality and potential of such optimisation.

We will replicate the same setup on the same meshes but use \acf{FFD} instead of \acf{RBF} to create a deformation and evaluate if the evolution-criteria still work as a predictor given the different deformation.

What is \acf{FFD}?

First of all we have to establish how a \ac{FFD} works and why this is a good tool for deforming meshes in the first place.

Was ist evolutionäre Optimierung?

Wieso ist evo-Opt so cool?

Evolvierbarkeitskriterien

• Konditionszahl etc.

Hauptteil

Was ist FFD?

• Definition
• Wieso Newton-Optimierung?
  • Was folgt daraus?

Szenarien vorstellen

1D

Optimierungszenario

• Ebene -> Template-Fit

Matching in 1D

• Trivial

Besonderheiten der Auswertung

• Analytische Lösung einzig beste
  • Ergebnis auch bei Rauschen konstant?
  • normierter 1-Vektor auf den Gradienten addieren
    • Kegel entsteht

3D

Optimierungsszenario

• Ball zu Mario

Matching in 3D

• alternierende Optimierung

Besonderheiten der Optimierung

• Analytische Lösung nur bis zur Optimierung der ersten Punkte gültig
• Kriterien trotzdem gut

Evaluation

Spearman/Pearson-Metriken

• Was ist das?
• Wieso sollte uns das interessieren?
• Wieso reicht Monotonie?
• Haben wir das gezeigt?
• Stastik, Bilder, blah!

Schluss

HAHA .. als ob -.-