103 lines
2.3 KiB
Markdown
103 lines
2.3 KiB
Markdown
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fontsize: 11pt
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---
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# How to read this Thesis
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As a guide through the nomenclature used in the formulas we prepend this chapter.
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Unless otherwise noted the following holds:
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- lowercase letters $x,y,z$
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refer to real variables and represent a point in 3D-Space.
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- lowercase letters $u,v,w$
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refer to real variables between $0$ and $1$ used as coefficients in a 3D B-Spline grid.
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- other lowercase letters
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refer to other scalar (real) variables.
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- lowercase **bold** letters (e.g. $\vec{x},\vec{y}$)
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refer to 3D coordinates
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- uppercase **BOLD** letters (e.g. $D, M$)
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refer to Matrices
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# Introduction
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In this Master Thesis we try to extend a previously proposed concept of predicting
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the evolvability of \acf{FFD} given a Deformation-Matrix\cite{anrichterEvol}.
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In the original publication the author used random sampled points weighted with
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\acf{RBF} to deform the mesh and defined three different criteria that can be
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calculated prior to using an evolutional optimisation algorithm to asses the
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quality and potential of such optimisation.
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We will replicate the same setup on the same meshes but use \acf{FFD} instead of
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\acf{RBF} to create a deformation and evaluate if the evolution-criteria still
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work as a predictor given the different deformation.
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## What is \acf{FFD}?
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First of all we have to establish how a \ac{FFD} works and why this is a good
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tool for deforming meshes in the first place.
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## Was ist evolutionäre Optimierung?
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## Wieso ist evo-Opt so cool?
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## Evolvierbarkeitskriterien
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- Konditionszahl etc.
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# Hauptteil
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## Was ist FFD?
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- Definition
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- Wieso Newton-Optimierung?
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- Was folgt daraus?
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## Szenarien vorstellen
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### 1D
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#### Optimierungszenario
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- Ebene -> Template-Fit
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#### Matching in 1D
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- Trivial
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#### Besonderheiten der Auswertung
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- Analytische Lösung einzig beste
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- Ergebnis auch bei Rauschen konstant?
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- normierter 1-Vektor auf den Gradienten addieren
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- Kegel entsteht
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### 3D
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#### Optimierungsszenario
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- Ball zu Mario
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#### Matching in 3D
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- alternierende Optimierung
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#### Besonderheiten der Optimierung
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- Analytische Lösung nur bis zur Optimierung der ersten Punkte gültig
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- Kriterien trotzdem gut
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# Evaluation
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## Spearman/Pearson-Metriken
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- Was ist das?
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- Wieso sollte uns das interessieren?
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- Wieso reicht Monotonie?
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- Haben wir das gezeigt?
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- Stastik, Bilder, blah!
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# Schluss
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HAHA .. als ob -.-
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