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In order to deform the shape model, ASM uses… A closed form solution Gradient descent Both depending on the application
-       A closed form solution
Model evaluation criteria (metrics):
Compactness: How good data reduction process is (compact model à allows to generate of new model with as few parameters) à compact needed for computational reasons Generalization: ability of the model to generate new instances from the class (performed using cross validation) Specificity: how good the model is in generating instances similar to those presented in the training set (helps to describe the density/ variability of the original data)
Principal component analysis (PCA)
Mathematical tool to reduce the dimensionality of a linear system (data) Projection of the data onto a lower-dimensional space à compacter representation (s loose of information) Uses of singular value decomposition SVD to transform (SVD diagonalizes the covariance matrix on the original data) Assume that the original data follows gaussian distribution Results in an orthogonal lower dimensional system Linear method
Active Shape Model (ASM):
Main idea: Start with SSM and image Initially place SSM (important good initialization) à types: user interaction, centroid alignment etc. Sample along SSM surface normal, find largest gradient (=edge) Deform pose (scale, rotation, translation) and shape (PCA modes) of model to best fit to extracted image features (largest gradient)
-       Active Shape Models employ…. Edge information, and shape statistics Texture information and shape statistics All of the above
Edge information, and shape statistics
ASM requires: A gradient descent optimization to converge An iterative combination of pose estimation and shape deformation A closed form solution, exists, no iteration is needed
An iterative combination of pose estimation and shape deformation
Optimization Schemes
-       Optimization: Choose optimizer for pose estimation (e.g. gradient descent) Closed form solution for shape (extreme fast) Iterative method Compute profile along normals Adjust pose Adjust shape Iterate from beginning until convergence
We saw an application in cranio-maxilo facial surgery. ASM can encode more info thanks to…. It is based on a implicit shape representation, like level-sets Mesh iso-topology(i.e. mesh point indexes have a semantic meaning) The PCA analysis can encode whatever information we include
-       The PCA analysis can encode whatever information we include
Shape representations:
Point clouds: The surface is represented by concatenating (Verkettung) the points Point to point Correspondence: For other anatomy we have other number of points in point clouds (other vector lengths)à take just a few points to correspond the two different anatomy Point distribution model (PMD) à matrix (M) representation of the shape vectores à needet for PCA
Pose/Shape estimation:
-       Pose: Goal: Rough alignment of both shapes Optimize registration process according to certain cost function Shape: PCA-based deformation
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