List of Figures

• Image interpretation using  a priori knowledge. What is depicted here? Courtesy of Preece et al. [56].
• The three steps of handling shape and texture in AAMs.
• Four exact copies of the same shape, but under different euclidean transformations.
• A hand annotated using 11 anatomical landmarks and 17 pseudo-landmarks.
• Metacarpal-2 annotated using 50 landmarks.
• The Procrustes distance.
• A set of 24 unaligned shapes. Notice the position-outlier to the right.
• (a) The PDM of 24 aligned shapes. (b) Ellipsis fitted to the single point distribution of figure (a).
• Principal axis. 2D example.
• Shape covariance matrix. Black, grey & white maps to negative, none & positive covariance.
• Shape correlation matrix. Black, white maps to low, high correlation.
• (a) Mean shape and deformation vectors of the 1st eigenvector. (b) Mean shape, deformation vectors of the 1st eigenvector and deformed shape.
• Mean shape deformation using 1st, 2nd and 3rd principal mode. $b_i=-3\sqrt {\lambda _i}$, b_i=0, $b_i=3\sqrt {\lambda _i}$.
• Shape eigenvalues in descending order.
• PC1 (b_s,1) vs. PC2 (b_s,2) in the shape PCA.
• Training set of 100 unaligned artificially generated rectangles containing 16 points each.
• Point cloud from aligned rectangles sized to unit scale, |x| = 1. The mean shape is fully shown.
• Point-cloud from aligned rectangles sized to unit scale, |x| = 1, and transformed into tangent space. The mean shape is fully shown.
• Tadpole example of a PCA breakdown. Notice in mode 1, how the head size and length is correlated with the bending. This is easily seen in the scatter plot of PCA parameter 1 vs. 3 (lower right), where b₃ has a simple non-linear dependency of b₁. Adapted from [#!Sozou95!#].
• Image warping.
• Circumcircle of a triangle satisfying the Delaunay property.
• Delaunay triangulation of the mean shape.
• Problem of the piece-wise affine warping. Straight lines will usually be kinked across triangle boundaries.
• Bilinear interpolation. The intensity at $\varepsilon$ is interpolated from the four neighboring pixels, $\alpha , \beta , \gamma$ and $\varphi$.
• PC1 (b_g,1) versus PC2 (b_g,2) in the texture PCA.
• Texture eigenvalues in descending order.
• Three largest combined metacarpal modes from top to bottom; $c_i=-3\sqrt {\lambda _i}$, c_i=0, $c_i=3\sqrt {\lambda _i}$.
• Combined eigenvalues.
• Displacement plots for a series of model predictions versus the actual displacement. Error bars are equal to 1 std.dev.
• AAM Optimization. Upper left: The initial model. Upper right: The AAM after 2 iterations. Lower left: The converged AAM (7 iterations). Lower right: The original image.
• Removal of unwanted triangles resulting from the Delaunay triangulation of concave shapes.
• (a) Concave shape with convex triangles. (b) Concave shape with convex triangles removed.
• The shrinking problem.
• Shape neighborhood added using an artificial border placed along the normals.
• (a) Shape annotated using 150 landmarks. (b) Shape with a neighborhood region added resulting in $2\times 150=300$ landmarks.
• ASM-like AAM generated by adding shape neighborhood and a hole.
• (a) Shape annotated using 83 landmarks. (b) Border shape with $3\times 83=249$ landmarks.
• Example of AAM search and Simulated Annealing fine-tuning, without (left) and with (right) the use of a robust similarity measure (Lorentzian error norm). Landmark error decreased from 7.0 to 2.4 pixels (pt.-to-crv. error).
• A shape, a, with a blob, b, inside that is hard to annotate.
• A finite element model interpreted as a set of point masses interconnected by springs.
• High frequency FEM-modes of a square surface modelled by 25 unit masses.
• Warp modification by FEMs.
• Warp modification by FEMs using piece-wise affine warps.
• A square shape deformed by adding FEM-deformed AIPs and fixating the original outer shape points.
• Left: Point to point (pt.pt.) error. Right: Point to associated border (pt.crv.) error.
• The effect of using the Mahalanobis distance in two dimensions. Model instance B is valid, while model instance A is classified illegal
• Hand anatomy. Metacarpals numbered at the fingertips.
• The mismath at metacarpal 3, 4, 5 instead of 2, 3, 4. in test 1.
• Point to curve histograms for radiograph AAMs. Bin size = .25 pixel.
• Mean point to point deviation from the ground truth annotation of each metacarpal. Low location accuracy is observed at the distal and proximal ends.
• Test 3: (a) Worst model fit, 1.01 pixels (pt.crv.). (b) Best model fit, 0.53 pixels (pt.crv.).
• (a) AAM after automatic initialization. (b) Optimized AAM. Both cropped to show details.
• Left: Set 1 Cardiac A-slice with papillary muscles. Right: Set 1 Cardiac B-slice without papillary muscles. Both cropped and stretched to enhance features.
• Left: Set 2 Cardiac A-slice with papillary muscles. Right: Set 2 Cardiac B-slice without papillary muscles. Both cropped and stretched to enhance features.
• Test 1 on B-slices of Set 1: (a) Worst model fit, 2.43 pixels (pt.crv.). (b) Best model fit, 0.65 pixels (pt.crv.).
• Point to curve histograms for the AAMs built on A-slices from Set 1. Bin size = .5 pixel.
• Point to curve histograms for the AAMs built on B-slices from Set 1. Bin size = .5 pixel.
• Point to curve histograms for the AAMs built on A- and B-slices from Set 2. Bin size = .5 pixel.
• A: AAM after automatic initialization. B: Optimized AAM. Both cropped to show details.
• Point to curve histograms for different pork carcass AAMs. Bin size = .25 pixel.
• Test 3: (a) Worst model fit, 1.34 pixels (pt.crv.). (b) Best model fit, 0.60 pixels (pt.crv.).
• Point cloud of the unaligned annotations.
• Point cloud of the aligned annotations with mean shape fully drawn.
• Delaunay triangulation of the mean shape.
• Independent principal component analysis of each model point.
• Mean shape deformation using 1st, 2nd and 3rd principal mode. $b_i=-3\sqrt {\lambda _i}$, b_i=0, $b_i=3\sqrt {\lambda _i}$.
• Shape eigenvalues in descending order.
• PC1 (b_s,1) vs. PC2 (b_s,2) in the shape PCA.
• Texture eigenvalues in descending order.
• PC1 (b_g,1) versus PC2 (b_g,2) in the texture PCA.
• Correlation matrix of the annotations.
• Texture variance, black corresponds to high variance.
• Combined eigenvalues.
• Point cloud of the unaligned annotations.
• Point cloud of the aligned annotations with mean shape fully drawn.
• Delaunay triangulation of the mean shape.
• Independent principal component analysis of each model point.
• Mean shape deformation using 1st, 2nd and 3rd principal mode. $b_i=-3\sqrt {\lambda _i}$, b_i=0, $b_i=3\sqrt {\lambda _i}$.
• Shape eigenvalues in descending order.
• PC1 (b_s,1) vs. PC2 (b_s,2) in the shape PCA.
• Texture eigenvalues in descending order.
• PC1 (b_g,1) versus PC2 (b_g,2) in the texture PCA.
• Correlation matrix of the annotations.
• Texture variance, black corresponds to high variance.
• Combined eigenvalues.
• Point cloud of the unaligned annotations.
• Point cloud of the aligned annotations with mean shape fully drawn.
• Delaunay triangulation of the mean shape.
• Independent principal component analysis of each model point.
• Mean shape deformation using 1st, 2nd and 3rd principal mode. $b_i=-3\sqrt {\lambda _i}$, b_i=0, $b_i=3\sqrt {\lambda _i}$.
• Shape eigenvalues in descending order.
• PC1 (b_s,1) vs. PC2 (b_s,2) in the shape PCA.
• Texture eigenvalues in descending order.
• PC1 (b_g,1) versus PC2 (b_g,2) in the texture PCA.
• Correlation matrix of the annotations.
• Texture variance, black corresponds to high variance.
• Combined eigenvalues.
• Displacement plot for a series of y-pose parameter displacements. Actual displacement versus model prediction. Error bars are 1 std.dev.
• Model border after automated initialization (cropped).
• Optimized model border.
• AAM after automated initialization (cropped).
• Optimized AAM (cropped).
• Mean point to point deviation from the ground truth annotation of each metacarpal. Low location accuracy is observed at the distal and proximal ends.
• Model border after automated initialization.
• Optimized model border.
• AAM after automated initialization (cropped).
• Optimized AAM (cropped).
• Original image (cropped).
• Point cloud of four unaligned heart chamber annotations.
• Point cloud of four aligned heart chamber annotations with mean shape fully drawn.
• Correlation matrix of the four annotations. Observe the obvious point correlations.
• Delanay triangulation of the mean shape.
• Point variation of the four annotations; radius = $\sigma _x+\sigma _y$. Notice the large point variation to the lower left.
• The first eigenvector plotted as displacement vectors. Notice that the large point variation observed in figure B.16 is point variation along the contour, which only contributes to a less compact model contrary to explaining actual shape variation.
• Mean shape and shape deformed by the first eigenvector. Notice that this emphasizes the point above; that a lot of the deformation energy does not contribute to any actual shape changes.