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- 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.
, bi=0,
.
- Shape eigenvalues in descending order.
- PC1 (bs,1) vs. PC2 (bs,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
is interpolated from the four neighboring pixels,
and
.
- PC1 (bg,1) versus PC2 (bg,2) in the texture PCA.
- Texture eigenvalues in descending order.
- Three largest combined metacarpal modes from top to bottom;
, ci=0,
.
- 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
landmarks.
- ASM-like AAM generated by adding shape neighborhood and a hole.
- (a) Shape annotated using 83 landmarks. (b) Border shape with
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.
, bi=0,
.
- Shape eigenvalues in descending order.
- PC1 (bs,1) vs. PC2 (bs,2) in the shape PCA.
- Texture eigenvalues in descending order.
- PC1 (bg,1) versus PC2 (bg,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.
, bi=0,
.
- Shape eigenvalues in descending order.
- PC1 (bs,1) vs. PC2 (bs,2) in the shape PCA.
- Texture eigenvalues in descending order.
- PC1 (bg,1) versus PC2 (bg,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.
, bi=0,
.
- Shape eigenvalues in descending order.
- PC1 (bs,1) vs. PC2 (bs,2) in the shape PCA.
- Texture eigenvalues in descending order.
- PC1 (bg,1) versus PC2 (bg,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 =
. 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.
Active Appearance Models (be)
2000-09-20