... models.^1.1

Alternatively: deformable templates or deformable models.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... processes.^3.1

Though the texture mode in reality is defined in terms of the shape model.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... points^4.1

Can be either sparse or dense.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... recently^4.2

ECCV, Dublin, June 2000.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... analysis^4.3

And all other learning-based image analysis techniques for that matter.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... analysis^4.4

As a curiosity Procrustes was the nickname of a robber in Greek mythology called  Damastes, who lived by the road from Eleusis to Athens. He offered travelers hospitality on a magical bed that would fit any guest. His humor was to stretch the ones who were too short to fit the bed - until they died - or, if they were too tall, to cut off as much of their limbs as would make them short enough. This rather unpleasant practice continued until Damastes was killed by Theseus, son of Æthra and the Athenian king Ægeus. Another nickname for Damastes was The one who stretches. The term Procrustes Analysis was coined by Hurley & Cattell in 1962 [20].

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... size^4.5

This metric also posses the interesting property that 2nS(x)² equals the sum of the inter-landmark distances [20].

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... matrices^4.6

In the planar case k=2.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... shape?^4.7

Also called the shape  prototype.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... (b).^4.8

Where the major and minor axes are the eigenvectors of the point covariance matrix (scaled to 3 std.dev.). More about this technique used on the complete set of points in the following chapter.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... data.^4.9

However - one should also consider the multidimensional scaling - MDS technique for this special purpose.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... estimated^4.10

Notice that this estimate naturally equals the mean shape.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... downwards^4.11

Since the PCA chooses its signs on the axes arbitrary.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... behavior^4.12

For example if certain parts of an object, only can reside in certain positions. Think of the second hand on a quarts watch.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... network^4.13

A multi-layer perceptron to be precise.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... shape^5.1

Here the mean shape is used as reference shape.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... 3D^5.2

Here the circumcircle becomes a "circumsphere".

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... shape.^5.3

An exception to this, is when one wants to back-project the AAM texture onto the image, which is a pretty tedious task requiring two warps (and great care).

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... case.^5.4

This is usually also the case for shape models, but not always. Consider the training set of Cootes et al. [14] using 400 faces each annotated using 122 landmarks which equals a dimensionality of 244 and 400 observations.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... deformations^7.1

This is shape/texture changes in the model parameter case and position, scale and orientation in the pose case.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... parameters^7.2

In this case it's the displacement of the c-model parameters, $\delta \mathbf{c}$, and the pose displacement parameters, $\delta \mathbf{t}$.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... differences^7.3

Thus m equals the number of texture samples in the model.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... subspace^7.4

Where $k \ge t$ since choosing a k<t would not make R span the whole space of V.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... conducted^7.5

Obviously since a large number of experiments, constitutes a better prediction model.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... objects^8.1

Objects lacking a definite form.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... inference^8.2

The act or process of deriving logical conclusions from premises known or assumed to be true.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... distribution.^8.3

I.e. $\int_{\Omega_{\mathbf{v}},\Omega_{\mathbf{I}}} P(\mathbf{v}\vert\mathbf{I},\theta) d\mathbf{v}d\mathbf{I} = 1$.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... Algorithms^9.1

Notice however, while GAs are probabilistic, our technique is deterministic. Further more are the aspects of mutation and crossover in GAs not utilized here.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... theorem^9.2

I.e. $\mathcal{F}(f*g) = \mathcal{F}(f)\mathcal{F}(g)$, where f, g are two signals, $\mathcal{F}$ denotes the  Fourier transform and * the  convolution operator.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

...[58]^9.3

To achieve performance the log-function was implemented using precomputed look-up tables.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... independence^9.4

Unfortunately dependence is the fundamental characteristic of the concept of an image.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... ring.^9.5

Though this is highly unlikely since the metacarpals is situated in the middle of the hand.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... recently^10.1

ECCV, Dublin, June 2000.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... landmark^10.2

Although any neighborhood could be used, a 1-pixel wide profile at each landmark normal is used.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... sponsor^11.1

The Danish company Pronosco A/S.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... AAM-API^11.2

This is without any 3rd party libraries or auto-generated code.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... program^11.3

Doc++ [http://www.linuxsupportline.com/$\sim$doc++/].

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... site^11.4

At http://www.imm.dtu.dk/$\sim$aam/

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... AAM-API^11.5

At least in binary form with header files and stub libraries.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

...leave-one-out^12.1

Model building where each training example is missed out in turn and evaluated upon.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... estimate.^13.1

Which is used in the diagnosis of  osteoporosis.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... ventricle^14.1

This could for example be hearts where the epicardial boundary is embedded in fatty tissue.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... estimators^16.1

Error norms where the first derivative - the so-called  influence function [3] - goes to zero for gross errors.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... model.^16.2

Using a suitable weighting - e.g. a function of the number of examples in the training set.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... recently^16.3

ECCV Dublin, June 2000.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... 20:1.^17.1

On top of this; the spatial filtering of wavelets is also quite desirable in  multi-resolution frameworks such as the AAMs.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... 2000^17.2

At Herlev Hospital and IMM, DTU respectively.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... radiometric^17.3

The amplitude accuracy - i.e. number of bits per pixel in digital imagery.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

...^20.1

Corresponding author: aam@imm.dtu.dk

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... 2000^20.2

Probably under the GNU Public License.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... AAM-site.^20.3

http://www.imm.dtu.dk/$\sim$aam/

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... Doc++^22.1

Doc++ resides at http://www.linuxsupportline.com/$\sim$doc++/

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... printed^22.2

In the PostScript and PDF format.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.