Footnotes

Dr. Roy S. Schestowitz holds a Ph.D. in Medical Biophysics, which he received from the Victoria University of Manchester where he specialised in statistical analysis of shape and intensity characterising soft tissue. He also worked on a novel approach for assessing dissimilarity using combined models of 2-D faces and 3-D brain data (notably MRI) before working on cardiac MRI for real-time tracking purposes.

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... progress ²

A lot of material in textual form was being assembled throughout development, including technical explanations and explanations in the form of visual elements that demonstrate textual descriptions (e.g. tables, images, screenshots).

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... job ³

Humans are used to recognising faces by texture and crude stereo vision, not full 3-D.

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... parallelisation ⁴

In his IJCV paper, Bronstein stresses that ``[t]he inner geodesic distances were computed using an efficient parallel version of FMM optimized for the Intel SSE2 architecture (using our implementation, a matrix of distances of size 25002500 can be computed in about 1.5 seconds on a PC workstation).''

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... index ⁵

The challenge of searching for matches in large databases is a complex problem in itself. It can use a coarse-to-fine (multi-scale) approach or signatures that act somewhat like hashing.

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... components ⁶

There are different possible colour schemes, but they need not have any effect on principles of sampling intensities.

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... shape ⁷

Warps can be applied using a strategy borrowed from graphics. In all experiments described in this thesis this was achieved by a triangulated mesh generated from the landmark points and barycentric coordinates to mesh the intersections put in vector $\mathbf{g}$ .

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...⁸

The letter

stands for shape, as by default this matrix scales the shape parameters only. It gives logically equivalent results to these of applying the factor $\mathbf{W}_{g}=\frac{1}{\mathbf{W}_{s}}$ to intensities.

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... model ⁹

There is finally code in place for plotting the http://en.wikipedia.org/wiki/Pareto_distributionPareto distribution of the built model, which can be used to show how much of the variation each mode accounts for and how this ratio degrades. The problem is, without resolving difficulties of fully automatic face cropping and then applying that to a large set, the data will just be noisy and the modes rather uninteresting. For small dataset (run for testing purposes) there are hardly any modes at all, in lieu with the size of the sampled set fed into PCA.

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... pixels ¹⁰

The common computer vision approach of locating and segmenting image parts, e.g. for partial similarity on a per-part basis with scoring, with or without weighting based on statistical/topological/irregular/anatomical significance - that which can more uniquely identify in image within a group or even externally, as belonging to one group of images and not other groups.

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... FRGC ¹¹

We do vectorise the code as much as possible, for the sake of speed. Alas, it is still cumbersome and slow.

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... dataset ¹²

find | grep .abs | wc allows us to count and handle all images by taking them one by one and then just handling them one single image at the time. There are many in the current collection, 4950 to be precise; all of them are compressed, as find | grep .abs.gz | wc helps reveal. To get a list of the 3-D faces, one can run, e.g. find | grep .abs.gz | awk '/{print $1}' 1>~/files_list.txt, which yields something like the following: ``./nd1/Spring2003range/04334d218.abs.gz; ./nd1/Spring2003range/04419d182.abs.gz; [...] ./nd1/Spring2004range/04936d102.abs''.

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... Australia ¹³

Faisal R. Al-Osaimi completed his degree in 2010. He was Mian's first Ph.D. student.

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... alignment ¹⁴

This is very much needed for landmark points and thus correspondences to be identified, otherwise we model nonsensical examples.

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... swapped ¹⁵

In one of their original papers, the authors' abstract states that they present an ''algebro-geometric solution to the problem of segmenting an unknown number of subspaces of unknown and varying dimensions from sample data points. We represent the subspaces with a set of homogeneous polynomials whose degree is the number of subspaces and whose derivatives at a data point give normal vectors to the subspace passing through the point. When the number of subspaces is known, we show that these polynomials can be estimated linearly from data; hence, subspace segmentation is reduced to classifying one point per subspace. We select these points optimally from the data set by minimizing certain distance function, thus dealing automatically with moderate noise in the data. A basis for the complement of each subspace is then recovered by applying standard PCA to the collection of derivatives (normal vectors). Extensions of GPCA that deal with data in a highdimensional space and with an unknown number of subspaces are also presented.``

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... now ¹⁶

In page 12 of the IJCV paper they state that about 2% of the probe scans were misdetected due to these errors that we have, but they have had more time to work on these. It's the less finely documented part of their work, which presents itself as trivial by hiding the creases.

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... benchmark ¹⁷

To grossly define a classification benchmark in this context, it ought to be possible to model different 'families' of variation (such as anger, fear, etc.) and then classify an unseen image based on model fit. It would seem quite novel and it probably ought to work.

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... translation ¹⁸

Mian-style objective function needed for comparisons, with rotation/clipping addressed as part of him transformation needs fixing.

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... time ¹⁹

It ought to be a simple problem to fix as it is very clear based on the score whenever bad detection has occurred, the score being an order of magnitude higher than expected.

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... Web ²⁰

To assess everything more formally, the http://en.wikipedia.org/wiki/Face_Recognition_Vendor_TestFace Recognition Vendor Test was later on used for reference.

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... cases ²¹

To accentuate discriminative properties, e.g. for comparative purposes and debugging.

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... unavailable ²²

Although implemented in http://en.wikipedia.org/wiki/OpenCVOpenCV which means we may have to code it from scratch, at least if moving in this direction. Upon closer inspection, there is an implementation we can reuse over at http://www.mathworks.com/matlabcentral/fileexchange/29437-viola-jones-object-detectionMATLAB Central.

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... all ²³

Among the available functions there are displayFiltered_Single.m, displayFiltered_SingleFromVideo.m, displayRaw_Single.m, displayRaw_SingleFromVideo.m, readFrameProperties.m, readGipFile.m, and readGipFileHeader.m.

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