Selecting Landmarks

In order to combine results from different faces and accurately compare the surface descriptions of a point against those on other faces a dense correspondence is needed in the test set. If a correspondence is known for each point on a face, then comparing the surface descriptions of points is trivial. Since the Basel face model (BFM)[26] generates faces with a dense correspondence, we will use a dataset of faces generated with random parameters using the Basel face model, detailed in section 3.2.2. The resolution of these faces has been reduced in order to speed up computation.

For the comparisons of corresponding surface descriptions to be valid, the correspondence be-tween faces must be correct. It is difficult to quantitatively test the correspondence of all points on the generated faces as points with easily identifiable positions are needed across the face, i.e.

landmarks. The BFM was produced by fitting a deformable mesh model[38] to faces anchored using landmarks. To test the correspondence in a qualitative way, the fourteen landmarks in table 4.1 were hand labelled on a test face from the down sampled dataset. The landmarks were ob-served on a sample of faces from the dataset by displaying the corresponding point on each face to those selected in the hand labelling. A small sample of these faces is shown in figure 4.2; we observe that the correspondence of these landmark points is good. However, these points are most likely to be in correspondence because they are where the initial model was anchored. Testing the correspondence of the surface between these points is more difficult and beyond the scope of this work. The results in this chapter will assume that the correspondence across the entire face surface is valid.

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Figure 4.2: Corresponding points on three different faces in the down sampled BFM dataset. Landmarks were hand labelled on a fourth face (not shown), the corresponding points on three other faces are shown here. These faces show that the correspondence has been preserved through the down sampling process.

4.3 Descriptors

In chapter 2, two types of surface description are described: surface measures and signature meth-ods. Surface measures are a single measurement of the surface at each point while a signature method more richly describes the surrounding surface of the point being described. To select land-marks that are most easily detected using a particular description, points are selected that have the most distinctive descriptions and vary the least between faces. In order to test the hypothesis that the standard landmarks can be optimised for a particular surface description two descriptions will be used: curvature (a surface measure) and spin images (a signature method). For both de-scriptions, methods will be presented that visualise how each point description compares to other points on the same face and corresponding points on other faces. Landmarks will be chosen from those points that best satisfy the distinctiveness and repeatability criteria.

Curvature was chosen because one type of landmark points is completely defined by the maxima of this surface description and boundary points usually correspond to high curvature regions. When testing for curvature landmarks it is expected that many of the landmark points shown in figure 4.1 and table 4.1 will be found. The second surface description, spin images, has been chosen because it is one of the most well known histogram style surface description with a proven performance.

Additionally, it can be thought of as complementary to curvature since both surface descriptions depend on the surface normal but are sensitive in differing ways. Curvature, being a spatial derivative of the surface normal, is maximised when the normal direction is changing rapidly and is therefore least stable, whereas spin images require a stable normal to function well. Although there are high curvature regions on the face, these are not extreme and therefore both descriptions

(a) Mean Curvature (b) Gaussian Curvature

Figure 4.3: Examples of mean and Gaussian curvature on the mean face from the FRGC dataset, the curvature at each point is calculated using a bi-cubic polynomial surface[64].

can perform well. It is hypothesised that some high curvature points may be more difficult to detect using spin images because the surface description will be less stable.

4.3.1 Curvature

Curvature is the second differential property of a surface, it has been commonly utilised as a feature detection function [59, 53]. In this chapter we use two types of curvature: mean and Gaussian curvature. An example of each type of curvature over the surface of the face is shown in figure 4.3. These curvature measures were chosen because many detectors have been based on these measurements before [59, 53, 79]. Additionally, as stated in section 4.2, many anthropometric and morphometric landmarks are selected because they are a point of highest curvature. Therefore, the highest absolute curvature points on the face will be selected, these are expected to largely correspond to the traditional face landmarks. There are anthropometric landmark points, like the exocanthions, that are expected to be missed by curvature because the area around the landmark is relatively flat.

Curvature Extrema

To select landmarks based on mean or Gaussian curvature, points should be selected that have the highest absolute curvature values. For the selected points to act as good landmarks it is important that they consistently have high curvature values across the entire population of faces and the variation in curvature over the population be minimal for these points. If these criteria are true

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