PY - Y1 - N2 - In this paper we revisit the process of constructing a high resolution 3D morphable model of face shape variation. We demonstrate how the statistical tools of thin-plate splines and Procrustes analysis can be used to construct a morphable model that is both more efficient and generalises to novel face surfaces more accurately than previous models. We also reformulate the probabilistic prior that the model provides on the distribution of parameter vector lengths. This distribution is determined solely by the number of model dimensions and can be used as a regularisation constraint in fitting the model to data without the need to empirically choose a parameter controlling the trade off between plausibility and quality of fit. As an example application of this improved model, we show how it may be fitted to a sparse set of 2D feature points approximately This provides a rapid means to estimate high resolution 3D face shape for a face in any pose given only a single face image.

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We demonstrate how the statistical tools of thin-plate splines and Procrustes analysis can be used to construct a morphable model that is both more ef? We also reformulate the probabilistic prior that the model provides on the distribution of parameter vector lengths.

This distribution is determined solely by the number of model dimensions and can be used as a regularisation constraint in? As an example application of this improved model, we show how it may be? This provides a rapid means to estimate high resolution 3D face shape for a face in any pose given only a single face image. We present experimental results using ground truth data and hence provide absolute reconstruction errors.

On average, the per vertex error of the reconstructed faces is less than 3. This is a low-dimensional parametric model of 3D face shape and texture. To solve the problem of face shape recovery, the challenge is to? This amounts to solving a highly complex nonlinear minimization problem which requires estimation of: 1. This approach has been shown to be robust and provides high accuracy on real world data.

Indeed, the estimated appearance parameters contain useful identity information and provide a route to state-of-the-art performance in face recognition across pose and illumination variation from a single gallery image [16]. The most recent work in this area has focused on developing more sophisticated morphable model?

At the expense of simplifying the re? On the other hand, both Romdhani and Vetter [17] and Moghaddam et al. In both cases, they avoid the problems of local minima in the optimisation function by using features derived from the input images rather than the intensity data itself. Romdhani and Vetter [17] used edges and specular highlights to obtain a smooth cost function, while Moghaddam et al.

Knothe et al. All of these methods are based on explicitly modelling the underlying physical processes that give rise to an observed image, by rendering each hypothesised appearance. It is not clear that this is either necessary, nor the most practical approach. As already mentioned, the optimisation is complex and prone to becoming trapped in local minima.

An alternative approach proposed by Blanz et al. Introduction The problem of estimating 3-dimensional face shape from one or more images has attracted considerable attention in recent years [4, 8, 10, 11, 18, 19]. The primary motivation for this work is that 3D shape information provides a pose and illumination invariant description of a face, which can either be used for recognition directly [4, 7, 18], or to produce illumination and pose normalised images for input to a 2D recognition system [2, 18, 19].

The bene? Although shape-from-shading provides a possible route to estimating facial shape, the most promising results have been obtained using a statistical model of 3D face shape. Restrictions apply. In this case, shape parameters are found by minimising the error between the observed and predicted positions of the feature points in the image plane. The model is also used as a regularisation constraint to balance quality of?

In this paper we make a number of contributions to the use of morphable models for face shape recovery. First, we provide a new framework for constructing a 3D morphable model from a training set of facial meshes.

By making use of techniques from the statistical shape analysis literature, we show how to construct a morphable model whose captured variance is of greater utility in the sense that the generalisation error i. Second, we show that the distribution of parameter vector lengths follows a chi-square distribution and discuss how the parameters of this distribution can be used as a regularisation constraint on the length of parameter vectors.

Finally, we use our improved model and statistical prior in the setting of? We verify empirically that our analytical prediction of the parameter vector length constraint coincides with the optimum operating point of our algorithm. Morphable model construction The process of constructing a morphable model is divided into three stages: 1. In each case, we outline previous methods before describing our approach. We begin by describing how our approach allows us to construct a morphable model as a shape space.

However, the statistical analysis of continuous curves or surfaces which contain only relatively sparse salient points is not so well developed.

For example, only a relatively small proportion of the face surface contains salient points which may be identi? The remainder of the face comprises large areas of smoothly shaded, textureless surface. It is therefore not obvious how a landmark-based statistical approach can be applied to model the variations in the face surface.

The morphable model of Blanz and Vetter [3] described above is based on transforming a set of face surfaces into a vector space such that any convex combination of members of the training set results in a viable new face.

However, their model is not a shape space. They only coarsely remove the effects of rotation, translation and scale before the dense correspondence between samples is known. In other words, they ultimately treat every vertex in the model as a landmark but do not remove pose effects with respect to these landmarks.

Our work closely follows the semilandmark approach of Bookstein [6]. This is done in a principled manner by minimising a physically motivated bending energy of the data about its Procrustes average.

We use Procrustes analysis to obtain pose free shape vectors. This combination of techniques allows us to construct a dense 3D morphable model as a shape space. This is possible because a modi? These correspondences are based on matching regions with similar colour and topography to a reference face and subsequently resampling every face in a consistent manner.

The advantage of their approach is that a model may be constructed automatically with little manual intervention. However, the similarity measure used to? It is unclear which features should be chosen and how their relative importance should be weighted. Moreover, the utility of different features will vary spatially and between samples.

For example, when registering a sample with a beard to one without, texture is an unreliable feature to use. The second problem is that large areas of the face contain no salient structures, 2. The model is learnt from a sample of high resolution 3D face scans. There is a comprehensive toolbox of techniques available for the statistical analysis of shape using data which is provided in terms of coordinates of named point locations or landmarks.

This group of techniques has become to be known as geometric morphometrics. A landmark is a hypothesis of equivalence under a particular measure of similarity, e. In effect, the implied meaning of a landmark point is, in some sense, the Authorized licensed use limited to: University of Science and Technology of China. For example, the forehead and cheeks. In these regions the calculated? Blanz and Vetter [3] overcome this problem by smoothing and interpolating the?

Finally, the choice of reference face will affect the quality of detected correspondences and ultimately the? At the expense of introducing some manual intervention, we suggest an alternative approach which offers potentially more stable performance. Because our method does not require the selection of a reference face, only one possible model can be constructed from a given set of training data. We commence with a set of face surfaces obtained by a Cyberware PS laser range scanner.

These surfaces are parameterised in cylindrical coordinates. This provides a convenient representation of the facial manifold in 2 dimensions, u, v.

A set of sparse 2D landmark points are manually identi? The landmark points are chosen such that they can be reliably located on all training samples. With these sparse, but reliable, correspondences in hand, the mean coordinates of each landmark point are found. The x, y and z coordinates of each vertex can be expressed as a function in u, v space, e.

Similarly for each colour channel in the texture map. We warp the landmark points of each sample to the mean landmarks. We interpolate this warp using a physically motivated bending energy, through the application of a thin-plate spline warp [5]. Finally, we resample the vertex coordinate functions in a consistent manner across all faces.

The result is that a point u, v corresponds to the same point on each face in the training set, i. This process is demonstrated in Figure 1. Construction of the morphable model is done of? Hence the manual processing required by our methods is an acceptable burden if it results in more accurate correspondences. Figure 1. Shows the correspondence of scans based on the principle of thin-plate splines. Using two sets of 2D points white dots , a novel scan left is warped to the mean scan right using the thin-plate spline function?

We propose instead to use Procrustes analysis as a rigorous means to remove pose effects without having to choose a reference face the reference face is instead the Procrustes mean which is iteratively updated. With our sample of faces in dense correspondence forming a vector space we can proceed with shape alignment using the standard tools of statistical shape analysis.

The idea here is to remove any effects of scale, rotation and translation to obtain a pure shape model that captures only variation in identity. Our aim is to transform the shape vectors into a shape space. We do this by aligning the shape vectors to a common coordinate frame using generalised Procrustes analysis. This is an iterative procedure which alternates between aligning all samples to the current estimate of the mean shape and then re-estimating the mean from the aligned vectors. These two steps are iterated until convergence.

Our mean shape estimate for m face scans is the Procrustes mean: m 1 xi. The raw face meshes are marked with a small number of feature points and a 3D-3D transform is used to align each face to a reference face. In other words, when this alignment takes place, the dense correspondence between faces is unknown and the scale, translation and rotation necessary to register each face to the reference is only a very coarse approximation.

Find the Euclidian mean of the face shape vectors 1. Rescale the the mean shape vector to unit length 2.

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## 3D MORPHABLE FACE MODELS REVISITED PDF

William A. BronsteinMichael M. Topics Discussed in This Paper. Their combined citations are counted only for the first article.

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Nikora Sparse matrix Reconstruction filter. Reconstruction and validation, Reisited Vision and Applicationspp. Gender Classification using Shape from Shading. Procrustes analysis Ground truth Thin plate spline. We demonstrate how the statistical tools of thin-plate splines and Procrustes analysis can be used to construct a morphable model that is both more efficient and generalises to novel movels surfaces more accurately than previous models. GrahamActive shape models? From This Paper Figures, tables, and topics from this paper.

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We demonstrate how the statistical tools of thin-plate splines and Procrustes analysis can be used to construct a morphable model that is both more efficient and generalises to novel face surfaces more accurately than previous models. We also reformulate the probabilistic prior that the model provides on the distribution of parameter vector lengths. This distribution is determined solely by the number of model dimensions and can be used as a regularisation constraint in fitting the model to data without the need to empirically choose a parameter controlling the trade off between plausibility and quality of fit. As an example application of this improved model, we show how it may be fitted to a sparse set of 2D feature points approximately This provides a rapid means to estimate high resolution 3D face shape for a face in any pose given only a single face image. We present experimental results using ground truth data and hence provide absolute reconstruction errors. On average, the per vertex error of the reconstructed faces is less than 3.

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We demonstrate how the statistical tools of thin-plate splines and Procrustes analysis can be used to construct a morphable model that is both more efficient and generalises to novel face surfaces more accurately than previous models. We also reformulate the probabilistic prior that the model provides on the distribution of parameter vector lengths. This distribution is determined solely by the number of model dimensions and can be used as a regularisation constraint in fitting the model to data without the need to empirically choose a parameter controlling the trade off between plausibility and quality of fit. As an example application of this improved model, we show how it may be fitted to a sparse set of 2D feature points approximately This provides a rapid means to estimate high resolution 3D face shape for a face in any pose given only a single face image. We present experimental results using ground truth data and hence provide absolute reconstruction errors. On average, the per vertex error of the reconstructed faces is less than 3.