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Due to self-occlusions different parts of the object become visible or invisible. After subtracting their average, S, the exemplars are arranged in a data matrix A and the eigenvectors of its covariance matrix C are computed using the singular value decomposition [37] of A.

Additionally, as the shape of the ears is not correctly measured by the scanner, we mark the outline of the ears in the images to get at least the overall shape of the ears right.

While these linear combinations do contain all new faces, they also contain non faces.

### 3D face modelling using a 3D morphable model

The projection of each pixel of the high resolution texture photos onto the geometry is calculated, resulting in three overlapping texture maps. We use a regularization which minimizes the second derivative of the deformation measured along the template surface.

It is very unlikely that we will encounter such a face in the real world. This huge diversity of face images makes their analysis difficult. An alternative approach to construct a 3D Morphable Model is to generate the model directly from a video sequence [12] using nonrigid structure from motion.

Each face is registered to a standard mesh, so that each vertex has the same location on any registered face.

### CGTalk | 3D morphable model face animation by Volker Blanz

We detail two fitting algorithms in Sect. Here, we use a nonrigid ICP method similar to [1], that is applied in the 3D domain on triangulated meshes.

However, the coefficients anomation the linear combination do not have a uniform distribution. It is first registered to the target scans, then the average over all animxtion is used as a new template.

Most other features can change their spatial configuration or position via articulation of the jaw or muscle action e. Each individual face can generate a variety of images when seen from different viewpoints, under different illumination and with different expressions.

The number of modes of variation depends on the size of the mesh, and also is different for shape and texture. The component vec S vectorizes S by stacking its columns. The 3D shape and appearance are modeled by taking linear combinations of a training set of example faces.

## 3D face modelling using a 3D morphable model

The weighting is performed with a reliability value computed from the distance between the scan border and the morohable between surface normal and camera direction. The advantage of this formulation is that the probabilities associated with a shape and texture are readily available. Face images vary widely with respect to the imaging conditions illumination and the position of the camera relative to the face, called pose and with respect to the identity and the expression of the face.

The system captures the face shape from ear to ear Fig. Such models have become a well-established technology which is able to perform various tasks, not only face recognition, but also face morphzble analysis [6] e. To establish correspondencethere exist two different approaches: It progressively deforms a template towards the measured surface.

This fills in unknown regions with the deformed template shape.

## Morphable Models of Faces (Face Image Modeling and Representation) (Face Recognition) Part 1

Wherever no correspondences are found, the deformation is extended smoothly along the template surface by the regularization. A concise description of the variability of human faces on the other hand can not be derived from physics. We model this probability by a Gaussian distribution with midel block diagonal matrix, which assumes that shape and texture are decorrelated.

This introduces a consistent labeling of all Nv 3D vertices across all the scans: Based on these two fitting algorithms, identification results are presented in Sect. We now detail the construction of the face subspace for a 3D Morphable Model.

Then a principal component analysis is performed to estimate the statistics of the 3D shape and color of the faces. This process is iterated a few times involving further manual corrections to achieve a good template shape.

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