# Matlab tutorial deutsch pdf

Eigenfaces is the name given to a set of eigenvectors when they are used in the computer vision problem of human face recognition. The Eigenface approach began with a search for a low-dimensional representation of face images. These basis images, known matlab tutorial deutsch pdf Eigenpictures, could be linearly combined to reconstruct images in the original training set. Pentland expanded these results and presented the Eigenface method of face recognition.

Once established, the eigenface method was expanded to include methods of preprocessing to improve accuracy. Multiple manifold approaches were also used to build sets of eigenfaces for different subjects and different features, such as the eyes. The eigenfaces that are created will appear as light and dark areas that are arranged in a specific pattern. This pattern is how different features of a face are singled out to be evaluated and scored. There will be a pattern to evaluate symmetry, if there is any style of facial hair, where the hairline is, or evaluate the size of the nose or mouth. The technique used in creating eigenfaces and using them for recognition is also used outside of face recognition. Prepare a training set of face images.

The pictures constituting the training set should have been taken under the same lighting conditions, and must be normalized to have the eyes and mouths aligned across all images. The average image a has to be calculated and then subtracted from each original image in T. Calculate the eigenvectors and eigenvalues of the covariance matrix S. The eigenvectors of this covariance matrix are therefore called eigenfaces.

Sort the eigenvalues in descending order and arrange eigenvectors accordingly. The number of principal components k is determined arbitrarily by setting a threshold ε on the total variance. The eigenvalues associated with each eigenface represent how much the images in the training set vary from the mean image in that direction. Here is an example of calculating eigenfaces with Extended Yale Face Database B. Note that although the covariance matrix S generates many eigenfaces, only a fraction of those are needed to represent the majority of the faces. Performing PCA directly on the covariance matrix of the images is often computationally infeasible. Let T be the matrix of preprocessed training examples, where each column contains one mean-subtracted image.

Tui is an eigenvector of S. Facial recognition was the source of motivation behind the creation of eigenfaces. For this use, eigenfaces have advantages over other techniques available, such as the system’s speed and efficiency. As eigenface is primarily a dimension reduction method, a system can represent many subjects with a relatively small set of data.

To recognise faces, gallery images, those seen by the system, are saved as collections of weights describing the contribution each eigenface has to that image. When a new face is presented to the system for classification, its own weights are found by projecting the image onto the collection of eigenfaces. This provides a set of weights describing the probe face. These weights are then classified against all weights in the gallery set to find the closest match. Intuitively, recognition process with eigenface method is to project query images into the face-space spanned by eigenfaces we have calculated and in that face-space find the closest match to a face class. The weights of each gallery image only convey information describing that image, not that subject. An image of one subject under frontal lighting may have very different weights to those of the same subject under strong left lighting.