Eigenfaces for Recognition

Title: Eigenfaces for Recognition
Author: Matthew Turk and Alex Pentland
Year of Publication: 1991

Eigenfaces is a approach that decomposes face images into a small set of characteristic feature images and is based on information theory. In other words, the approach extracts the information contained in a collection of face images and uses the variation of these images to encode and compare individual face images to do face recognition.

In mathematical terms, treat an image as a vector in a very high dimensional space and regard the eigenvectors as a set of features that characterize the variation between face images. By using principal component analysis(PCA), it is possible to construct the subspace of face images, called “face space”, with lower dimension. Each individual face can be represented in terms of linear combination of the vectors which are referred to as “eigenfaces” because of face-like appearance. Simply, there are operations as following.

(1) Collect several face images for each person.
(2) Calculate the eigenfaces with the highest associated eigenvalues.
(3) For each known individual, project their face images onto the “face space”. Choose a threshold that defines the maximum allowable distance from any face class.
(4) Calculate the pattern vector for each new face images and the distances to each know class.
(5) If the input image is near face space, it is recognized. And if it is near a known face class, it is known and added to the original set of similar face images to recalculate the eigenfaces; otherwise, it is unknown and it may be used to a new face class.

Moreover, it is possible to detect motion after filtering and rescaling the input image appropriately. Calculate the orientation of the motion of the head or use simple symmetric operators can benefit the recognition of the face rotation.

In my opinion, the approach applying PCA to reduce the dimension is not very difficult, and it is really a good method to construct the eigenfaces. That is, face recognition is nothing but extract the features of face images and decide whether a face is efficiently, and this approach reaches the goal. However, the variant background, the scale of the input images, or the illumination still affect the recognition result a lot. The training set also has a significant effect for the precision of the recognition. How to decide the tradeoff between remained dimensions and the precision rate is another problem.

Scale & Affine Invariant Interest Point Detectors

Title:Scale & Affine Invariant Interest Point Detectors
Author: KRYSTIAN MIKOLAJCZYK AND CORDELIA SCHMID
Date of Publication: January 22, 2004

The paper describes two approaches for scale and affine invariant interest point detection. The scale invariant interest point detector, Harris-Laplace detector, combines the Harris detector with automatic scale selection. The algorithm involves a multi-scale point detection and an iterative selection of the scale and the location. The affine invariant interest point detector is initialized by the multi-scale Harris detector. Compute integration and differentiation scale to obtain shape matrix for each interest point. Finally, converge to a local structure in the iterative procedure.

What a pity is that there is a trade off between scale detection and affine detection because of different effects of the two kinds of detector.

Distinctive Image Featuresfrom Scale-Invariant Keypoints

Title:Distinctive Image Featuresfrom Scale-Invariant Keypoints
Author:David G. Lowe
Date of Publication: January 5, 2004

This paper describes an approach, Scale Invariant Feature Transform(SIFT), which transforms image data into scale-invariant coordinates relative to local features. There are several major stages of computation.

(1) The scale-space extrema detection stage searches all scales and image location and uses a cascade filtering approach to identify potential interest points that are invariant to scale and orientation. That is, compute the scale space of an image, a function produced from convolution of a variable-scale Gaussian with an input image, for scale feature description across all possible scales, and then use the function to compute the difference-of-Gaussian and find the maxima and minima of the DOG which can produce the most stable image features.

(2) The keypoint localization stage fits detailed model to determine location and scale at each candidate location and selects keypoints based on measures of their stability.

(3) The orientation assignment stage assigns one or more orientations to each keypoint location based on local image gradient directions; therefore, achieve invariance to image rotation.

(4) The keypoint descriptor stage measures the local image gradients at the selected scale in the region around each keypoint, which allows for significant levels of local shape distortion and change in illumination. In other words, a keypoint descriptor is created by computing the gradient magnitude and orientation at each image sample in a region. After weighted by a Gaussian window, the samples are accumulated into orientation histograms summarizing the contents over subregions. To improve the effects of shift and illumination change, trilinear interpolation, vector normalization and thresholding are taken into consideration.

In experiment on object recognition, an approximation algorithm, Best-Bin-First(BBF), is used for efficient nearest neighbor indexing to find minimum Euclidean distance in matching. Take Hough transform to cluster features. After solving affine parameters by least-square, accept a model if final probability is higher than a threshold.