1 / 23

Face detection and recognition

Face detection and recognition. Many slides adapted from K. Grauman and D. Lowe. Face detection and recognition. Detection. Recognition. “Sally”. Consumer application: iPhoto 2009. http://www.apple.com/ilife/iphoto/. Consumer application: iPhoto 2009. Can be trained to recognize pets!.

Download Presentation

Face detection and recognition

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.


Presentation Transcript

  1. Face detection and recognition Many slides adapted from K. Grauman and D. Lowe

  2. Face detection and recognition Detection Recognition “Sally”

  3. Consumer application: iPhoto 2009 http://www.apple.com/ilife/iphoto/

  4. Consumer application: iPhoto 2009 • Can be trained to recognize pets! http://www.maclife.com/article/news/iphotos_faces_recognizes_cats

  5. Consumer application: iPhoto 2009 • Things iPhoto thinks are faces

  6. Outline • Face recognition • Eigenfaces • Face detection • The Viola & Jones system

  7. The space of all face images • When viewed as vectors of pixel values, face images are extremely high-dimensional • 100x100 image = 10,000 dimensions • However, relatively few 10,000-dimensional vectors correspond to valid face images • We want to effectively model the subspace of face images

  8. The space of all face images • We want to construct a low-dimensional linear subspace that best explains the variation in the set of face images

  9. Principal Component Analysis • Given: N data points x1, … ,xNin Rd • We want to find a new set of features that are linear combinations of original ones:u(xi) = uT(xi – µ)(µ: mean of data points) • What unit vector u in Rd captures the most variance of the data? Forsyth & Ponce, Sec. 22.3.1, 22.3.2

  10. Principal Component Analysis • Direction that maximizes the variance of the projected data: N Projection of data point N Covariance matrix of data The direction that maximizes the variance is the eigenvector associated with the largest eigenvalue of Σ

  11. Principal component analysis • The direction that captures the maximum covariance of the data is the eigenvector corresponding to the largest eigenvalue of the data covariance matrix • Furthermore, the top k orthogonal directions that capture the most variance of the data are the k eigenvectors corresponding to the k largest eigenvalues

  12. Eigenfaces: Key idea • Assume that most face images lie on a low-dimensional subspace determined by the first k (k<d) directions of maximum variance • Use PCA to determine the vectors or “eigenfaces” u1,…uk that span that subspace • Represent all face images in the dataset as linear combinations of eigenfaces M. Turk and A. Pentland, Face Recognition using Eigenfaces, CVPR 1991

  13. Eigenfaces example • Training images • x1,…,xN

  14. Eigenfaces example Top eigenvectors: u1,…uk Mean: μ

  15. Eigenfaces example Principal component (eigenvector) uk μ + 3σkuk μ – 3σkuk

  16. Eigenfaces example • Face x in “face space” coordinates: =

  17. Eigenfaces example • Face x in “face space” coordinates: • Reconstruction: = = + ^ x = µ + w1u1+w2u2+w3u3+w4u4+ …

  18. Reconstruction demo

  19. Recognition with eigenfaces • Process labeled training images: • Find mean µ and covariance matrix Σ • Find k principal components (eigenvectors of Σ) u1,…uk • Project each training image xi onto subspace spanned by principal components:(wi1,…,wik) = (u1T(xi – µ), … , ukT(xi – µ)) • Given novel image x: • Project onto subspace:(w1,…,wk) = (u1T(x– µ), … , ukT(x– µ)) • Optional: check reconstruction error x – x to determine whether image is really a face • Classify as closest training face in k-dimensional subspace ^ M. Turk and A. Pentland, Face Recognition using Eigenfaces, CVPR 1991

  20. Recognition demo

  21. Limitations • Global appearance method: not robust to misalignment, background variation

  22. Limitations • PCA assumes that the data has a Gaussian distribution (mean µ, covariance matrix Σ) The shape of this dataset is not well described by its principal components

  23. Limitations • The direction of maximum variance is not always good for classification

More Related