We’re going to discuss a popular technique for face recognition called eigenfaces . And at the heart of eigenfaces is an unsupervised. The basic idea behind the Eigenfaces algorithm is that face images are For the purposes of this tutorial we’ll use a dataset of approximately aligned face. Eigenfaces is a basic facial recognition introduced by M. Turk and A. Pentland [9] .. [6] Eigenface Tutorial

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The main purpose behind writing this tutorial was to provide a more detailed set of instructions for someone who is trying to implement an eigenface based face detection or recognition systems. It is assumed that the reader is familiar at least to some extent with the eigenface technique as described in the original M.

Pentland papers see “References” for more details. The idea behind eigenfaces is similar to a certain extent to the one behind the periodic signal representation eigenfacees a sum of simple oscillating functions in a Fourier decomposition. The technique described in this tutorial, as well as in the original papers, also aims to represent a face as a linear composition of the base images called the eigenfaces.

To download the software shown in video for bit x86 platform, click here. First of all, we have to obtain a training set of grayscale face images. Once we have that, we should change the representation of a face image from a matrix, to a point in -dimensional space. Now here is how we do it: Can it get any more simpler than that?

## Face Recognition with Eigenfaces

Since we are much more interested in the characteristic features of those faces, let’s subtract everything what is common between them, i. The average face of the previous mean-adjusted images can be defined asthen each face differs from the average by the vector. Now we should attempt to find a set of orthonormal tutirial which best describe the distribution of our data. The necessary steps in this at a first glance daunting task would seem to be:.

However, note two things here: To put things into perspective – if your image size isthen the size of the matrix would be. Determining eigenvectors and eigenvalues for a matrix this size would be an absolutely intractable task!

So how do we go about it?

### Chapter Face recognition Eigenfaces

A simple mathematical trick: Then let’s find it’s eigenvectors of of the -th dimension. Now observe, that ifthen. Make sure to thtorialsuch that. We will call these eigenvectors the eigenfaces. Scale them to and render on the screen, to see why. It turns out that quite a few eigenfaces with the smallest eigenvalues can be discarded, so leave only the ones with the largest eigenvalues i. After you have done that – congratulations! We won’t need anything else, but the matrix for the next steps – face detection and classification.

Once the eigenfaces are created, a new face image can be transformed into it’s eigenface components by a simple operation:.

The weights describe the contribution of each eigenface in representing the input face image. We can use this vector for face recognition by finding the smallest Euclidean distance between the input face and training faces weight vectors, i.

Ifwhere is a treshold chosen heuristically, then we eigenfacex say that the input image is recognized as the image with which it gives the lowest score. The weights vector can also be used for an unknown face detectionexploiting the fact that the images of faces do not change radically when projected into the face space, while the projection of non-face images appear quite different. To do so, we can calculate the distance from the mean-adjusted input image and its projection onto face spacei.

Again, if for some treshold also obtained heuristically, for example, by observing for an input set consisting only of face images and a set of non-face images we can conclude that the input image is a face. Turk and Alex P. Eigenfaces for Recognition, Matthew A. Sheng Zhang and Matthew TurkScholarpedia, 3 9: Hi, just thought i’d say that you’ve done a great tutorial from what i understand of it lol. Apologies, but the source code is not available at the moment On the other hand – it’s literally following the maths described in this tutorial, so if eigejfaces worried about implementing these algebraic operations – you might want to look at GSL GNU Scientific Library, you can find a pretty good documentation for it online.

Also, to get a better grip on the method behind eigenfaces tutoriwl, I suggest you to read a bit about PCA Principal Component Analysisthere are quite a few tutorials online on the subject. It is great Tutorial.

### EigenFace | Learn OpenCV

After calculate eigenvectors,eigenvectors is already become [0. Hi Viduruvan, technically there is no reason why you shouldn’t try coloured encoding and see if you obtain a better recognition rate.

It might be the case that digital noise from the webcam will introduce a lot of variance in 8-bit color mode, but No, the eigenvectors in general will not be in the range [ You should scale them to that range if you want to render them on the screen, however, for the face classification step make sure that your eigenvectors are normalized. The values I get for my eigenVectors are floats some are negative valueswhen you say normalized. Eeigenfaces I take the absolute value of the numbers?

You should iegenfaces sure that the length of the each eigenvector the square root of the sum of its squared components is eigenffaces to one. See this link if you need more details: Thanks Bro this is greatest tutorial.

Every thing is explained very beautifully and completely. Thank you very much for this post, it was hands down hutorial best around. I’ve successfully implemented this method. Or did I miss something? I’ve fixed it in the tutorial above, very well spotted! Thank you very much for the helpful explanation on eigenfaces. Did you use OpenCV or its equivalent?

Also, if I successfully captured the training images, how can I align them so that their eyes are in same level and face of the same scale? Thanks for your help. Nice tutorial, it was clear and complete. However, may I ask how you were able to get input from your webcam? I can’t seem to find any sources how. I think there is an error in the dimensions tutirial the “picture-vector” which you obtained by concatenating the rows of the image matrix tutoriall a vector.

Your email address will not be published. Introduction The idea behind eigenfacds is similar to a certain extent to the one behind the periodic signal representation as a sum of simple oscillating functions in a Fourier decomposition. Demonstration To download the software shown in video for bit x86 platform, click here.

Establishing the Eigenface Basis First of all, we have to obtain a training set of grayscale face images. This is how it looks formally: The necessary steps in this at a first glance daunting task would seem to be: Obtain a covariance matrixwhere.

Find the eigenvectors and eigenvalues of. Face Classification Using Eigenfaces Once the eigenfaces are created, a new face image can be transformed into it’s eigenface components by a simple operation: January 1, at January 3, at 9: Great, thank eigenfacse much.

## Eigenfaces for Dummies

Your tutorial helps me a lot. January 12, at 3: January 12, at 4: Thanks, Midorj, glad to hear that! DearGood Artical. Actually why tutogial we need a grayscale face images? June 7, at 3: November 24, at 5: November 25, at Hi Yuya, No, the eigenvectors in general will not be in the range [ Hi, Brilliant tutorial, one question however Thanks for your help Tom.

December 22, at 2: Hi Tom, You should make sure that the length of the each eigenvector the square root tutorisl the sum of its squared components is equal to one. Hi, Brilliant tutorial, one question howeverâ€¦ The values I get for my eigenVectors are floats some are negative valueswhen you say normalized. December 25, at June 3, at 2: June 16, at 5: September 8, at 6: October 21, at 2: Hi, Thank you very much for the helpful explanation on eigenfaces. March 4, at 5: