# How to choose (and many) threshold in Eigenface?

I edited my question trying to make it as short and precise.

I am developing a prototype of a facial recognition system for my Graduation Project. I use Eigenface and my main source is the document Turk and Pentland. It is available here: http://www.face-rec.org/algorithms/PCA/jcn.pdf.

My doubts focus on step 4 and 5.

I can not correctly interpret the number of thresholds: If two types of thresholds, or only one (Notice that the text speaks of two types but uses the same symbol). And again, my question is whether this (or these) threshold(s) is unique and global for all person or if each person has their own default.

I understand the steps to be calculated until an matrix O() of classes with weights or weighted. So this matrix O() is of dimension M'x P. Since M' equal to the amount of eigenfaces chosen and P the number of people.

What follows and confuses me. He speaks of two distances: the distance of a class against another, and also from a distance of one face to another. I call it D1 and D2 respectively. NOTE: In the training set there are M images in total, with F = M / P the number of images per person.

I understand that threshold(s) should be chosen empirically. But there must be a way to approximate. I was initially designing a matrix of distances D1() of dimension PxP. Where the row vector D(i) has the distances from the vector average class O(i) to each O(j), j = 1..P. Ie a "all vs all."

Until I came here, and what follows depends on whether I should actually choose a single global threshold for all. Or if I should be chosen for each individual value. Also not if they are 2 types: one for distance classes, and one for distance faces.

I have a theory as could proceed but not so supported by the concepts of Turk:

Stage Pre-Test:

Gender two matrices of distances D1 and D2: In D1 would be stored distances between classes, and in D2 distances between faces. This basis of the matrices W and A respectively.

Then, as indeed in the training set are P people, taking the F vectors columns D1 for each person and estimate a threshold T1 was in range [Min, Max]. Thus I will have a T1(i), i = 1..P

Separately have a T2 based on the range [Min, Max] out of all the matrix D2. This define is a face or not.

Step Test:

Buid a test set of image with a 1 image for each known person Itest = {Itest(1) ... Itest(P)}

For every image Itest(i) test:

1. Calculate the space face Atest = Itest - Imean

2. Calculate the weight vector Otest = UT * Atest

3. Calculating distances:

dist1(j) = distance(Otest, O (j)), j = 1..P

Af = project(Otest, U)

dist2 = distance(Atest, Af)

1. Evaluate recognition:

MinDist = Min(dist1)

For each j = 1..P

If dist2 > T2 then "not is face" else:

If MinDist <= T1(j) then "Subject identified as j" else "subject unidentified"

Then I take account of TFA and TFR and repeat the test process with different threshold values until I find the best approach gives to each person.

Already defined thresholds can put the system into operation unknown images. The algorithm is similar to the test.

I know I get out of "script" of the official documentation but at least this reasoning is the most logical place my head. I wondered if I could give guidance.

EDIT:

i No more to say that has not already been said and that may help clarify things.

Could anyone tell me if I'm okay tackled with my "theory"? I'm moving into my project, and if this is not the right way would appreciate some guidance and does not work and you wrong.

• Welcome to SciComp! I suggest that you shorten your question a bit. As written, it's currently very long (4 screens), and asks multiple questions (five or six, at least). Stick to one question, and try to make it brief, but self-contained. – Geoff Oxberry Mar 10 '15 at 20:46
• @GeoffOxberry Thanks for answering my concern. I'll try to keep it short and precise. English is not my primary language. It will take a while. – Delphius Mar 10 '15 at 22:11
• If is need to clarify something, please let me know they did. – Delphius Mar 11 '15 at 18:10
• Could anyone tell me if I'm okay tackled with my "theory"? I'm moving into my project, and if this is not the right way would appreciate some guidance and not waste time on something wrong. – Delphius Mar 12 '15 at 13:52