This document discusses using sparse representation for face recognition systems. It introduces face recognition as a pattern analysis problem involving identifying people from images or video. The key idea is to use sparse representation to represent face images in terms of a over-complete dictionary of facial features like the eyes, nose, and mouth. The algorithm works by finding the sparsest representation of a query face over the dictionary and classifying it based on which representation has the minimum error. References are provided on sparse representation techniques for computer vision and pattern recognition applications, including face recognition.

1. Sparse
Representation
IN FACE RECOGNITION SYSTEM.
Made by : Saddam Hussain Karar
Student of BSCS university Of Karachi

2. Introduction
 Face is a complex varied high dimensional pattern
 As a scientific issue, face recognition is a typical pattern analysis,
understanding and classification problem, closely related to many disciplines
such as pattern recognition, computer vision, intelligent human-computer
interaction, computer graphics, and
cognitive psychology etc.
 This techniques are believed having a great deal of potential applications in
public security, law enforcement, information security, and financial security .
 The main idea is to use a number of feature points of the person's face such as
nose, mouth, eyebrow, etc.

3. FACE RECOGNITION
 Face recognition is to use the facial characteristic for recognition and
judgment.
 Identification devices whose uses the existing face database, from a given
image or video scene, identify one or a few people's identity.
 Features are divided into the external geometry of the face including the
eyes, nose, mouth.
 Face recognition consists of three main steps: face detection, facial feature
extraction and classification.

4.  For face recognition there are two types of comparisons.
1. Verification.
This is where the system compares the given individual with who that
individual says
they are and gives a yes or no decision.
2. Identification.
This is where the system compares the given individual to all the Other
individuals in the
database and gives a ranked list of matches.

5. FACE RECOGNITION BASED ON
SPARSE REPRESENTATION
 cognitive process to things is often experienced from simple to complex.
 In practice, many complicated things are composed of
many simple elements.
 Sparse Representation based Classification (SRC) seeks a representation of
the query image in terms of the over-complete dictionary, and then
performs the recognition by checking which class yields the least
representation error.

6. Representation of face images
 Suppose that we are given a sufficiently large generic training set.
 Since the high-dimensional face images usually lie on a lower-dimensional subspace or
sub-manifold, a sample in the gallery set, denoted by g, could be represented as g = Rγ,
where R is a subset of the generic training set and γ is the representation coefficient of g
over R.
 Let g(v) denote a sample which has the same identity as g but has some variations of
illumination, expression, or pose w.r.t. g, where subscript v indicates the type of variation.
Similarly, we could represent g(v) as
(1)
 where R(v) is the counterpart of R with variation type v. Since g(v) and R(v) show similar
variations to g and R, the representation coefficients γ and γ(v) should also be similar:
(2)
 Eq. (2) is actually based on the fact that people with similar normal frontal appearance
should also have similar appearance in other variations.

7. Algorithm Flow

8.  By the sparse representation and compressed sensing theory,
If the vector is sparse enough, L0 norm sparse solution problem can be converted to solve the
L1 norm problem. Then we can obtain as following:
 with the i-th class, and other entries are as much as possible to zero. It can approximate the
input text face image as . Then, we classify the input image by assigning it to the
class that minimizes the residual between and , the residual error is expressed as following:

9. REFERENCES
1. Sparse Representation For Computer Vision and
Pattern Recognition
John Wright∗, Member, Yi Ma∗, Senior Member, Julien Mairal†, Member, Guillermo Sapiro‡, Senior Member,
Thomas Huang§, Life Fellow, Shuicheng Yan¶, Member
2. SPARSE REPRESENTATION THEORY AND ITS APPLICATION FOR FACE RECOGNITION
Yongjiao Wang 1, 2, Chuan Wang 3, and Lei Liang2
[1]School of Computer Science, University of Uuban Construction, Pingdingshan, 467036, China
[2]National Engineering Laboratory for Fiber Optical Sensing Technology, Wuhan University of
Technology, Wuhan, 430070, China
[3]College of Computer and Information Engineering, Henan Normal University, Xinxiang,
453007, China