Sparse Representation-based Object Recognition - Sparse Representations and Compressive Sensing for Imaging and Vision - page 65

Algorithm 2: Sparse Representation-based Classification (SRC) Algorithm
Input: D

N .
1. Solve the BP ( 5.7 )orBPDN( 5.8 ) problem.
2. Compute the residual using ( 5.10 ).
3. Identify y using ( 5.11 ).
Output: Class label of y .

N × ( n . L ) , y

∈ R ∈ R

Here the vector Π k has value one at locations corresponding to the class k and zero

for other entries. The class, d , which is associated with an observed vector, is then
declared as the one that produces the smallest approximation error

=

r k (

) .

d arg min

k

y (5.11)

The sparse representation-based classification method is summarized in

Algorithm 2 .
For classification, it is important to be able to detect and then reject the test
samples of poor quality. To decide whether a given test sample has good quality,
one can use the notion of Sparsity Concentration Index (SCI) proposed in [156].
The SCI of a coefficient vector α ∈ R ( L . n ) is defined as

L . max Π i ( α ) 1

α 1

− 1

SCI ( α )= . (5.12)

L − 1

SCI takes values between 0 and 1. SCI values close to 1 correspond to the case
where the test image can be approximately represented by using only images from
a single class. The test vector has enough discriminating features of its class, so has
high quality. If SCI

=

0 then the coefficients are spread evenly across all classes. So
the test vector is not similar to any of the classes and has of poor quality. A threshold
can be chosen to reject the images with poor quality. For instance, a test image can
be rejected if SCI

(

α ) < λ

ˆ

and otherwise accepted as valid, where λ is some chosen

threshold between 0 and 1.

5.2.1 Robust Biometrics Recognition using Sparse

Representation

To illustrate the effectiveness of the SRC algorithm for face and iris biometrics,
we highlight some of the results presented in [156] and [112]. The recognition
rates achieved by the SRC method for face recognition with different features and
dimensions are summarized in Table 5.1 on the extended Yale B Dataset [64]. As it
can be seen from Table 5.1 the SRC method achieves the best recognition rate of
98 . 09% with randomfaces of dimension 504.