**Algorithm:**

Let each face image x i, j ½ � is applied with QTP to obtain non-overlapping subblock xs. Also, consider the initial block size Sini, minimum block size as Smin and the Lagrangian multiplier as *α*. The energy summation of the prediction error (ESPE)

Where Fs,n½ � i, j are the filtered responses obtained by applying the prediction filter K<sup>p</sup> along with the predefined directions θ. B<sup>n</sup> is the number of bits spent on signaling the selection of directions. When a sample is predicted from the nearest samples, each candidate direction from (5) is checked and the direction with the smallest ESPE is ultimately selected. The optimal direction which gives the least

The value of the lagrangian multiplier α determines the complexity of the QTP scheme and its value needs to be selected sensibly. Moreover, to detect the local edge details and to suit it to the adaptability of the IDW method, a face image needs to be segmented into partitions of clear orientation bias. To resolve this problem an improved QP scheme is proposed to suit the face identification problem as mentioned in [19]. The 1-D IDW can be simply extended to the 2-D IDW where second dimension lifting is yet again performed in the horizontal direction on high-pass signal H i, j ½ � and low-pass signals L i, j ½ � to generate four sub-bands i.e.

The LBP [7] is estimated with sampling points xp ∈ð Þ 0, … , P � 1 in the neigh-

p�1

p¼0

8 < :

Where tsð Þ d is a threshold function. The sampling points which does not fit within the center of a pixel are bilinearly interpolated [7]. Another extension of

resulting in P � ð Þþ P � 1 3 feature dimension. After obtaining the LBP coded image, codes of the input image XLð Þ i, j pixels are formed into a histogram as a

> 8 < :

8,1, the feature dimension is 59 [18].

LBPP,R <sup>¼</sup> <sup>X</sup>

tsð Þ¼ d

LBP is the uniform patterns and it is mapped from LBPP,R to LBPu2

F Xf g <sup>L</sup>ð Þ¼ i, j <sup>l</sup> ,F y� � <sup>¼</sup>

� � at a radial distance given by R [7],

� �*:*2p (8)

P,R [18],

, l ¼ 0, 1, 2 … , n � 1 (10)

(9)

ts*:* xp � xm

1, dð Þ≥ 1

0, dð Þ< 1

1, if y is true

0, if y is false

Where n is the number of different labels produced by the LBP operator. With

xs k k ½ �� i, j Fs,n½ � i, j <sup>2</sup>

θ<sup>s</sup> ¼ arg minn f g ESPEs,n (7)

<sup>2</sup> <sup>þ</sup> <sup>α</sup>B<sup>n</sup> (6)

for each block is computed as [19],

*Biometric Systems*

value of ESPE is selected as,

LH i, j ½ �, LL i, j ½ �, HH i, j ½ �, and HL i, j ½ �.

borhood of a center pixel xm ic, jc

**3. Local binary patterns**

feature descriptor,

Hl <sup>¼</sup> <sup>X</sup> i, j

the usage of LBPu2

**38**

ESPEs,n <sup>¼</sup> <sup>X</sup>

i, j∈Rs,n

	- **1.1.** Consider the input face image X.
	- **1.2.** Resize the image to the resolution of 128 � 128 pixels.
