Please summarize the following paragraph below.
Please summarize the following paragraph below. You can do it in jot notes. the paragraph below are about how you can use fractal techniques for facial recognition the number number if brackets are for the images below
ractal theory of iterated contractive transformation has been used in several areas of image processing and computer vision. In this method, similarity between different parts of an image is used for representing of an image by a set of contractive trans- forms on the space of images, for which the fixed point is close to the original image. This concept was first proposed by Barnsley (9) (11) . Jacquin was the first to publish an implementation of fractal image coding in (11) Despite the number of researchers and the proposed methods, several factors can significantly affect face recognition performances, such as the pose, the presence/absence of structural components, facial expressions, occlusion, and illumination variations. Different image compression methods have been focused for a long time to reduce this massive information, but fractal image compression is a relatively recent technique based on representation of an image by contractive transforms, for which the fixed point is close to original im- age.
Suppose we are dealing with a 64*64 binary image in which each pixel can have on of 256 levels (ranging from black to white). Let R1, R2,....., R256 be 4*4 non- overlapping sub-squares of the image (range blocks); and let D be the collection of all 8*8 pixel overlapping sub-squares of the image (Domain blocks) as depicted in Fig .2 The collection D contains 57*57=3249 squares. For each R block, search through all of D blocks a Di D which minimizes equation (12) .There 8 ways to map one square onto another. Each square can be rotated to 4 orientations or flipped and rotated into 4 other orientations as shown in Fig.2 having 8 different affine transformations means comparing 8*3249=25992 domain squares with each of the 256 range squares.
As mentioned before ,a block has 4 times as many pixels as an ,so we must either sub-sample (choose 1 from each 2*2 sub-square of ) or average the 2*2 sub- squares corresponding to each pixel of R when we minimize equation (12) .minimizing equation means two things .First it means finding a good choice for Di second, it means finding a good contrast and brightness setting and for . In equation (13)
A choice of , along with a corresponding and determines a map . The type of image partitioning used for the range blocks can be so different. A wide variety of partitions have been investigated, the majority being composed of rectangular blocks. Different types of range block partitioning were described in[12].In this research we used the simplest possible range partition consists of the size square blocks, that is called fixed size square blocks (FSSB) partitioning. The procedure for finding a frac- tal model for a given image is called encoding; compression; or searching for a fractal image representation. After finding the best match ,fractal elements which of 6 real numbers ( ) are selected as follows ( ) are ( ) coordinates of the D block and its corresponding R block respectively .(e) is the index of affine transformation that makes the best match.(it is a number between 1 and 8) ,(f) is the intensity is a number between 0 and 256.
In this paper, fractal code is introduced in order to extract the face features from the normalized face image based WPD. After fractal coding, where each domain is com- pared with all regions of the image, we obtain a set of transformations which can approximate the face image. Each transformation is represented by parameters of contrast , brightness , spatial coordinates of Range/Domain, and rotation .The output of fractal code is the feature matrix with 2D-dimension used as a
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