Posted on January 2, 2013
Looking for Eigenvalue and Eigenvalue Eigenvector

Eigenvalue of a square matrix is ​​the characteristic polynomial of the matrix; if λ is the eigenvalue of A it will be equivalent to a linear equation (A - λI) v = 0 (where I is the identity matrix) which has a non-zero solution v (an eigenvector), so it will be equivalent to the determinant.


 det (A - λI) = 0

Function p (λ) = det (A - λI) is a polynomial in λ because the determinant is calculated by the sum of product. All the eigenvalues ​​of a matrix A can be calculated by solving the equation pA (λ) = 0. If A is a matrix of size nxn, then pA has degree n and A would have at most n eigenvalues.

Looking for eigenvector

If the eigenvalue λ is known, eigenvector can be found by solving:

 (A - λI) v = 0

In some cases it can be found without eigenvalue matrix, for example:



wherein the characteristic number polynomialnya is λ2 + 1 so that the eigenvalue is a complex number i, -i. Eigenvector associated also not real. Continue reading →

Posted in Digital Image | 1 Reply
January
02
Eigenface
Posted on January 2, 2013
Theory Eigenface

The introduction Eigenface Jerrnan language derived from the prefix "eigen", which means "alone / individual". Eigenface method is considered as the first automatic face recognition technology ever invented. This theory was developed by Turk and Pentland.

This theory was developed by dividing a facial image into data sets characteristic feature called eigenface. This characteristic feature is the main component (principal component) of initial training set of face images. Research conducted by Carey and Diamond shows that the facial features of a direct relationship between the individual and the feature can not match the human ability to observe and recognize faces.

Eigenface is a set of face standardize ingredient derived from statistical analysis of many facial image (Layman in Al Fatta, Hanif, 2009).

To produce Eigenface, a collection of digital images of the human face taken in the same lighting conditions then normalized and processed at the same resolution (eg mxn), then was treated as a vector image dimensions mxn where the components are drawn from the value of the image pixel.

Eigenvalue and eigenvector

Transformation of the room such as translation, rotation, reflection, stretchting and compression, or a combination of these transformations, can be visualized with the resulting effect on the vector. Vectors can be visualized as an arrow pointing 1 (one) point to another point.

Eigenvector of a transformation vector is a vector that does not change or only multiplied by the scale factor after the transformation.
Eigenvalue of the eigenvector is a scale factor which multiplied eigenvector.


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January
02
Cropping operations
Posted on January 2, 2013
Cropping

Cropping is the process of cutting the image at specific coordinates in the image area. To cut a part of the image used two coordinates, the coordinates of an early start to the image coordinates and the coordinates of cutting end result which is an end point coordinates of the image of the cuts. So that will form the wake rectangle which each pixel is in an area specific coordinate will be stored in the new image.

Cutting process image

The original image cropping Results



From the picture above is explained that the process of cutting the image. At first pixel of the original image size is 5 × 5 pixels, after the cutting process at the beginning of the coordinate (1,1) and end coordinates (3,3) or by 3 pixel width and height of 3 pixels will form a new image with a size of 3 × 3 pixels. The new image containing the pixel value of the coordinate (1,1) to coordinate (3,3).

Posted in Digital Image | 1 Reply
January
02
Grayscale
Posted on January 2, 2013
Minimum value and maximum of

Gray scale image has a minimum value (normally = 0) and maximum value. The amount of the minimum and maximum possible values ​​depend on the number of bits used (generally uses 8 bits). Examples for 4-bit gray scale, the number of possible value is 24 = 16, and the maximum value is 24-1 = 15, while for the 8-bit gray scale, the number of possible value is 28 = 256, and the maximum value is 28-1 = 255.

Array grayscales

Digitally a grayscale image can be represented in the form of a two-dimensional array. Each element in the array indicates the intensity (greylevel) of the image at the corresponding position coordinates. When an image is represented in 8 bits then it means the image there are 28 or 256-level grayscale, (usually worth 0-255), where 0 indicates the level of intensity of the darkest and 255 show the intensity of the brightest. Each element in the array above is referred to as picture elements or commonly known as pixels. By making changes in the intensity of each pixel, the overall representation of the image will change. The image represented by the matrix M x N has a certain intensity at a particular pixel. The position of picture elements (i, j) and the coordinates (x, y) is different.

The number of pixels starting from the upper left corner while the x and y coordinates are at the bottom left corner.



This image format called gray scale because in general the color used is between the minimum and the color black as white as the color of which is the maximum so that the color gray.

Being colored image conversion of gray image

The equation used to convert color images into gray scale image is as follows (Basuki, A: 2005):

 Gray = (R + G + B) / 3

Conversion of color information of an image to gray scale can also be done by members of weights on each color element (Achmad: 2005), so that the above equation is modified into:

 Gray = WRR + wGG + WBB

 with wR, WG, and WB respectively the weights to the elements of red, green and blue. NTSC (National Television System Committee) defines weights for converting color images to gray scale is as follows:

        wR = 0.299 WG = 0.587 Wb = 0.114

For a color image pixel value of an example is X, then to get the value of Red, Green, Blue can use the formula:

Blue = X / 216

Green = (X - Blue * 216) / 28

Red = X - Blue * 216 - Green * 28

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January
02
Principal Component Analysis (PCA) / Projection Eigen
Posted on January 2, 2013
PCA history

PCA is a statistical technique that has been used widely both in terms of facial recognition and pattern recognition of an image. Methods of Principal Component Analysis (PCA) was first created by statisticians and was discovered by Karl Pearson in l90l who wear them in the field of biology. Then there are no new developments in the technique, and. The new development began rapidly at the end of l930 and early 1940. After the development was reduced for a while until the computer has been successfully designed so that they can apply these techniques to problems makes sense. In 1947 this theory appears again and quite independent as probability theory invented by Karhunen, and later developed by Loeve in l963, so this theory is also called the Karhunen-Loeve transform the field of telecommunications.

PCA technique

PCA is a linear transformation that is used for data compression. PCA is a statistical technique that is useful in the field of recognition, classification and image data compression. PCA is also a common technique used to draw the features of the data on a high-dimensional scale. By transforming the image into the eigenfaces linearly, projecting the image into the form of an n-dimensional scale, which reveal the properties of the sample the clearest along the coordinates. PCA projecting the image into the subspace, and calculate the variation of the image. In other words, PCA is a linear transformation to define a new coordinate system of the dataset. PCA technique can reduce the dimensions of the dataset without not omit important information from the dataset.

Pattern Recognition Posted in | Leave a reply
January
02
Theory Face Recognition (Face Recognition)
Posted on January 2, 2013
The steps in the process of facial recognition systems are different from one another. This is due to factors such as the size of the database or a training set of face images, the type of input used (the image of the photo or video), noise (noise) to the image and others.

Facial Recognition Process

Basically the face recognition process is divided into several sections as in the block diagram below:



Each section in the above diagram can be done through different methods. For example, to detect a face, we can use feature-based method (feature-based methods) to detect the facial features (eyes, nose, mouth), or can also use skin color detection. Continue reading →

Pattern Recognition Posted in | Leave a reply
January
02
Pattern Recognition Approach
Posted on January 2, 2013
Pattern recognition applications can be created with multiple approaches. There are approaches that use statistical basis to produce a pattern. Another approach uses the structure of a pattern which provides fundamental information for pattern recognition. Another approach is to build and train an architecture that accurately associate specific input pattern with the expected response.

Pattern Recognition statistical approach

Stastistikal pattern recognition assumes a statistical basis for classification algorithms. A group of measurement characteristics menunujukkan characteristics extracted from the input data and used to determine each vector features into a single class. Characteristic (feature) is assumed to be produced naturally, so that the model concerned is classes probability or probability density function (Probability Density Function), which has been conditioned.

Pattern disaggregated statistical models of traits.
Statistical model is defined as a class conditional density function space.
Pr (x | ci) with i = 1, 2, 3, ..., N

Pattern Recognition syntactic approach

An approach to an image pattern by analyzing the structure of a pattern of image

Patterns disaggregated structural similarity measure.
"Knowledge" represented a formal grammar or a description of the relational hierarchy generates descriptions of the complex pattern composed of a pattern of simpler parts.
 Neural Pattern Recognition Approach

The third approach that neural pattern recognition, this method is a combination of both previous statistical way and syntactically, it means that the approach in this way will keep all the facts of the object. So the more often the more intelligent training system is also a system generated. This approach is part of an artificial neural network to identify patterns.

Sorting is done based on the responses of a network signal processors (neurons) of the input stimulus (pattern).
"Knowledge" is stored in synaptic connections between neurons and weighting.