## IMAGE COMPRESSION ON SCANNING TECHNIQUES: METHODOLOGY (3)

Threshold T can be calculated using the formula

N= R, G, B layer

i=row,

j=column.

Scanning Techniques

An image is subdivided into a sequence of strips known as “scan lines”. These techniques are Row (raster) order scan and Morton (z) order scan.

(A)Row (raster) Order Scan

Each numbering cell represents a sub-block. Pixels in these blocks are transmitted one after another. Pixels are transmitted serially row after row. Data are acquired in the form from remote sensing, photogrammetry or scanning. Raster algorithms are often simpler and faster, there are many options for storing raster data, some are more efficient in access and processing speed. Raster data is normally stored row by row from the top left.

(B) Morton (z) Order Scan

Block clusters of pixels, can be easily extracted, since pixels in these blocks are transmitted one after another (row ordering does not posses this valuable feature because pixels are transmitted serially row after row). This feature can be handy for spatial image processing, such as resolution reduction. Morton scan, Figure 5:  Morton Order Scan IV. Karhunen-Loeve Transform compared to the conventional row scan, enables faster and efficient average computation of square image blocks.

KLT is an optimal transform for data compression. It minimizes the mean square error between the reconstructed and original image to any other transform. To calculate the KLT of an image, the covariance matrix is first estimated. The estimate is calculated from the set of sequential non overlapping blocks for the image. KLT is constructed from Eigen values and corresponding Eigen vectors of a covariance matrix of data to be transformed. The transform has a number of important performance characteristics for image compression. At moderate compression ratios, very little distortion is visible. As the compression ratio increases more distortion become evident. However because the transform is based on data from the image, some area remain faithfully reproduced at even low bit rates. The Karhunen-Loeve transform is a reversible linear transform that exploits the statistical properties of the vector representation. It optimally decorrelates the input signal.

The covariance matrix,

Cx= E {(x-mx) (x-mx) T}

X=(x1, x2…xn) T,

Where,

X is one of the correlated original vectors set, “T” indicates transpose and n is the number of sub-blocks.

In the appropriate mathematical form,

mx = Mean,

rsb is the sub-block row number csb is the sub-block column number Therefore, KLT will be, y = VT (x-mx)

Calculate the Eigen value and Eigen vector corresponding to the covariance matrix of Cx. It is denoted by V, take the transpose of these values multiplied by the difference between matrix and the mean value.

y = (y1, y2 — y n) T, where y is one of the decorrelated.

Transformed vector set V is a matrix whose columns are the eigenvectors of Cx.

When applying the calculus of eigenvectors, two matrices Arise, V y Cy, being Cy a diagonal matrix, where the elements On its main diagonal are de eigen values of Cy.

If we wish to calculate the covariance matrix of vectors y, Results

C y= E {(y-my) (y-my) T} = E {yyT}

Because, my is a null vector. Besides, Cy is a diagonal Matrix. Depending on the correlation degree between the Original sub-blocks, KLT will be more or less efficient Decorrelating them. Such efficiency depends on how the elements of the main diagonal of the covariance matrix Cy fall. In value, from right to left. The faster they fall in value; the KLT will be more efficient decorrelating them.