A simplified approach to merging partial plane image

Acta Montanistica Slovaca Ročník 17 (2012), číslo 3, 234-240 A simplified approach to merging partial plane images Mária Kruláková 1 This paper introduces a method of image recognition based on the gradual generating and analysis of data structure consisting of the 2D space using the difference from the row and column vectors’ sums as an application of the linear algebra. The result of the data processing is a graphical interpretation of the measure of the similarity of the generated results of overlapping of 2 images. Maximal measure of the similarity is a measure for image registration. The study result is to create a list of the images order, in which one follows the other, included in the non-registered set of images that can be used for the final image-stitching Keywords: image-stitchining, image recognition, measure of the similarity Introduction The mathematical model used for the study describes the 2D space and the model application can be classified as image recognition method with consequent registration Oldridge et al. (2009), Szeliski and Coughlan (1997). In order to accomplish the final image-stitching, we need to create a mathematical model first Ch-Y.Chen and Klette (1999). The mathematical expressions consist of the pixel values of the image in the coordination system. Then the expressions of two images are processed for overlapping. Mathematical models applied for the data frame were classified into patch-based and feature-based algorithms (Lowe (1999), Pazzi et al. (2010), Chen and Williams (1993)). Applying them we can define the image as graphical interpretation using similarity of the patches and features. In the linear algebra there is a part devoted to the matrix theory including the algorithms developed in order to find out the rate of similarity based on the linear equations. The process of the algorithms development is based on the assumption that the values generated from the image data frames into the row and column vectors of sums can be applied using them in the formation of the square matrix. The main aim is to determine the similarities based on the estimation out of the differences of the matrixes. In this study the algorithms based on the logical values coming from the data frame of red component applied in the square binary matrices of the image were used for the first stage of the pre-processing of the images. The RGB image is stored as mxnx3 data array that determines red, green and blue component layer for each pixel separately. The image preprocessing is based on the transformation of the colour structure of the image into the binary data matrix that consists of the red component layer only. Binary images, commonly called bi-level, have each pixel stored as a single bit (0 or 1). Pixel with 0 value is displayed in black that described the occurrence of the red component layer of the image. These values of the data frame of the red component layer of the image are gradually summed up into the row and column vectors of sums based on the rows and column structures from each data array of image i. Then the components of the vectors are generated and organized into the data matrix Rredmxi of the row vector of sums and Credixn of the column vector of the sums, where i is defined as number of processed of the data arrays of the images. The first absolute difference Vrow is a result of the 2 data arrays with arranged row vectors of sums into the 2 square matrixes Vi Rred and Vi+1 Rred. The second absolute difference Rv is a diffrence of the first absolute difference T . This will define the level of the of the data matrix Vrow and the transponned matrix made of the Vrow called Vrow similarity of the components arranged in rows of the vector after the development of the row vector of the sums Rrow j from the second absolute difference of the square matrix Rv . The same process is executed for generating of the column vectors of the sums. They will determine the level of similarity of the components arranged in the vector but the column arrangement of the vector’s components after the row vector of sums Crow j from the second absolute difference of the square matrix Cu is created. The arrangement of the components of the row vectors of sums Rrow j a Crow j into square matrices and consequent calculation of the differences of the data arrays of the vectors lead to creating data array of the matrix Fdi f f from which we can create definitive row vector of sums match j . This row vector of sums matchj consists of zero values in its components. Based on these values the similarity in two compared data arrays of the images was determined. 1 Ing. Mária Kruláková., Technical Univerzity of Košice, FBERG, Institute of Control and Informatization of Production Processes, B. Němcovej 3, 040 01 Košice, 234 Acta Montanistica Slovaca Ročník 17 (2012), číslo 3, 234-240 Definitions and notation Red_I is a finite set of the Z 2 . It is a matrix with m rows and n columns with the pixel values of 0 a 1 of binary image as its elements. For m ∈ Z there is row m determined as {Red_I(x, y)2 : y = m}, where m is an index of particular row. For n ∈ Z there is a column n determined as {Red_I(x, y)2 : x = n}, where n is an index of particular column. Sum of the row,Rredm is a number of the elements of the matrix array Red_I generated from the number of the elements of m rows that sums the values of the matrix columns together into the row vector of sums Rredm = ∑n∈Z Red_I(mxm) . Sum of the column, Credn is a number of the elements of the matrix array Red_I generated from the number of the elements of n columns that sums the values of the matrix rows together into the column vector of sums Credn = ∑m∈Z Red_I(nxn) . Then the Rredm is the row vector of sums ( 1) and Credn is the column vector of the sums ( 2) generated from the matrix Rred_I. Rredm = (rred1 , rred2 , rred3 , rred4 , ........., rredm ) (1) Credn = (cred1 , cred2 , cred3 , cred4 , ........., credn ) (2) The result of the scipt createComponentR.m is a matrix Rredmxi . The size of this matrix is [mxi]. The script createComponentR.m has created the row vector of the sums Rredm ( 1) as a sum of the binary values of all 4 images processed from the data arrays of the matrices of each image. For example first element of resulting Rredmx i is a sum of elements in the first column of the Red_I.     Rredmxi =     rred1,i−i+1 rred1,i−i+2 rred1,i−i+3 .. . rred1,i−i+i rred2,i−i+1 rred2,i−i+2 rred2,i−i+3 .. . rred2,i−i+i rred3,i−i+1 rred3,i−i+2 rred3,i−i+3 .. . rred3,i−i+i . . . rredm,i−i+1 . . . rredm,i−i+2 . . . rredm,i−i+3 .. ... . . . . rredm,i−i+i         The result of the scipt createComponentC.m is a matrix Credixn . The size of this matrix is [ixn]. The script createComponentC.m has created the column vector of the sums Credn ( 2) as a sum of the binary values of all 4 images processed from the data arrays of the matrices of each image.   credi−i+1,1 credi−i+2,1 cred (...truncated)