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**Context 1**

... magnification is a process of obtaining an image at resolution higher than taken from image sensor. Image magnification synonyms are interpolation, enlargement, zooming, etc. To create higher resolution image, previous image must be complemented with new pixels and their intensity must be calculated. Commonly, image magnification is accomplished through convolution of the image samples with a single kernel – typically the nearest neighbour [1, 2] bilinear, bicubic [3] or cubic B-spline kernel [4] interpolation and training-based algorithms [5, 6]. Intensity surface can be explained as landscape with hills and hollows, rides and valleys. Any 3 dimensional (3D) surfaces, with some approximation, can be created from triangles. Look at the image intensity as 3D surface build from triangles where vertexes are image pixels with intensity as z axis (Fig. 1). To magnify image, new image must be complemented with new pixels, added necessary columns and rows of pixels, and calculated new pixels intensity. In this work is made assumption, that new pixels intensity is situated on suitable triangle planes (Figure 1). During image magnification contours are blurred because of slope sharpness reduction. This is the main problem for all known magnification methods. Look at small part of intensity surfaces in Figure 2. It is evident, that, in this situation, sharpness of slope is better when triangles are created like in Figure 2b than in Figure 2a. Accordingly the base of both triangles must be diagonal with less intensity gradient. That partially reduce magnification blur. So must be located distinctive points on intensity surface and different magnification algorithm applied. There are two things that must be solved: choose the best arrangement of triangles and calculate new pixels intensity. To explain triangle based magnification method, get four neighbouring pixels from original image and create two triangles planes throws these pixels as vertexes (black dots in Figure 2). These pixels 3D coordinates is known, because they are taken from original image. White dots are new pixels that were inserted to magnify image. Their intensity must be calculated. Early was decided, that new pixels will situated on two triangles planes. Triangle plane can be formulated as equation of three coplanar vectors over spatial points M 00 ( 0 , 0 , Z 00 ) , M 10 ( S , 0 , Z 10 ) , M 01 ( 0 , S , Z 01 ) where x and y coordinates are related with magnification S ...

**Context 2**

... magnification is a process of obtaining an image at resolution higher than taken from image sensor. Image magnification synonyms are interpolation, enlargement, zooming, etc. To create higher resolution image, previous image must be complemented with new pixels and their intensity must be calculated. Commonly, image magnification is accomplished through convolution of the image samples with a single kernel – typically the nearest neighbour [1, 2] bilinear, bicubic [3] or cubic B-spline kernel [4] interpolation and training-based algorithms [5, 6]. Intensity surface can be explained as landscape with hills and hollows, rides and valleys. Any 3 dimensional (3D) surfaces, with some approximation, can be created from triangles. Look at the image intensity as 3D surface build from triangles where vertexes are image pixels with intensity as z axis (Fig. 1). To magnify image, new image must be complemented with new pixels, added necessary columns and rows of pixels, and calculated new pixels intensity. In this work is made assumption, that new pixels intensity is situated on suitable triangle planes (Figure 1). During image magnification contours are blurred because of slope sharpness reduction. This is the main problem for all known magnification methods. Look at small part of intensity surfaces in Figure 2. It is evident, that, in this situation, sharpness of slope is better when triangles are created like in Figure 2b than in Figure 2a. Accordingly the base of both triangles must be diagonal with less intensity gradient. That partially reduce magnification blur. So must be located distinctive points on intensity surface and different magnification algorithm applied. There are two things that must be solved: choose the best arrangement of triangles and calculate new pixels intensity. To explain triangle based magnification method, get four neighbouring pixels from original image and create two triangles planes throws these pixels as vertexes (black dots in Figure 2). These pixels 3D coordinates is known, because they are taken from original image. White dots are new pixels that were inserted to magnify image. Their intensity must be calculated. Early was decided, that new pixels will situated on two triangles planes. Triangle plane can be formulated as equation of three coplanar vectors over spatial points M 00 ( 0 , 0 , Z 00 ) , M 10 ( S , 0 , Z 10 ) , M 01 ( 0 , S , Z 01 ) where x and y coordinates are related with magnification S ...

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## Citations

... Evaluation of pixels values[37] This code allows evaluation of accuracy of processing. Quantitative image quality parameters were evaluated by determination following errors[38][39]x(i, j) is the color value of the original image at (i, j), color value of the encoding image, s, l are maximal indices of row and column pixels. b) Laplacian Mean Square Error (ELapl): ...

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... They can avoid jagged edges, but these methods introduce visible artifacts in the magnified images. Yu et al. proposed triangulation method [10,11], however this method fails to give curved edges specially at large scaling factors. M o r se and Schwar tzwald [12 ] p r op o sed a level-set reconstruction method to solve the problem of jagged edges. ...

The technology of computer graphics and digital cameras are prevalent. High-resolution display and printer are available. High-resolution images are needed in order to produce high quality display images and high quality prints for use in desktop publishing, large artistic printing, mobile phone etc. However, since high-resolution images are not usually provided, there is a need to magnify the original images. This paper proposes an algorithm for image magnification by linear interpolation, which is better than some of the prevalent methods such as pixel replication, bilinear interpolation and bicubic interpolation. The proposed algorithm uses linear interpolation method to magnify pixels that lie in the perimeter, whereas it uses directed bilinear interpolation method to magnify the interior region inside the magnified blocks. Determination of the right direction for interpolation is the key for achieving better performance of the proposed algorithm.

The technology of computer graphics and digital cameras are prevalent. High-resolution display and printer are available. High-resolution images are needed in order to produce high quality display images and high quality prints for use in desktop publishing, large artistic printing, mobile phone etc. However, since high-resolution images are not usually provided, there is a need to magnify the original images. This paper proposes an algorithm for image magnification by linear interpolation, which is better than some of the prevalent methods such as pixel replication, bilinear interpolation and bicubic interpolation. The proposed algorithm uses linear interpolation method to magnify pixels that lie in the perimeter, whereas it uses directed bilinear interpolation method to magnify the interior region inside the magnified blocks. Determination of the right direction for interpolation is the key for achieving better performance of the proposed algorithm.

The paper analyses a problem of effective image processing in mobile devices with limited resources. We analyse various approximate calculation methods for improving energy characteristics of components of image processing algorithms that are especially energy and CPU resource greedy. We research an image transformation applying the Twirl effect using data specialization (caching in look-up tables) and approximate computation of the trigonometric functions using Taylor series, Padé rational fractions and Chebyshev polynomials. Quality of transformed images is evaluated using standard image quality metrics. Based on the experimental results, the recommendations for mobile application developers are formulated.

The technology of computer graphics and digital cameras are prevalent. High-resolution display and printer are available. High-resolution images are needed in order to produce high quality display images and high quality prints for use in desktop publishing, large artistic printing, mobile phone etc. However, since high-resolution images are not usually provided, there is a need to magnify the original images. This paper proposes an algorithm for image magnification by linear interpolation, which is better than some of the prevalent methods such as pixel replication, bilinear interpolation and bicubic interpolation. The proposed algorithm uses linear interpolation method to magnify pixels that lie in the perimeter, whereas it uses directed bilinear interpolation method to magnify the interior region inside the magnified blocks. Determination of the right direction for interpolation is the key for achieving better performance of the proposed algorithm.

Different image magnification methods are related very close with each other except the simplest Box method that does not use any interpolation. All tested methods show about the same RMSE results for the same picture. Lanczos methods show the best results and simplest Box method shows the worst results. Statistically, difference between interpolation methods, is less than one percent. But, for example, Lanczos works well where intensity gradient is higher, but brings more errors when intensity changes softly. Pixels with errors surround the edges, but can cover wide areas near edges. Image noise can increase RMSE value dramatically, concurrently noise can be invisible on image and produce a little intensity ripple but have a lot of pixels and produce high RMSE value.