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# Image intensity surface

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## Contexts in source publication

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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