Border pixels

Multiple bonds, internal rings, and other molecular substructures or subgraphs (see Figure 4.10a) are recognized through a circular inspection method. A circle of inspection centered on each detected atom is considered (see Figure 4.10b). Unknown border pixels found in this way are kept and used as the initial point for a new counterclockwise contour search, and the perception of new vertices and probable new atoms is carried out as described earlier. 

Back-ground / Object Edges. A couple of pixels is included in the border between an object and the bottom of the image if one of pixels belongs to the object and the other to the bottom, one can therefore define the border as the totality of pixels of the object that belong to a couple of pixels linked to the main issue. The size of tliis totality corresponds to the number of couples of pixels included in the border and depends on the option of the vector d. 

Taking a larger number of pixels can smooth the jagged borders. 

Fig. 1. Left side microphotographs of visible gold occurrences in relation to pyrite crystals. Right side related micro-XRF elemental mapping of As and spot location of LA-ICP-MS analyses with As values (ppm). The exact location of the micro-XRF map is indicated by the white square on the microphotographs (left side). On right side images, the light grey pixels indicate a relative enrichment of As in pyrites. For reference, the white contorted lines are the pyrite crystal borders. White and black spots are As-rich and As-poor portions of pyrites respectively. Note the discordant aspect of the As-enrichment corridors relative to the pyrite crystals and the sharp transition from As-poor and As-rich zones indicated by the LA-ICP-MS analytical As values.

A computer simulation of diffusion via the vacancy mechanism is performed on a square lattice of screen pixels with a spacing of a = 0.5 mm. The computer performs the calculations so that the vacancy jumps at a constant rate of T = 1000 s-1. The simulation cell is a square of edge length 5 cm containing 10,000 pixels. There is just one vacancy in the simulation cell, and as it moves by nearest-neighbor jumps, it remains within the cell (by using periodic boundary conditions or reflection at the borders). 

Figure 12.8 Care must be taken at the border elements. The pixel values outside of the grid of processing elements are unknown. No assumption should be made about these pixel values. Therefore, we only average the data of the current element and the interpolated value along the line of constant illumination.

Figure 22a shows a hole in polymethylmethacrylate (PMMA) written with a mask containing an isolated white pixel [261]. The hole is surrounded by a border wall of variable dimensions, higher than the unmodified surface. Both the shape of the hole and of the border wall depend on the tip shape. Also the position of the border wall with respect to the hole depends on the tip, but not on the scanning direction. The hole has the shape of the tip, i.e. a pyramid with an equilateral triangle as the base. 

The sample area however is difficult to measure due to the air inclusions (holes) and the rough boundaries of the sample. Therefore we scanned the samples with a HP deskscan (ScanJet 3c) at highest resolution (600 dpi) to a pcx-file. Every pixel corresponds to a square of 42.3 pm X 42.3 pm. A determination of the surface area is possible by a summation of the number of black pixels (i.e. the pixels that are covered by the sample area). The error is due to the fact, that the CCD-elements of the scanner counts a pixel as black if more than 50 % (but not necessarily all) of the pixel area is covered by the sample. This happens only at the border of the sample. Therefore the error is as low as 0.5 %. 

The data shown below, in Fig. 4.4, illustrate the richness of local information that can be extracted. On a micropattemed surface of organic molecules exposing hydrophobic -CH3 and hydrophilic -COOH groups at the film surface (prepared by microcontact printing [23]), the border region of the printed pattern was investigated in AFM-FV measurements. F-d curves were acquired pixel-per-pixel and provided information of local tip-surface interactions as shown in panels a and b. Here, the difference in pull-off force between the two chemically distinct regions and the tip is clearly pronounced. 

Let S be the complement of S. We assume that the image is surrounded by a border of pixels all belonging to 5. The component of S that contains this border is called the background of S all other components of 5, if any, are called holes in S. 

The border of 5 consists of those pixels of 5 that are adjacent to (i.e., have neighbors in) 5. More precisely, if C is any component of 5 and D any component of 5, the D-border of C consists of those pixels of C (if any) that are adjacent to D. In general, if 5 = C is connected, it has an outer border composed of pixels adjacent to the background, and it may also have hole borders composed of pixels adjacent to holes. 

The area of 5 is the number of pixels in 5. The perimeter of 5 is the total length of all its borders it can be defined more precisely, for any given border, as the number of moves from pixel to pixel required to travel completely around the border and return to the starting point. The compactness of 5 is sometimes measured by where... 

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