Grid of processing elements

Computing Local Space Average Color on a Grid of Processing Elements... 

The shift and rescale method was implemented in parallel as follows. Local space average color was calculated on a grid of processing elements as described in the preceding text. Let... 

Figure 12.6 Two methods of interpolation (a) The color at point P is obtained by interpolating the colors from points A and B. (b ) If we have a grid of processing elements with diagonal connections, then we can use bilinear interpolation to calculate the color at point P using the data from points A, B, C, and D.

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.

As an additional test, we ran all algorithms on input images that were similar to the stimuli used in Helson s experiments. This is particularly important as some of the algorithms operate on a grid of processing elements and the output may not be uniform over the entire sample. Also, some simplifying assumptions had to be made in the theoretical analysis. We will see in a moment that the calculated output colors correspond to the colors that were theoretically computed. 

The first step in applying FEA is the construction of a model that breaks a component into simple standardized shapes or (usual term) elements located in space by a common coordinate grid system. The coordinate points of the element corners, or nodes, are the locations in the model where output data are provided. In some cases, special elements can also be used that provide additional nodes along their length or sides. Nodal stiffness properties are identified, arranged into matrices, and loaded into a computer where they are processed with certain applied loads and boundary conditions to calculate displacements and strains imposed by the loads (Appendix A PLASTICS DESIGN TOOLBOX). 

Fig. 7.41 Computation of the velocity pattern in the Kenics mixer, (a) the flow domain (b) the finite-element grid (c) the velocities at the cross section in the middle of an element (d) the same just after the transition. The contours in (c) and (d) are isolines of axial velocity, and the arrows show the lateral velocity. [Reprinted by permission from O. S. Galaktionov, P. D. Anderson, G. W. M. Peters, and H. E. H. Meijer, Analysis and Optimization of Kenics Mixers, Int. Polym. Process., 18,138-150, (2003).]...

Note that the correlation analysis has not produced any inconsistencies in the grid, only that certain of the elements were not totally distinguished one from another. Ordinarily, this type of analysis process is an iterative one, where a new trait is supplied to more totally distinguish between two elements, or perhaps where two traits are combined into one (for instance, atomic number and atomic weight are related). What is left is a non-ambiguous grid. 

It has been achieved through the processing of an array of data, obtained as the result of solving the equations describing the turbulent motion of a continuous medium, and using the K-s turbulence model (Equations 2.1-2.12) with the method of finite elements on a nonuniform calculation grid. 

---