Figure 7
The image illustrates how local geometry matrices are extracted from an arrangement matrix using padding. On the left, a large grid labeled “Arrangement matrix” contains rows and columns filled with numbers from 1 to 5. The matrix is surrounded on the top two rows and left two columns by a green shaded region filled with zeros, identified as the padding area. The zeros extend beyond the visible numeric grid, indicating boundary padding. Five five-by-five neighborhoods within the arrangement matrix are highlighted using colored rectangular outlines: columns 1 to 5 of rows 1 to 5; columns 2 to 6 of rows 1 to 5; columns 3 to 7 of rows 1 to 5; columns 1 to 5 of rows 2 to 6; and columns 8 to 12 of rows 8 to 12. Inside these outlines, one central cell is emphasized with a light background color, marking the focal value. Red arrows above some highlighted cells indicate horizontal movement or indexing across adjacent cells. Different highlighted regions correspond to different focal positions within the matrix, including positions near the padded boundaries and positions fully inside the matrix. On the right side, four smaller square grids, with an ellipsis, are shown under the label “Extracted local geometry matrices”. Each small grid represents a local five-by-five matrix extracted from the larger arrangement matrix. Three of these local matrices include green-shaded rows or columns of zeros, showing how padding values are incorporated when the focal cell lies near the boundary. In each extracted matrix, the central cell is highlighted and contains a value such as “1” in the first, “3” in the second, “4” in the third, and “5” in the fourth, while the surrounding cells display neighboring values taken from the arrangement matrix or zeros from the padding area. Arrows connect selected highlighted regions in the arrangement matrix to their corresponding extracted local geometry matrices. The row-wise numbers from the corresponding matrices are as follows: First matrix, row 1: 0, 0, 0, 0, 0; row 2: 0, 0, 0, 0, 0; row 3: 0, 0, 1, 3, 4; row 4: 0, 0, 3, 2, 5; row 5: 0, 0, 2, 4, 1. Second matrix, row 1: 0, 0, 0, 0, 0; row 2: 0, 0, 0, 0, 0; row 3: 0, 1, 3, 4, 5; row 4: 0, 3, 2, 5, 4; row 5: 0, 2, 4, 1, 3. Third matrix, row 1: 0, 0, 0, 0, 0; row 2: 0, 0, 0, 0, 0; row 3: 1, 3, 4, 5, 2; row 4: 3, 2, 5, 4, 1; row 5: 2, 4, 1, 3, 4. Fourth matrix, row 1: 5, 2, 3, 2, 5; row 2: 1, 4, 2, 1, 3; row 3: 3, 1, 5, 4, 2; row 4: 5, 2, 4, 2, 1; row 5: 2, 1, 3, 5, 2.Illustration of the sliding-window extraction process used to generate local 5 × 5 geometry matrices from a larger arrangement. A 5 × 5 window is moved across the full arrangement matrix (padding boundary cases), and at each position, the centered unit cell and its first- and second-layer neighbors are captured as a distinct input sample for the neural network