Predefined Gradient Kernels
The following tables list the predefined gradient 3 × 3 kernels.
Prewitt Filters
The Prewitt filters have the following kernels. The notations West (W), South (S), East (E), and North (N) indicate which edges of bright regions they outline.
| #0 W/Edge | #1 W/Image | #2 SW/Edge | #3 SW/Image |
| -1 0 1 -1 0 1 -1 0 1 |
-1 0 1 -1 1 1 -1 0 1 |
0 1 1 -1 0 1 -1-1 0 |
0 1 1 -1 1 1 -1-1 0 |
| #4 S/Edge | #5 S/Image | #6 SE/Edge | #7 SE/Image |
| 1 1 1 0 0 0 -1-1-1 |
1 1 1 0 1 0 -1-1-1 |
1 1 0 1 0-1 0-1-1 |
1 1 0 1 1-1 0-1-1 |
| #8 E/Edge | #9 E/Image | #10 NE/Edge | #11 NE/Image |
| 1 0-1 1 0-1 1 0-1 |
1 0-1 1 1-1 1 0-1 |
0-1-1 1-0 1 1 1 0 |
0-1-1 1 1-1 1 1 0 |
| #12 N/Edge | #13 N/Image | #14 NW/Edge | #15 NW/Image |
| -1-1-1 0 0 0 1 1 1 |
-1-1-1 0 1 0 1 1 1 |
-1-1 0 -1 0 1 0 1 1 |
-1-1 0 -1 1 1 0 1 1 |
Sobel Filters
The Sobel filters are very similar to the Prewitt filters except that they highlight light intensity variations along a particular axis that is assigned a stronger weight. The Sobel filters have the following kernels. The notations West (W), South (S), East (E), and North (N) indicate which edges of bright regions they outline.
| #16 W/Edge | #17 W/Image | #18 SW/Edge | #19 SW/Image |
| -1 0 1 -2 0 2 -1 0 1 |
-1 0 1 -2 1 2 -1 0 1 |
0 1 2 -1 0 1 -2-1 0 |
0 1 2 -1 1 1 -2 1 0 |
| #20 S/Edge | #21 S/Image | #22 SE/Edge | #23 SE/Image |
| 1 2 1 0 0 0 -1-2-1 |
1 2 1 0 1 0 -1-2-1 |
2 1 0 1 0-1 0-1-2 |
2 1 0 1 1-1 0-1-2 |
| #24 E/Edge | #25 E/Image | #26 NE/Edge | #27 NE/Image |
| 1 0-1 2 0-2 1 0-1 |
1 0-1 2 1-2 1 0-1 |
0-1-2 1 0-1 2 1 0 |
0-1-2 1 1-1 2 1 0 |
| #28 N/Edge | #29 N/Image | #30 NW/Edge | #31 NW/Image |
| -1-2-1 0 0 0 1 2 1 |
-1-2-1 0 1 0 1 2 1 |
-2-1 0 -1 0 1 0 1 2 |
-2-1 0 -1 1 1 0 1 2 |
Other Kernels
The following table lists the predefined gradient 5 × 5 kernels.
| #0 W/Edge | #1 W/Image | #2 SW/Edge | #3 SW/Image |
| 0 -1 0 1 0 -1 -2 0 2 1 -1 -2 0 2 1 -1 -2 0 2 1 0 -1 0 1 0 |
0 -1 0 1 0 -1 -2 0 2 1 -1 -2 1 2 1 -1 -2 0 2 1 0 -1 0 1 0 |
0 0 1 1 1 0 0 2 2 1 -1 -2 0 2 1 -1 -2 -2 0 0 -1 -1 -1 0 0 |
0 0 1 1 1 0 0 2 2 1 -1 -2 1 2 1 -1 -2 -2 0 0 -1 -1 -1 0 0 |
| #4 S/Edge | #5 S/Image | #6 SE/Edge | #7 SE/Image |
| 0 1 1 1 0 1 2 2 2 1 0 0 0 0 0 -1 -2 -2 -2 -1 0 -1 -1 -1 0 |
0 1 1 1 0 1 2 2 2 1 0 0 1 0 0 -1 -2 -2 -2 -1 0 -1 -1 -1 0 |
1 1 1 0 0 1 2 2 0 0 1 2 0 -2 -1 0 0 -2 -2 -1 0 0 -1 -1 -1 |
1 1 1 0 0 1 2 2 0 0 1 2 1 -2 -1 0 0 -2 -2 -1 0 0 -1 -1 -1 |
| #8 E/Edge | #9 E/Image | #10 NE/Edge | #11 NE/Image |
| 0 1 0 -1 0 1 2 0 -2 -1 1 2 0 -2 -1 1 2 0 -2 -1 0 1 0 -1 0 |
0 1 0 -1 0 1 2 0 -2 -1 1 2 1 -2 -1 1 2 0 -2 -1 0 1 0 -1 0 |
0 0 -1 -1 -1 0 0 -2 -2 -1 1 2 0 -2 -1 1 2 2 0 0 1 1 1 0 0 |
0 0 -1 -1 -1 0 0 -2 -2 -1 1 2 1 -2 -1 1 2 2 0 0 1 1 1 0 0 |
| #12 N/Edge | #13 N/Image | #14 NW/Edge | #15 NW/Image |
| 0 -1 -1 -1 0 -1 -2 -2 -2 -1 0 0 0 0 0 1 2 2 2 1 0 1 1 1 0 |
0 -1 -1 -1 0 -1 -2 -2 -2 -1 0 0 1 0 0 1 2 2 2 1 0 1 1 1 0 |
-1 -1 -1 0 0 -1 -2 -2 0 0 -1 -2 0 2 1 0 0 2 2 1 0 0 1 1 1 |
-1 -1 -1 0 0 -1 -2 -2 0 0 -1 -2 1 2 1 0 0 2 2 1 0 0 1 1 1 |
The following table lists the predefined gradient 7 × 7 kernels.
| #0 W/Edge | #1 W/Image | #2 S/Edge |
| 0 -1 -1 0 1 1 0 -1 -2 -2 0 2 2 1 -1 -2 -3 0 3 2 1 -1 -2 -3 0 3 2 1 -1 -2 -3 0 3 2 1 -1 -2 -2 0 2 2 1 0 -1 -1 0 1 1 0 |
0 -1 -1 0 1 1 0 -1 -2 -2 0 2 2 1 -1 -2 -3 0 3 2 1 -1 -2 -3 1 3 2 1 -1 -2 -3 0 3 2 1 -1 -2 -2 0 2 2 1 0 -1 -1 0 1 1 0 |
0 1 1 1 1 1 0 1 2 2 2 2 2 1 1 2 3 3 3 2 1 0 0 0 0 0 0 0 -1 -2 -3 -3 -3 -2 -1 -1 -2 -2 -2 -2 -2 -1 0 -1 -1 -1 -1 -1 0 |
| #3 S/Image | #4 E/Edge | #5 E/Image |
| 0 1 1 1 1 1 0 1 2 2 2 2 2 1 1 2 3 3 3 2 1 0 0 0 1 0 0 0 -1 -2 -3 -3 -3 -2 -1 -1 -2 -2 -2 -2 -2 -1 0 -1 -1 -1 -1 -1 0 |
0 1 1 0 -1 -1 0 1 2 2 0 -2 -2 -1 1 2 3 0 -3 -2 -1 1 2 3 0 -3 -2 -1 1 2 3 0 -3 -2 -1 1 2 2 0 -2 -2 -1 0 1 1 0 -1 -1 0 |
0 1 1 0 -1 -1 0 1 2 2 0 -2 -2 -1 1 2 3 0 -3 -2 -1 1 2 3 1 -3 -2 -1 1 2 3 0 -3 -2 -1 1 2 2 0 -2 -2 -1 0 1 1 0 -1 -1 0 |
| #6 N/Edge | #7 N/Image | |
| 0 -1 -1 -1 -1 -1 0 -1 -2 -2 -2 -2 -2 -1 -1 -2 -3 -3 -3 -2 -1 0 0 0 0 0 0 0 1 2 3 3 3 2 1 1 2 2 2 2 2 1 0 1 1 1 1 1 0 |
0 -1 -1 -1 -1 -1 0 -1 -2 -2 -2 -2 -2 -1 -1 -2 -3 -3 -3 -2 -1 0 0 0 1 0 0 0 1 2 3 3 3 2 1 1 2 2 2 2 2 1 0 1 1 1 1 1 0 |