[BV] Finished assignment 8

Signed-off-by: Jim Martens <github@2martens.de>

bv/uebung8.txt

@@ -0,0 +1,130 @@
+1.
+                  ------
+                  | 1  |
+--------------    ------
+| 1 | -2 | 1 |  + | -2 |
+--------------    ------
+                  | 1  |
+                  ------
+
+The image has to be padded by 2 rows of zeros. The result of the correlation
+follows:
+
+---------------
+| 1 | -2 |  1 |
+---------------
+|-2 |  4 | -2 |
+---------------
+| 1 | -2 |  1 |
+---------------
+
+The resulting filter is the result of the outer product of both used filters
+which makes it a separable filter. 
+
+
+2.
+
+The Prewitt edge detector for vertical edges follows:
+
+-------------
+|-1 | 0 | 1 |
+-------------
+|-1 | 0 | 1 |
+-------------
+|-1 | 0 | 1 |
+-------------
+
+The image of the exercise follows with 1 specifying white and 0 black.
+
+-------------------------
+| 0 | 0 | 0 | 1 | 1 | 1 |
+-------------------------
+| 0 | 0 | 0 | 1 | 1 | 1 |
+-------------------------
+| 0 | 0 | 0 | 1 | 1 | 1 |
+-------------------------
+| 0 | 0 | 0 | 1 | 1 | 1 |
+-------------------------
+| 0 | 0 | 0 | 1 | 1 | 1 |
+-------------------------
+| 0 | 0 | 0 | 1 | 1 | 1 |
+-------------------------
+
+The image has to be padded with 1 row and column of zeros to have a same size
+result image. After that the convolution is applied. The padded image follows:
+
+---------------------------------
+| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
+---------------------------------
+| 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 |
+---------------------------------
+| 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 |
+---------------------------------
+| 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 |
+---------------------------------
+| 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 |
+---------------------------------
+| 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 |
+---------------------------------
+| 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 |
+---------------------------------
+| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
+---------------------------------
+
+The result of the convolution follows (without scalar product):
+
+
+---------------------------
+| 0 | 0 | -2 | -2 | 0 | 2 |
+---------------------------
+| 0 | 0 | -3 | -3 | 0 | 3 |
+---------------------------
+| 0 | 0 | -3 | -3 | 0 | 3 |
+---------------------------
+| 0 | 0 | -3 | -3 | 0 | 3 |
+---------------------------
+| 0 | 0 | -3 | -3 | 0 | 3 |
+---------------------------
+| 0 | 0 | -2 | -2 | 0 | 2 |
+---------------------------
+
+When the non zero values are replaced by ones, this is the result:
+
+
+-------------------------
+| 0 | 0 | 1 | 1 | 0 | 1 |
+-------------------------
+| 0 | 0 | 1 | 1 | 0 | 1 |
+-------------------------
+| 0 | 0 | 1 | 1 | 0 | 1 |
+-------------------------
+| 0 | 0 | 1 | 1 | 0 | 1 |
+-------------------------
+| 0 | 0 | 1 | 1 | 0 | 1 |
+-------------------------
+| 0 | 0 | 1 | 1 | 0 | 1 |
+-------------------------
+
+3.
+
+-----
+| 1 |
+-----     --------------
+| 2 |  *  | -1 | 0 | 1 |
+-----     --------------
+| 1 |
+-----
+
+To accurately process this convolution the image has to be padded by 2 columns
+of zeros.
+
+The result of the convolution follows:
+--------------
+| -1 | 0 | 1 |
+--------------
+| -2 | 0 | 2 |
+--------------
+| -1 | 0 | 1 |
+--------------
+
+This resulting filter is called Sobel edge detector for horizontal edges.