From 4bb454a31fc54e72aa7a1348884fb03e2d807bc6 Mon Sep 17 00:00:00 2001
From: Sebastian Dietz <151366475+ad33edub@users.noreply.github.com>
Date: Tue, 14 Jan 2025 12:54:19 +0100
Subject: [PATCH] Update edgedetection.md
---
content/edgedetection.md | 21 +++++++++++++++++++--
1 file changed, 19 insertions(+), 2 deletions(-)
diff --git a/content/edgedetection.md b/content/edgedetection.md
index 2394fdf5..fc5ec0e9 100644
--- a/content/edgedetection.md
+++ b/content/edgedetection.md
@@ -25,7 +25,24 @@ ___
## 4.1: The Filter-Kernels
There are a variety of different Kernels used for edge detection; some of the most common ones are Sobel, Scharr, and Prewitt - Kernels.
-
+
+Sobel:
+
+X-Direction: $\begin{bmatrix}1&0&-1\\2&0&-2\\1&0&-1\end{bmatrix}$ Y-Direction: $\begin{bmatrix}1&2&1\\0&0&0\\-1&-2&-1\end{bmatrix}$
+
+---
+
+Scharr:
+
+X-Direction: $\begin{bmatrix}47&0&-47\\162&0&-162\\47&0&-47\end{bmatrix}$ Y-Direction: $\begin{bmatrix}47&162&47\\0&0&0\\-47&-162&-47\end{bmatrix}$
+
+---
+
+Prewitt:
+
+X-Direction: $\begin{bmatrix}1&0&-1\\1&0&-1\\1&0&-1\end{bmatrix}$ Y-Direction: $\begin{bmatrix}1&1&1\\0&0&0\\-1&-1&-1\end{bmatrix}$
+
+
When applying these Filter-Kernels to an image through __convolution__, you essentially create the derivative of the image.
This is because these Kernels result in higher pixel-values in regions, where the image contains a sharp change in brightness (similar to derivatives in analysis). This "derivation" is performed in X- and Y-direction seperately.
@@ -113,4 +130,4 @@ The part of your report concerning Task_4 should contain the following:
+ Images you generated with your code
-[Next](../cannyedge)
\ No newline at end of file
+[Next](../cannyedge)