From afe2b67d061ee76c175e737d3be36781bb353e5c Mon Sep 17 00:00:00 2001
From: Jim Martens <github@2martens.de>
Date: Tue, 6 Dec 2016 12:41:24 +0100
Subject: [PATCH] [BV] Finished assignment 7

Signed-off-by: Jim Martens <github@2martens.de>
---
 bv/uebung7.m | 37 +++++++++++++++++++++++++++++++++----
 1 file changed, 33 insertions(+), 4 deletions(-)

diff --git a/bv/uebung7.m b/bv/uebung7.m
index e84ed50..faf2e69 100644
--- a/bv/uebung7.m
+++ b/bv/uebung7.m
@@ -1,15 +1,44 @@
+% 1.
+% Let's take two sequences f(x) = {0 -> 1, 1 -> 1, 2 -> 100} and
+% g(x) = { 0 -> 2, 1 -> 3, 2 -> 0}. The sum of both is 
+% h(x) = {0 -> 3, 1 -> 4, 2 -> 100}. The mean values are: mean(f) = 34,
+% mean(g) = 5/3, mean(h) = 107/3 = 34 + 5/3. The linearity mean(f) +
+% mean(g) = mean(f + g) is satisfied. The median values are: median(f) = 1,
+% median(g) = 2, median(h) = 4. But median(f) + median(g) != median(f + g).
+% Therefore the linearity isn't satisfied which means that median is
+% non-linear.
+
 % 2.
 peppers = rgb2gray(imread('peppers.png'));
 peppers_1 = imnoise(peppers, 'salt & pepper', 0.02);
 peppers_2 = imgaussfilt(peppers);
 peppers_3 = imnoise(peppers, 'salt & pepper', 0.6);
+peppers_4 = imnoise(peppers, 'poisson');
+peppers_5 = imgaussfilt(peppers, 3);
 
 peppers_fft = fftshift(log(abs(fft2(peppers))));
 peppers1_fft = fftshift(log(abs(fft2(peppers_1))));
 peppers2_fft = fftshift(log(abs(fft2(peppers_2))));
 peppers3_fft = fftshift(log(abs(fft2(peppers_3))));
+peppers4_fft = fftshift(log(abs(fft2(peppers_4))));
+peppers5_fft = fftshift(log(abs(fft2(peppers_5))));
 
-figure (1), imshow(peppers_fft, []);
-figure (2), imshow(peppers1_fft, []);
-figure (3), imshow(peppers2_fft, []);
-figure (4), imshow(peppers3_fft, []);
+%figure (1), imshow(peppers_fft, []);
+%figure (2), imshow(peppers1_fft, []);
+%figure (3), imshow(peppers2_fft, []);
+%figure (4), imshow(peppers3_fft, []);
+%figure (5), imshow(peppers4_fft, []);
+%figure (6), imshow(peppers5_fft, []);
+
+%3.
+low_pass = fspecial('gaussian', [3 3], 1);
+low_pass_fft = fft2(low_pass, size(peppers, 1), size(peppers, 2));
+high_pass = fspecial('laplacian', 0.2);
+high_pass_fft = fft2(high_pass, size(peppers, 1), size(peppers, 2));
+peppers_fft2 = fft2(peppers);
+peppers_filtered_low_fft = peppers_fft2 .* low_pass_fft;
+peppers_filtered_high_fft = peppers_fft2 .* high_pass_fft;
+peppers_filtered_low = real(ifft2(peppers_filtered_low_fft));
+peppers_filtered_high = real(ifft2(peppers_filtered_high_fft));
+figure (7), imshow(peppers_filtered_low, []);
+figure (8), imshow(peppers_filtered_high, []);