Add solutions for part 02 (#8)

* Add solutions for part 02

* Tweak solution

tutorial/02_image_filtering.md

@@ -236,6 +236,10 @@ Look up the documentation of `scipy.ndimage.convolve`. Apply the same convolutio
 # Solution here
 ```
 
+```python
+%load solutions/02_exercise_1.py
+```
+
 <!-- #region slideshow={"slide_type": "slide"} -->
 ### A difference filter
 <!-- #endregion -->
@@ -739,10 +743,18 @@ vertical_kernel.shape
 # Solution here
 ```
 
+```python
+%load solutions/02_exercise_3a.py
+```
+
 ```python
 # Solution here
 ```
 
+```python
+%load solutions/02_exercise_3b.py
+```
+
 <!-- #region editable=true slideshow={"slide_type": "slide"} -->
 ### Sobel edge filter
 <!-- #endregion -->

tutorial/solutions/02_exercise_1.py

@@ -0,0 +1,9 @@
+# Solution for exercise 1
+import scipy as sp
+
+smoothed_with_scipy = sp.ndimage.convolve(noisy_signal, mean_kernel11, mode="reflect")
+
+fig, ax = plt.subplots()
+ax.plot(smooth_signal11same, label="padding with zeros")
+ax.plot(smoothed_with_scipy, label="mode reflect")
+ax.legend()

tutorial/solutions/02_exercise_3a.py

@@ -0,0 +1,9 @@
+# Solution for exercise 3a
+horiz_kernel = vertical_kernel.T
+
+gradient_horiz = ndi.correlate(pixelated.astype(float),
+                               horiz_kernel)
+
+fig, ax = plt.subplots(ncols=2)
+ax[0].imshow(gradient_vertical, cmap="gray");
+ax[1].imshow(gradient_horiz, cmap="gray");

tutorial/solutions/02_exercise_3b.py

@@ -0,0 +1,6 @@
+# Solution for exercise 3b
+gradient = np.sqrt(gradient_vertical**2 + gradient_horiz**2)
+
+fig, ax = plt.subplots()
+im = ax.imshow(gradient, cmap="gray");
+fig.colorbar(im)