Add Image_Transformations

I am trying to get a better idea of what happens with the transforms by looking
at the images as they go through various stages.

My first step of checking out if I can get illumination from original image and filtered
"reflectance". I messed it up, as you can the illunimation looks nothing like how its
supposed to look, I should rethink on the illumination-reflectance model itself.

Signed-off-by: Aditya A Prasad <[email protected]>

Author: anantham

DCT.py

@@ -5,7 +5,7 @@
 import numpy as np
 import matplotlib.pyplot as plt
 from scipy import fftpack
-import urllib2
+from urllib.request import urlopen
 import IPython
 
 # [Source](http://bugra.github.io/work/notes/2014-07-12/discre-fourier-cosine-transform-dft-dct-image-compression/)
@@ -15,7 +15,7 @@
 image_url='file:///C:/Users/Aditya/Pictures/crazygirl.jpg'
 # reads the image from url using PIL and converting it into a numpy array after converted grayscale image.
 def get_image_from_url(image_url='http://i.imgur.com/8vuLtqi.png', size=(128, 128)):
-    file_descriptor = urllib2.urlopen(image_url)
+    file_descriptor = urlopen(image_url)
     image_file = io.BytesIO(file_descriptor.read())
     image = Image.open(image_file)
     img_color = image.resize(size, 1)

Image_Transformations.py

@@ -0,0 +1,57 @@
+from urllib.request import urlopen
+import io
+from PIL import Image
+import numpy as np
+import matplotlib.pyplot as plt
+
+# Image Transformations 
+original_image ='http://i.imgur.com/GAazZeX.png'
+after_homo = 'http://i.imgur.com/KqMjJWV.png'
+
+def get_image(image_url='http://i.imgur.com/8vuLtqi.png', size=(128, 128)):
+	file_descriptor = urlopen(image_url)
+	image_file = io.BytesIO(file_descriptor.read())
+	image = Image.open(image_file)
+	img_color = image.resize(size, 1)
+	img_grey = img_color.convert('L')
+	img = np.array(img_grey, dtype=np.float)
+	# This returns a 128*128 size matrix
+	return img
+
+np_image_before = get_image(original_image,(384,510))
+np_image_after = get_image(after_homo,(384,510))
+
+print("\nWe have the greyscale version of the original image image of size - "+str(np_image_before.shape))
+print(np_image_before)
+print(np.max(np_image_before))
+print(np.min(np_image_before))
+
+print("\nWe have the greyscale version of the image  after filtering of size - "+str(np_image_after.shape))
+print(np_image_after)
+print(np.max(np_image_after))
+print(np.min(np_image_after))
+
+
+img_before = Image.fromarray(np_image_before)
+img_before.show()
+
+img_after = Image.fromarray(np_image_after)
+img_after.show()
+
+# This is consistent with the actual image as we have 250 as the whitest pixel while after filtering its 114 (no really white area after filtering)
+print("\n\nSo as we can see larger values closer to 256 is white, smaller values close to 0 are black")
+# if you are confused about the white edges as seen in the image and the numpy array - its because i couldnt crop it properly.
+
+'''
+Okay so reflectence is what we get after filtering - 'np_image_after' - r(x,y)
+? or is it, maybe its original-filtered or something?
+
+and image itself is 'np_image_before' - i(x,y)
+
+Based on the illumination-reflectance model of images, we can find illumination by dot division
+'''
+np_image_illumination = np.divide(np_image_before,np_image_after)
+print(np_image_illumination)
+
+img_illumination = Image.fromarray(np_image_illumination)
+img_illumination.show()

README.md

@@ -1,8 +1,10 @@
-# Image-Processing-
+# Image-Processing
 IC 040 IMAGE PROCESSING - Code Samples for concepts learned while pursuing this elective
 
 ## Homomorphic filtering
 
+I thank Steve Eddins, for his [blog post](http://blogs.mathworks.com/steve/2013/06/25/homomorphic-filtering-part-1/) on this.
+
 In case of homomorphic filtering, I am taking the image into the log domain so as to seperate the illumination and the reflectance of the image (Multiplicative model).
 
 As the irregualar illumination varies slowly and reflectance (property if the object being imaged) varies with a high frequency when we look at it with respect to the spatial domain.
@@ -11,4 +13,15 @@ After running my code I get this
 
 ![comparison of before and after homomorphic filtering](http://i.imgur.com/INI4d5W.png?1)
 
-As you can see the illumination is regular across the image. Thus we have removed the multiplicative noise.
+As you can see the illumination is regular across the image. Thus we have removed the multiplicative noise.
+
+## DCT
+
+This is the code I got from [here](http://bugra.github.io/work/notes/2014-07-12/discre-fourier-cosine-transform-dft-dct-image-compression/), I used it to get great insight into DCT. I added some comments to understand it better.
+
+
+## Image Transformations
+
+The plan is to explore the equations relating to the various transforms using actual images - numpy arrays. 
+
+My first attempt is at getting the illumination - from the homomorphic filtered - before and after image. 

homomorphic_filtering.m

@@ -22,7 +22,7 @@
 N = 2*size(I,2) + 1;
 
 % standard deviation of the equivalent spatial domain gaussian filter ??
-sigma = 10;
+sigma = 30;
 
 % X and Y are k*k size matrices with 
 % X has column i with all i's (this is true for i = 1,....k