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Reconstructing Images Using Damaged Copies (in Python)

posted on: Thursday, September 13, 2012 (4:01 pm) by Chase Stevens

I've recently been working on implementing various methods of image reconstruction in python. The idea is to, given several imperfect (that is to say, noisy, incomplete, photoshopped, or otherwise damaged) copies of some original image, attempt to arrive at something close to (if not precisely) the original image by combining said copies. Through these means, an approximation of the original image can be generated should the original be lost, itself damaged, irretrievable, or otherwise unavailable or useless. In writing the various functions for doing this, I implemented techniques used in signal averaging and variants thereof. I also implemented a “modal image" function which, for each pixel, uses the “modal" RGB values across all image copies or, failing that, performs a simple mean of values.

Examples and Analysis

Original Christian Bale photograph

For the following examples, I modified the above image of actor Christian Bale. Ironically enough, in testing for this article, I overwrote the original image and had to employ the use of Google's reverse image-search in order to find it.

Damaged images
Damaged Christian Bale #1 Damaged Christian Bale #2 Damaged Christian Bale #3
Delta: 105.122025 Delta: 88.026425 Delta: 68.5942
Function results (listed with difference from original image as given by get_delta, lower is better):
<function average_images_add at 0x00000000030E8F28> : 155.35693875
<function average_images_sub at 0x00000000030E95F8> : 72.4844575
<function average_images at 0x0000000002EF0208> : 43.92254625
<function average_noisefilter_all_sub at 0x0000000002EF0278> : 51.1805645833
<function average_noisefilter_all_delta at 0x0000000002EF02E8> : 36.9071316667
<function modal_image at 0x0000000002EF0358> : 42.53322
Christian Bale Reconstructed Using modal_image Christian Bale Reconstructed Using average_noisefilter_all_delta
Function: modal_image
Delta: 42.53322
Function: average_noisefilter_all_delta
Delta: 36.9071316667
As is readily visible, in this example the naïve “voting”-type approach used by modal_image is deceived in any case where forms of damage across multiple images “agree” with each other. Given a larger number of copies or a less artificial form of damage, this would likely cease to be an issue; in theory, modal_image could even go so far as to reconstruct the original image perfectly. average_noisefilter_all_delta produced the best results on average, although, to its detriment, its output relies on the order of the list of image copies passed to it. In addition, while it manages to be closer to the original image, the subtraction of image differences it employs creates a slightly “jarring” visual effect (as seen above). The inherent issue in reconstructing damaged images is one of knowledge. To humans, it seems obvious that the original image of Christian Bale didn't have streaks of white across it. However, this is a mere assumption based on our vast pool of experience in viewing photographs. Who's to say that the original photo didn't have white scribbles on it? The computer is hampered, from our perspective, by its inability to make these assumptions when reconstructing the original image, so although it produces results better than a mere superposition of the copies, they rarely are better than what could be accomplished by human hands.

Noisy images
Noisy Christian Bale #1 Noisy Christian Bale #2 Noisy Christian Bale #3
Delta: 92.715475 Delta: 93.352175 Delta: 93.08885
Function results (listed with difference from original image as given by get_delta, lower is better):
<function average_images_add at 0x00000000030E8F28> : 103.01672125
<function average_images_sub at 0x00000000030E95F8> : 81.929801875
<function average_images at 0x0000000002EF0208> : 82.971985
<function average_noisefilter_all_sub at 0x0000000002EF0278> : 69.6356495833
<function average_noisefilter_all_delta at 0x0000000002EF02E8> : 75.23682
<function modal_image at 0x0000000002EF0358> : 65.2880416667
Christian Bale De-Noised Using modal_image Christian Bale De-Noised Using average_noisefilter_all_sub
Function: modal_image
Delta: 65.2880416667
Function: average_noisefilter_all_sub
Delta: 69.6356495833
In this case, modal_image produced the best results, although its output is still quite noisy. Again, having more copies would significantly improve the end product. The output also appears to be slightly brighter than would be expected. average_noisefilter_all_sub comes in at a close second, although (to the human eye) its results appear to be quite a bit noisier than modal_image.

I tried to use these image reconstruction methods on compressed images with jpeg artifacts as well, although the results were much poorer. Output deltas ended up being worse than the least compressed copy of a given set, although better than an average copy. modal_image and average_images_add seemed to perform best. The overall problem was again one of knowledge: could less compressed images be prioritized or weighted given their closeness to the source, results would likely be much better. However, the computer has no means by which to determine what is closest to the original, and thus fails to leverage this. Some kind of programmatic detection of jpeg artifacts could be of great help in improving this situation.

As a final note before my code, I just recently launched Broverbs. Please do check it out if you've got the time!

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from __future__ import division
from PIL import Image as PILImage
from Tkinter import *
from tkFileDialog import askopenfilename as openfile
from itertools import product
from random import shuffle

class Image():
    def __init__(self,filename=None,dimensions=None):
        if filename!=None:
            self.pic = PILImage.open(filename)
            self.imgData = self.pic.load()
            self.size = self.pic.size
        else:
            if dimensions!=None:
                self.size = dimensions
            else:
                self.size = [0,0]
            self.pic = None
            self.imgData = {}
            for x,y in product(range(self.size[0]),range(self.size[1])):
                self.setpixel(x,y,0,0,0)
    def setpixel(self,x,y,r,g,b):
        self.imgData[x,y] = tuple(map(max,zip((r,g,b),(0,0,0))))
    def getpixellist(self):
        return product(range(self.size[0]),range(self.size[1]))
    def show(self):
        tempImage = PILImage.new('RGB',self.size)
        for x,y in self.getpixellist():
            tempImage.putpixel((x,y),self.imgData[x,y])
        tempImage.show()

def get_delta(image1,image2):
    if image1.size != image2.size: raise ValueError("Image sizes do not match")
    delta = 0
    for x,y in image1.getpixellist():
        delta += sum(abs_pixel_diff(image1,image2,x,y))
    return delta / (image1.size[0] * image1.size[1])

mode = (lambda l: max([(l.count(i), i) for i in set(l)])[1] if len(set(l)) < len(l) else sum(l)/float(len(l)))

pixel_operation = lambda f: lambda image1,image2,x,y: map(f,zip(image1.imgData[x,y],image2.imgData[x,y]))
abs_pixel_diff = pixel_operation(lambda (x,y): abs(x-y))
pixel_diff = pixel_operation(lambda (x,y): x-y)
pixel_avg = pixel_operation(lambda (x,y): (x+y)/2)
pixel_sum = pixel_operation(lambda (x,y): x+y)

def image_operation(operation,image1,image2):
    if image1.size != image2.size: raise ValueError("Image sizes do not match")
    result = Image(dimensions=image1.size)
    for x,y in result.getpixellist():
        r,g,b = operation(image1,image2,x,y)
        result.setpixel(x,y,r,g,b)
    return result

get_delta_image = lambda image1,image2: image_operation(abs_pixel_diff,image1,image2)
subtract_image = lambda minuend,subtrahend: image_operation(pixel_diff,minuend,subtrahend)
average_image = lambda image1,image2: image_operation(pixel_avg,image1,image2)
add_image = lambda image1,image2: image_operation(pixel_sum,image1,image2)

def get_average_image(image_list):
    output = Image(dimensions=set1[0].size)
    for x,y in output.getpixellist():
        r,g,b = reduce(lambda a,b: (a[0]+b[0],a[1]+b[1],a[2]+b[2]),[image.imgData[x,y] for image in image_list])
        output.setpixel(x,y,r/len(image_list),g/len(image_list),b/len(image_list))
    return output

def generalized_average(image_list, combination_function, function1, function2):
    shuffle(image_list)
    set1 = image_list[0::2]
    image1 = get_average_image(set1)
    set2 = image_list[1::2]
    image2 = get_average_image(set2)
    return combination_function(function1(image1,image2),function2(image1,image2))

def average_images_add(image_list): 
    return generalized_average(image_list,add_image,average_image,subtract_image)

def average_images_sub(image_list):
    return generalized_average(image_list,subtract_image,average_image,subtract_image)

def average_images(image_list): 
    return generalized_average(image_list,subtract_image,average_image,get_delta_image)

def generalized_noisefilter(image_list,function):
    shuffle(image_list)
    set1 = image_list[0::2]
    image1 = get_average_image(set1)
    set2 = image_list[1::2]
    image2 = get_average_image(set2)
    noise = function(image1,image2)
    denoise_set = [subtract_image(image,noise) for image in image_list]
    return get_average_image(denoise_set)

def average_noisefilter_all_sub(image_list):
    return generalized_noisefilter(image_list,subtract_image)

def average_noisefilter_all_delta(image_list):
    return generalized_noisefilter(image_list,get_delta_image)

def modal_image(image_list):
    shuffle(image_list)
    result = Image(dimensions=image_list[0].size)
    for x,y in result.getpixellist():
        r = mode([image.imgData[x,y][0] for image in image_list])
        g = mode([image.imgData[x,y][1] for image in image_list])
        b = mode([image.imgData[x,y][2] for image in image_list])
        result.setpixel(x,y,r,g,b)
    return result

def test_func(f,images,original,trials=25):
    results = list()
    for x in range(trials):
        print "Trial #"+str(x+1)
        results.append(get_delta(f(images),original))
    return sum(results)/len(results)

function_list = [average_images_add,average_images_sub,average_images,average_noisefilter_all_sub,average_noisefilter_all_delta,modal_image]

def test_functions(image_list,original,functions=function_list,trials=10):
    out = ''
    for f in functions:
        out += (str(f) + ' ')
        out += (': ')
        out += (str(test_func(f,image_list,original,trials)))
        out += ('n')
    print out

Tags: code, image processing, information theory, programming, python, voting