readme update

README.md

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 ## Automatic watermark detection and removal
-This was the project that was built as part of project for CS663 (Digital Image Processing).
+This was a project that was built as part of project for CS663 (Digital Image Processing).
+This is a crude Python implementation of the paper "On The Effectiveness Of Visible Watermarks", Tali Dekel, Michael Rubinstein, Ce Liu and William T. Freeman,
+Conference on Computer Vision and Pattern Recongnition (CVPR), 2017.
+
+### Rough sketch of the algorithm
+A watermarked image `J` is obtained by imposing a watermark `W` over an unwatermarked image `I` with a blend factor <a href="https://www.codecogs.com/eqnedit.php?latex=\alpha" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\alpha" title="\alpha" /></a>. Specifically, we have the following equation:
+
+<div align="center">
+<a href="https://www.codecogs.com/eqnedit.php?latex=J(p)&space;=&space;\alpha(p)W(p)&space;&plus;&space;(1-\alpha(p))I(p)" target="_blank"><img src="https://latex.codecogs.com/gif.latex?J(p)&space;=&space;\alpha(p)W(p)&space;&plus;&space;(1-\alpha(p))I(p)" title="J(p) = \alpha(p)W(p) + (1-\alpha(p))I(p)" /></a>
+</div>
+
+Where `p = (x, y)` is the pixel location. For a set of `K` images, we have:
+<div align="center"><a href="https://www.codecogs.com/eqnedit.php?latex=J_k&space;=&space;\alpha&space;W&space;&plus;&space;(1-\alpha)I_k,\quad&space;k=1,2....K" target="_blank"><img src="https://latex.codecogs.com/gif.latex?J_k&space;=&space;\alpha&space;W&space;&plus;&space;(1-\alpha)I_k,\quad&space;k=1,2....K" title="J_k = \alpha W + (1-\alpha)I_k,\quad k=1,2....K" /></a></div>
+
+Although we have a lot of unknown quantities (<a href="https://www.codecogs.com/eqnedit.php?latex=J_k,&space;W,&space;\alpha" target="_blank"><img src="https://latex.codecogs.com/gif.latex?J_k,&space;W,&space;\alpha" title="J_k, W, \alpha" /></a>), we can make use of the structural properties of the image to determine its location and estimate its structure. The coherency of <a href="https://www.codecogs.com/eqnedit.php?latex=\alpha" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\alpha" title="\alpha" /></a> and W over all the images can be exploited to solve the above problem with good accuracy. The steps followed to determine these values are:
+- Initial watermark estimation and detection
+- Estimating the matted watermark
+- Compute the median of the watermarked image gradients, independently in the `x` and `y` directions, at every pixel location `p`.
+
+<div align="center"><a href="https://www.codecogs.com/eqnedit.php?latex=\nabla{\hat{W_m}(p)}&space;=&space;median_k(\nabla{J_k(p)})" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\nabla{\hat{W_m}(p)}&space;=&space;median_k(\nabla{J_k(p)})" title="\nabla{\hat{W_m}(p)} = median_k(\nabla{J_k(p)})" /></a></div>
+
+- Crop `W_m` to remove boundary regions by computing its magnitude and taking the bounding box of the edge map. The initial estimated watermark <a href="https://www.codecogs.com/eqnedit.php?latex=\hat{W}_m&space;\approx&space;W_m" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\hat{W}_m&space;\approx&space;W_m" title="\hat{W}_m \approx W_m" /></a> is estimated using Poisson reconstruction. Here is an estimated watermark using a dataset of 450+ Fotolia images.
+<img src="https://github.com/rohitrango/automatic-watermark-detection/blob/master/watermark.png?raw=True" alt="watermark_est"/>
+
+- Watermark detection: Obtain a verbose edge map (using Canny edge detector) and compute
+its Euclidean distance transform, which is then correlated with <a href="https://www.codecogs.com/eqnedit.php?latex=\nabla{\hat{W_m}}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\nabla{\hat{W_m}}" title="\nabla{\hat{W_m}}" /></a>
+to get the Chamfer distance from each pixel to the closest edge.
+Lastly, the watermark position is taken to be the pixel with minimum
+distance in the map.
+
+#### Multi-image matting and reconstruction
+- Estimate <a href="https://www.codecogs.com/eqnedit.php?latex=I_k,&space;W_k" target="_blank"><img src="https://latex.codecogs.com/gif.latex?I_k,&space;W_k" title="I_k, W_k" /></a> keeping <a href="https://www.codecogs.com/eqnedit.php?latex=W,&space;\alpha" target="_blank"><img src="https://latex.codecogs.com/gif.latex?W,&space;\alpha" title="W, \alpha" /></a> fixed.
+- Watermark update - Update the value of <a href="https://www.codecogs.com/eqnedit.php?latex=W,&space;\alpha" target="_blank"><img src="https://latex.codecogs.com/gif.latex?W" title="W" /></a> keeping the rest fixed.
+- Matte update - Update the value of <a href="https://www.codecogs.com/eqnedit.php?latex=W,&space;\alpha" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\alpha" title="\alpha" /></a> keeping the rest fixed.
+
+Please refer to the paper and supplementary for a more in-depth description and derivation of the algorithm. 
+
+Results
+--------
+Here are some of the results for watermarked and watermark removed images: 
+
+<div align="center">
+<img src="https://github.com/rohitrango/automatic-watermark-detection/blob/master/final/fotolia_137840668.jpg?raw=True" width="45%">
+<img src="https://github.com/rohitrango/automatic-watermark-detection/blob/master/final/137840668.jpg?raw=True" width="45%"> <br>
+
+<img src="https://github.com/rohitrango/automatic-watermark-detection/blob/master/final/fotolia_168668046.jpg?raw=True" width="45%">
+<img src="https://github.com/rohitrango/automatic-watermark-detection/blob/master/final/168668046.jpg?raw=True" width="45%"> <br>
+
+<img src="https://github.com/rohitrango/automatic-watermark-detection/blob/master/final/fotolia_168668150.jpg?raw=True" width="45%">
+<img src="https://github.com/rohitrango/automatic-watermark-detection/blob/master/final/168668150.jpg?raw=True" width="45%"> <br>
+</div>
+
+However, this is a rough implementation and the removal of watermark leaves some "traces" in form of texture distortion or artifacts. I believe this can be corrected by appropriate parameter tuning. 
+
+More information
+-------
+For more information, refer to the original paper [here](http://openaccess.thecvf.com/content_cvpr_2017/papers/Dekel_On_the_Effectiveness_CVPR_2017_paper.pdf)
+
+Disclaimer
+--------
+I do not encourage or endorse piracy by making this project public. The code is free for academic/research purpose. Please feel free to send pull requests for bug fixes/optimizations, etc.
+
+
+
+
+
 
-### Introduction
-Visible watermarking is a widely-used technique for marking and protecting copyrights of many millions of images on the web, yet it suffers from an inherent security flaw - watermarks are typically added in a consistent manner to many images. For example, they can be added to the center or corner of an image, and usually they are added with the same opacity levels, and to provide a bit of variation, are usually scaled, rotated, or applied in a periodic fashion to images. While removing a watermark from a single image can be tedious even for a person with good photoshop skills, removing watermarks from a number of images with some consistent property can be done automatically (or semi-automatically). 
-This is a crude implementation of the paper