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Instructions  For this final project, you will implement SIFT feature extraction

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Instructions 
For this final project, you will implement SIFT feature extraction. Since the time is limit, you don't have to do the image matching part but just print out all the features extracted from a given image. For example: 
Keypoint index I Keypoint pixel location I featurel, feature2, ..., feature 8 
1. (300, 252) [1.0, 0.5, 0.3, 0.72, 0.52, 0.14, 0.22, 0.30], [..], 2. (520, 112) [1.0, 0.2, 0.5, 0.32, 0.12, 0.92, 0.12, 0.50], 3... 
Each feature starts from the index number, followed by the pixel 2D location, using "(...)". Then it will shows all the features from octave images for that specific location. For simplicity, we only need 8 octave images, so 8 features are shown. Notice each feature has the largest value at the start. This is because we pick the largest bin as the starting bin. Also, you need to normalize all the bins by computing the largest bin as "1.0". To accomplish it, you need to manually implement the following components: (a) DoG (Difference of Gaussian) - you can call the "filter2D" function of OpenCV or implement it yourself. The DoG will be used to find potential Key point positions. (20%) 
(b) Use Octave to find local maximums to identify the list of final key points (20%) (c) Implement the derivative images l_x(), l_y(), direction image l_d(), and the approximation image 

(c) Implement the derivative images l_x(), l_y(), direction image l_d(), and the approximation image La() (30%) 
(d) Based on the approximation image La and the key points, generate the final 8-D vector feature set (30%) 
Be aware this is the final project. No extension is acceptable. 
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