Project Overview
In part A of the project, we apply perspective transforms on images for rectification and for creating panoramas.
Part 1: Image Rectification
The first thing we need to do if to define some correspondences. For image rectification, we can find a planar shape in the original photo, and then define some points that we would like them to be transformed to. For example, in the following photo that I took at Bay Street, Emeryville, I marked the four corners of one painting and then define their correspondences into a frontal-parallel square shape. Then, we compute the homography (represented by a 3x3 matrix, 8 degrees of freedom) between the two set of points by performing least-squares on the correspondence points to find the coefficients in the homography matrix H. The formula is as follows.
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After finding H, I used inverse warping to create the rectified images. Because the transformed images can no longer fit into the same dimensions, I created a new bounding box based on where the four corners of the original image is mapped to according to H. Here are some rectified results.
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I also tried to rectify this famous painting Nighthawks by Edward Hopper. I warped the painting so that the view into the window of the bar is frontal-parallel. Interestingly, after the perspective is changed, the gloomy vibe and the portrayal of lonely urban life seems much less pronounced. Perspective really shapes the artistic mood!
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Finally, I rectified this photo I took at Bay Stree, Emeryville. It was a wall of paintings, and I'd argue some of them can compete with the nighthawks! I rectified this photo to force the one of the paintings (the one that has a face) into a square shape. Here are the results.
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