Lecture 10 Problems

1. Complete the following function with Python-esque pseudocode (or working code in the lecture codebase), which performs inverse warping with nearest-neighbor sampling in the source image.

def warp(img, tx, dsize=None)
    """ Warp img using tx, a matrix representing a geometric transformation.
    Pre: tx is 3x3 (or some upper-left slice of a 3x3 matrix). img is grayscale.
    Returns: an output image of shape dsize with the warped img"""
    H, W = img.shape[:2]

    # turn a 2x2 or 2x3 tx into a full 3x3 matrix
    txH, txW = tx.shape
    M = np.eye(3)
    M[:txH,:txW] = tx

    # set the output size to the input size if not specified
    if dsize is None:
        DH, DW = (H, W)
    else:
        DH, DW = dsize[::-1]
    out = np.zeros((DH, DW))

    # your code here
    
    return out

2. Suppose you are stitching a panorama with three images $I_1, I_2, I_3$ and you’ve fitted transformations $T_{12}$ and $T_{23}$ that map coordinates from image 1 to 2 and from 2 to 3, respectively. Give the transformation that maps points from image 3’s coordinates to image 1’s coordinates.
3. Give a strategy (describe, or write pseudocode) for finding the corners of the bounding box of a given image img after it has been warped using a homography T.