Intro to Image Understanding (CSC420)
Assignment 4
Posted: March 18, 2024 Submission Deadline : March 27, 11.59pm, 2024
Max points: 15
1. [3 points] In this exercise, you are asked to take a photo. In particular, please take a planar item/object for which you know the real-world width and height (in cm), for example a piece of paper or a dollar bill. Tape the item on the door. Take a picture of the door such that all four corners of the door are visible on the photo. Take this picture in an oblique view, ie, the door is not a perfect rectangle but rather a quadrilateral in the photo. Estimate the width and height of the door (in cm) from the picture.
2. [5 points] You are given a few photos of landscape. The goal is to take two photos, landscape 1 and landscape 2 and stitch them into one photograph. You can do this by extracting SIFT features from both photos, match them, and estimate a homography of one photo with respect to the other. Use RANSAC to find the best homography. Once you compute the homography, ¡°stitch¡± the two photos together, forming a small panorama. We will give half points if you compute affine transformation instead of a homography.
3. Attached is an image um 000038.png recorded with a camera mounted on a car. The focal length of the camera is 721.5, and the principal point is (609.6, 172.9). We know that the camera was attached to the car at a distance of 1.7 meters above ground.
(a) [1 point] Write the internal camera parameter matrix K.
(b) [1 point] Write the equation of the ground plane in camera¡¯s coordinate system. You can
assume that the camera¡¯s image plane is orthogonal to the ground.
(c) [2 points] How would you compute the 3D location of a 2D point (x,y) in the image by assuming that the point lies on the ground? You can assume that the camera¡¯s image plane is orthogonal to the ground. No need to write code, write a mathematical explanation.
4. [3 points] Describe (in mathematical form, no code) how to compute disparity for a pair of parallel stereo cameras. Please include an algorithm (pseudo-code) that includes mathematical details. What is the computational complexity of this algorithm? How do you compute depth for each pixel?
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