Projective test

Pure mathematics

Projective space

Bandwidth (computing)

Statistics

Computer graphics (images)

Distortion (music)

Amplifier

Computer science

Computer network

Mathematics

Vanishing point

Image (mathematics)

Artificial intelligence

Geometry

Horizon

Point (geometry)

Homography

Perspective (graphical)

Convolutional neural network

Line (geometry)

Computer vision

The objective of this paper is to rectify any monocular image by computing a homography matrix that transforms it to a geometrically correct bird's eye (overhead) view. We make the following contributions: (i) we show that the homography matrix can be parameterised with only four geometric parameters that specify the horizon line and the vertical vanishing point, or only two if the field of view or focal length is known; (ii) We introduce a novel representation for the geometry of a line or point (which can be at infinity) that is suitable for regression with a convolutional neural network (CNN); (iii) We introduce a large synthetic image dataset with ground truth for the orthogonal vanishing points, that can be used for training a CNN to predict these geometric entities; and finally (iv) We achieve state-of-the-art results on horizon detection, with 74.52% AUC on the Horizon Lines in the Wild dataset. Our method is fast and robust, and can be used to remove perspective distortion from videos in real time.

A Geometric Approach to Obtain a Bird's Eye View From an Image