He who loves practice without theory is like the sailor who boards ship without a rudder and compass and never knows where he may cast. — Leonardo Da Vinci (1452-1519)
And since geometry is the right foundation of all painting, I have decided to teach its rudiments and principles to all youngsters eager for art. — Albrecht Durer (1471-1528)
As for everything else, so for a mathematical theory: beauty can be perceived but not explained. — Arthur Cayley (1821–1895)
We will explain the basics of Euclidean, Affine and Projective geometry and show how to measure distances and angles in a scene from its images. We will introduce a model of the perspective camera, explain how images change when moving a camera and show how to find the camera pose from images. We will demonstrate the theory in practical tasks of panorama construction, finding the camera pose, adding a virtual object to a real scene and reconstructing a 3D model of a scene from its images. We will be building on our previous knowledge of Linear algebra and will provide fundamentals of geometry for computer vision, computer graphics, image processing and object recognition.
|01||18.2.||MM: Intro: Geometry of CV & G, LA L[2.1], image coordinate system L|
|02||25.2.||TP: Mathematical model of the perspective camera L|
|03||04.3.||PO: Camera calibration L and pose L, (PO)|
|04||11.3.||TP: Calibrated camera pose computation I L[7.2, 7.3]|
|05||18.3.||PO: Calibrated camera pose computation II L[7.3-par.38], vector product L[2.2], (PO)|
|06||25.3.||TP: Homography L, affine space L|
|07||01.4.||Projective plane L|
|08||08.4.||Camera calibration from vanishing points L|
|09||17.4.||Dual space L[2.3]|
|11||29.4.||Epipolar geometry L[12.1-12.3]|
|12||06.5.||3D reconstruction with a calibrated camera L[12.4]|
|13||13.5.||Calibrated camera motion computation L[12.5], SVD L[2.3]|
|14||20.5.||Questions & Answers|
Details about exercises (technical content and assessment) are in the separate section Labs.
The exam consists of a written and an oral part.
Points P a are calculated as
P = 100*(0.3*H/(9*5) + 0.3*T/(3*10) + 0.4*(0.5*we + 0.5*oe))
where H and T are points for home works and tests, and we and oe are success rates for oral exam and written exam, respectively. The grade is given by the points P and the table below.
|A (Excellent)||>= 90|
|B (Very good)||[80,90)|
|F (Failed)||< 50|