IMG_3667.jpeg

# Lecture 1 - Introduction ## Course Details * **Lecturer**: Prof. Andrew Zisserman * **Teaching Assistants**: * Dr. Iro Laina * Dr. Johannes Linder * Oisin Mac Aodha * Simon Hadfield * **Timetable**: * **Lectures**: Tue 14:00-16:00 (Rex Thompson Room) * *...

# Lecture 1 - Introduction ## Course Details * **Lecturer**: Prof. Andrew Zisserman * **Teaching Assistants**: * Dr. Iro Laina * Dr. Johannes Linder * Oisin Mac Aodha * Simon Hadfield * **Timetable**: * **Lectures**: Tue 14:00-16:00 (Rex Thompson Room) * **Practicals**: Fri 14:00-16:00 (Thom Building) * **Course Website**: Available on the department website * **Books**: * Richard Szeliski, Computer Vision: Algorithms and Applications * Simon Prince, Computer Vision: Models, Learning, and Inference * **Online Discussion**: Piazza ## Course Overview * Introduction to computer vision * Image formation * Feature detection and matching * Segmentation * Object recognition * 3D vision * Motion analysis ## Assessment * **Practicals**: 50% * Assessed on correctness, efficiency, and clarity of code * Late submissions will be penalized * **Exam**: 50% * Closed book * Tests understanding of concepts and algorithms * No past papers available ## What is Computer Vision? * Making computers see * Extracting meaningful information from images * Mimicking human vision * Applications: * Image search * Robotics * Medical imaging * Security * Autonomous driving ## Image Formation * How images are formed * Camera models * Geometric transformations * Radiometry * Color ### Pinhole Camera Model * Simple camera model * No lenses * Images are inverted * Perspective projection * 3D world points to 2D image points * Equation: $x = f \frac{X}{Z}$ $y = f \frac{Y}{Z}$ where: * $(X, Y, Z)$ is a 3D point * $(x, y)$ is the 2D projection * $f$ is the focal length * In matrix form including camera center $C$: $\begin{bmatrix} x \\ y \\ 1 \end{bmatrix} = \begin{bmatrix} f & 0 & 0 \\ 0 & f & 0 \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} R & -RC \end{bmatrix} \begin{bmatrix} X \\ Y \\ Z \\ 1 \end{bmatrix}$ where: * $R$ is the rotation matrix * $C$ is the camera center in world coordinates ### Radial Lens Distortion * Lenses distort images * Radial distortion is common * Barrel distortion * Pincushion distortion * Correcting for distortion: $x_{corrected} = x(1 + k_1r^2 + k_2r^4 +...)$ $y_{corrected} = y(1 + k_1r^2 + k_2r^4 +...)$ where: * $(x, y)$ is the original point * $(x_{corrected}, y_{corrected})$ is the corrected point * $k_1, k_2$ are distortion coefficients * $r$ is the radius: $r = \sqrt{x^2 + y^2}$ ### Homogeneous Coordinates * Represent points in projective space * Add an extra coordinate * 2D point $(x, y)$ becomes $(x, y, 1)$ * 3D point $(x, y, z)$ becomes $(x, y, z, 1)$ * Allows transformations to be represented as matrices * Scaling equivalence: $(x, y, z) = k(x, y, z)$ * Point at infinity: $(x, y, 0)$ * Line equation: $ax + by + c = 0$ becomes $\begin{bmatrix} a & b & c \end{bmatrix} \begin{bmatrix} x \\ y \\ 1 \end{bmatrix} = 0$ ### Coordinate Transformations * Translation: $\begin{bmatrix} x' \\ y' \\ 1 \end{bmatrix} = \begin{bmatrix} 1 & 0 & t_x \\ 0 & 1 & t_y \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} x \\ y \\ 1 \end{bmatrix}$ * Rotation: $\begin{bmatrix} x' \\ y' \end{bmatrix} = \begin{bmatrix} cos\theta & -sin\theta \\ sin\theta & cos\theta \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix}$ * Scaling: $\begin{bmatrix} x' \\ y' \end{bmatrix} = \begin{bmatrix} s_x & 0 \\ 0 & s_y \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix}$ * Affine transformation: $\begin{bmatrix} x' \\ y' \\ 1 \end{bmatrix} = \begin{bmatrix} a & b & c \\ d & e & f \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} x \\ y \\ 1 \end{bmatrix}$ * Projective transformation (Homography): $\begin{bmatrix} x' \\ y' \\ w \end{bmatrix} = \begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \end{bmatrix} \begin{bmatrix} x \\ y \\ 1 \end{bmatrix}$ $x = x'/w$ $y = y'/w$ ### Radiometry * Measuring light * Irradiance: power per unit area * Radiance: power per unit area per unit solid angle * BRDF: Bidirectional Reflectance Distribution Function * Lambertian surface: reflects light equally in all directions * Specular surface: reflects light in a mirror-like direction ## Color * Color perception * Color spaces: * RGB * HSV * Lab * Color constancy * White balance