About the course Instructors: Haibin Ling (hbling@temple, Wachman 35) Hours Lecture: Tuesda 5:3-8:pm, TTLMAN 43B Office hour: Tuesda 3: - 5:pm, or b appointment Textbook Computer Vision: Models, Learning, and Inference, b Simon J.D. Prince, Cambridge Universit Press. Computer Vision: Algorithms and Applications, b Richard Szeliski, Springer. Computer Vision: A Modern Approach, b David A. Forsth and Jean Ponce, Prentice Hall. Papers assigned in the class. Grading & Project Homework: 2% One page summar and critiques about papers presented in the class Need to submit at least 5 times Due (electronicall) BEFORE the start of the class in which the paper will be presented NO extension Paper Presentation: 25% Present at least one paper Responsible to the discussion in class Projects : 55% Topics suggested b the instructor or found b the students Small team, preferred -2 students per team. Midterm: 5% Final: 2% Report: 2% Course Content Introduction in high level Each student is expected to know for details of a selected topics (paper presentation and project) Tentative Schedule http://www.dabi.temple.edu/~hbling/teaching/5s_5543/index.html State-of-the-arts in frontier topics Paper presentation and summar for improve understanding Course project Students introduction Name Advisor (if an) Background or our current research (if an) An topics of particular interest (if an) Image formation - Cameras Send an email to me
How do we see the world? Pinhole camera Let s design a camera Idea : put a piece of film in front of an object Do we get a reasonable image? Add a barrier to block off most of the ras This reduces blurring The opening known as the aperture Pinhole camera model Dimensionalit Reduction Machine (3D to 2D) 3D world 2D image Pinhole model: Captures pencil of ras all ras through a single point The point is called Center of Projection (focal point) The image is formed on the Image Plane Point of observation What have we lost? Angles Distances (lengths) Slide b A. Efros Figures Stephen E. Palmer, 22 Projection properties Projection properties Man-to-one: an points along same ra map to same point in image Points points But projection of points on focal plane is undefined Lines lines (collinearit is preserved) But line through focal point projects to a point Planes planes (or half-planes) But plane through focal point projects to line Parallel lines converge at a vanishing point Each direction in space has its own vanishing point But parallels parallel to the image plane remain parallel All directions in the same plane have vanishing points on the same line How do we construct the vanishing point/line? Slide b Lazebnik Slide b Lazebnik 2
Modeling projection Modeling projection z z x x The coordinate sstem We will use the pinhole model as an approximation Put the optical center (O) at the origin Put the image plane (Π ) in front of O Source: J. Ponce, S. Seitz Projection equations Compute intersection with Π of ra from P = (x,,z) to O Derived using similar triangles x ( x,, z) ( f ', f ' ) Source: J. Ponce, S. Seit Homogeneous coordinates Is this a linear transformation? No division b z is nonlinear Trick: add one more coordinate: homogeneous image coordinates x ( x,, z) ( f ', f ' ) homogeneous scene coordinates Converting from homogeneous coordinates Perspective Projection Matrix Projection is a matrix multiplication using homogeneous coordinates: / f ' x x z z / f ' x ( f ', f ' ) divide b the third coordinate Slide b Steve Seit Perspective Projection Matrix Home-made pinhole camera Projection is a matrix multiplication using homogeneous coordinates: / f ' x x z z / f ' In practice: lots of coordinate transformations 2D point (3x) = Camera to pixel coord. trans. matrix (3x3) Perspective projection matrix (3x4) x ( f ', f ' ) divide b the third coordinate World to camera coord. trans. matrix (4x4) 3D point (4x) Wh so blurr? Slide b A. Efros http://www.debevec.org/pinhole 3
Shrinking the aperture Shrinking the aperture Wh not make the aperture as small as possible? Less light gets through Diffraction effects focal point f A lens focuses light onto the film Ras passing through the center are not deviated A lens focuses light onto the film Ras passing through the center are not deviated All parallel ras converge to one point on a plane located at the focal length f Thin lens formula + = D D f An point satisfing the thin lens equation is in focus. circle of confusion D f D A lens focuses light onto the film There is a specific distance at which objects are in focus other points project to a circle of confusion in the image Frédo Durand s slide 4
Real lenses Lens flaws: Vignetting Radial Distortion Caused b imperfect lenses Deviations are most noticeable for ras that pass through the edge of the lens Illumination condition Light and color No distortion Pin cushion Barrel 5