**Computer Visionand Robotics** Introduction to Artificial Intelligence CS440/ECE448 Lecture 27 1-unit projects for grad students: Get in touch with me ! Last homework out today!! Next Tuesday: Review (everything since mid-term) Final: May 8, 1:30 to 3pm, here

**Last lecture** • Support vectors machines This lecture • Computer vision • Robotics Reading • Chapters 24 and 25

**support hyperplanes** Linearly Separable Classes support vectors What is the maximum-margin separating plane?

**w.x+b = 1** w.x+b = -1 Support Vector Machines (Boser, Guyon & Vapnik, 1992; Vapnik 1995) w.x+b = 0 positive examples negative examples What is the maximum-margin separating plane?

**Support vector machines ctd** • Examples are of the form ( xi, yi ), where yi = ¨ 1. • They all verify yi ( w.xi + b ) ≥ 1. • The distance between the separating plane is 2 / | w |. • Thus finding the maximum margin plane amounts to • Minimizing: ½ | w |^2 • subject to: yi ( w.xi + b ) ≥ 1 for i = 1, … ,n. • A quadratic programming problem!

**Support Vector Machines ctd** The dual formulation of the problem is: • Maximize: i=1ni -1/2 i,j=1nyiyjij ( xi¢xj ) • subject to: i=1nyii =0, and i≥ 0 for i=1, … , n. Note 1: The weitghts i are nonzero only for support vectors. Note 2: The data points only appear in the optimization problem via their dot product K( xi , xj ) = xi¢xj . Note 3: This allows classes that are not linearly separable to be handled via nonlinear mappings and appropriate kernelsK.

**non-linear mapping** ( X1, X2, X3 ) Kernel Machines x12+x22=1 X1+X2=1 ( x1, x2)

**Computer Vision**

**Computer Vision Tasks** • Stereo, structure from motion, shape from X: What is the 3D shape of the objects present in the image? • Segmentation: Separate objects from background. • Recognition: Identify the objects present in the image.

**Pompei painting, 2000 years ago.** Brunelleschi, 1415 Van Eyk, XIVth Century Massaccio’s Trinity, 1425

**Pinhole Perspective Equation** NOTE:z is always negative..

**Affine projection models: Weak perspective projection** is the magnification. When the scene relief is small compared its distance from the Camera, m can be taken constant: weak perspective projection.

**Affine projection models: Orthographic projection** When the camera is at a (roughly constant) distance from the scene, take m=1.

**What is the image of a sphere?** Planar pinhole perspective Orthographic projection Spherical pinhole perspective

**Diffraction effects** in pinhole cameras. Shrinking pinhole size Use a lens!

**Lenses** Snell’s law n1 sina1 = n2 sin a2 Descartes’ law

**E=(P/4) [ (d/z’)2 cos4a ] L**

**Vignetting**

**Photography (Niepce, “La ** Table Servie,” 1822) Milestones: • Daguerréotypes (1839) • Photographic Film (Eastman, 1889) • Cinema (Lumière Brothers, 1895) • Color Photography (Lumière Brothers, 1908) • Television (Baird, Farnsworth, Zworykin, 1920s) CCD and CMOS Devices (1970)

**Image Formation: Radiometry** The light source(s) The sensor characteristics The surface normal The surface properties The optics What determines the brightness of an image pixel?

**How do we perceive depth?**

**(Binocular) Fusion**

**2** Minimize |w-w’|. Correlation Methods (1970--) Slide the window along the epipolar line until w.w’ is maximized. Normalized Correlation: minimize q instead.

**(Devernay and Faugeras, 1994)**

**(Furukawa & Ponce, 2006)**

**Koenderink (1984)**

**(Rousson and Deriche, 2002)**

**Human/Felix** Bug Barbara Steele Face Joe Camel Problem: Recognizing instances Recognizing categories

**What we can do today (Rothganger et al. 2004)**

**Candidate parts** Matching Response scores Part dictionary Validation images Learning validation images Classifier Valildation parts Test image Part detection Testing response vector Decision First steps toward category-level object recognition (Lazebnik et al., 2006) Training pairs … … … …

**What is an object?**

**The interaction of light and matter**

**ILM** Toyota What is it all for?

**Copan** Courtesy of S. Leigh Courtesy of G. Robinson & M.S. Sharma