Understanding Vision: From Early Stages to Reflectance Functions - Prof. Bruce Draper, Study notes of Computer Science

Download Understanding Vision: From Early Stages to Reflectance Functions - Prof. Bruce Draper and more Study notes Computer Science in PDF only on Docsity! 1 Vision (Part 1) Lecture #22 11/18/08 Announcements We are going to jump around a bit. Please read Chapter 24 for Thursday. Remember, programming assignment #3 is due Thursday, Dec. 11th. No ACM meeting this week. Topics for today 1. What is vision? Not as obvious as it might seem 2. Perspective projection and 3D recovery 3. Reflectance and appearance 4. The early stages of vision What is vision? What information do you extract visually? What tasks does vision support? – Local navigation (don’t bump into things) – Global navigation (where am I?) – Duck! (reflexes) – Who are you? (are you angry? sappy? sad?) – Threat detection (should I be scared?) – Day or night? – Have I seen this before? Myths about vision I see the whole world in detail – The fovea is the high-resolution part of your eye. It covers about 2½° of visual angle. I see the whole world in color – Most color-sensitive cones are in the fovea. Peripheral color vision is poor. I see depth – Stereo vision is only accurate to about 10 feet. Most depth perception is qualitative/comparative. I see everything in front of me – Change blindness / inattentional blindness More Myths I was born knowing how to see – Babies aren’t born knowing how to focus their eyes. You had to learn to see. Everyone sees the same (vis-à-vis glasses) – Vision is a set of skills. Some people are better than others at specific skills Prosopagnosia (Nakayama) Navigators vs identifiers (Kosslyn) Image interpreters (NGA) 2 Perspective Projection Humans view the 3D world through non- parallel viewing rays that pass through a 2D plane Perspective Projection (II) In perspective projection: – All rays of light pass through the focal point (a.k.a. principal reference point) – The image plane is an infinite plane in front of (or behind) the focal point. – Images are formed by rays of light passing through the image plane (on their way to the focal point) – Image points are (u,v) – World points are (x,y,z) Perspective Projection The key to perspective projection is that all light rays meet at the PRP (focal point). Again, lets start with some assumptions: • VPN is the z-axis, VUP is y-axis • The view plane is z = d (focal length) • The focal point is (0,0,0) u z P(x,y,z) Pu d Pz Py Then by similar triangles: Pu Px d Pz = Pv Py d Pz= Pu = Pxd Pz Pv = Pyd Pz Pu = Px (Pz/d) Pv = Py (Pz/d) What does this mean? 1. Information is lost You cannot recreate the 3D world from its 2D image 2. Every image point corresponds to a ray in the 3D world 3. If you can identify a point in images taken from two locations, you can infer its 3D position Stereo Motion Reflectance Functions Reflectance functions are defined in terms of: • The position of a (point) light source • The orientation of the reflecting surface • The viewing position. surface normal viewing angle angle of incidence 5 Early Vision Where do we start? – An image is, say, 1,000 × 1,000 color pixels – Too much information is handle all at once Approaches to early vision: – Edge detection – Segmentations (region detection) – Interest points (a.k.a. FOAs) – Context : guess what your looking at Edges as Facets The image can be thought of as a gray level intensity surface – piecewise flat (flat facet model) – piecewise linear (sloped facet model) – piecewise quadratic – piecewise cubic – Example http://www.mirametrics.com/brief_pro_graphics_2.htm Processing implicitly or explicitly estimates the free parameters. Facet Edge Detection Facet edge detectors assume a piecewise linear model, and calculate the slope of the planar facet (1st derivative). – If we assume that the noise is zero mean, and increases with the square of distance, then convolution with the Sobel Edge Operator is optimal: V HVHMag VH =+= ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ − − − = ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ −−− = θtan , 101 202 101 , 121 000 121 22 Examples of Facet Edges Source Dx Image Dy Image Properties of Facet Edges/Masks Magnitude = √(dx2 + dy2) Orientation = tan-1 dy/dx Dy/Dx responses are signed Edges tend to be “thick” Edge Masks: sum of weights is zero – Smoothing masks: sum of weights is one Canny Example Source image Canny: sigma = 2.0, low = 0.40, high = 0.90 6 What is an Edge? An edge is a description of a localized image pattern – It measures a slope in intensity An edge is a symbolic feature – We need to know what it denotes: surface marking, or surface discontinuity, or shadow (illumination discontinuity) – These things have precise positions