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Let’s design a camera Idea 1: put a piece of film in front of an object Do we get a reasonable image? Slide by Steve Seitz Pinhole camera : Pinhole camera Add a barrier to block off most of the rays This reduces blurring The opening known as the aperture How does this transform the image? Slide by Steve Seitz Pinhole camera model : Pinhole camera model Pinhole model: Captures pencil of rays – all rays through a single point The point is called Center of Projection (COP) The image is formed on the Image Plane Effective focal length f is distance from COP to Image Plane Slide by Steve Seitz Dimensionality Reduction Machine (3D to 2D) : Figures © Stephen E. Palmer, 2002 Dimensionality Reduction Machine (3D to 2D) 3D world 2D image What have we lost? Angles Distances (lengths) Funny things happen… : Funny things happen… Parallel lines aren’t… : Parallel lines aren’t… Figure by David Forsyth Lengths can’t be trusted... : Lengths can’t be trusted... Figure by David Forsyth B’ C’ A’ …but humans adopt! : …but humans adopt! http://www.michaelbach.de/ot/sze_muelue/index.html Müller-Lyer Illusion We don’t make measurements in the image plane Modeling projection : Modeling projection The coordinate system We will use the pin-hole model as an approximation Put the optical center (Center Of Projection) at the origin Put the image plane (Projection Plane) in front of the COP Why? The camera looks down the negative z axis we need this if we want right-handed-coordinates Slide by Steve Seitz Modeling projection : Modeling projection Projection equations Compute intersection with PP of ray from (x,y,z) to COP Derived using similar triangles (on board) Slide by Steve Seitz Homogeneous coordinates : Homogeneous coordinates Is this a linear transformation? Trick: add one more coordinate: homogeneous image coordinates homogeneous scene coordinates Converting from homogeneous coordinates no—division by z is nonlinear Slide by Steve Seitz Perspective Projection : Perspective Projection Projection is a matrix multiply using homogeneous coordinates: This is known as perspective projection The matrix is the projection matrix Can also formulate as a 4x4 Slide by Steve Seitz Orthographic Projection : Orthographic Projection Special case of perspective projection Distance from the COP to the PP is infinite Also called “parallel projection” What’s the projection matrix? Image World Slide by Steve Seitz Spherical Projection : Spherical Projection What if PP is spherical with center at COP? In spherical coordinates, projection is trivial: (q,f) = (q,f,d) Note: doesn’t depend on focal length d! Building a real camera : Building a real camera Camera Obscura : Camera Obscura The first camera Known to Aristotle Depth of the room is the effective focal length Camera Obscura, Gemma Frisius, 1558 Home-made pinhole camera : Home-made pinhole camera http://www.debevec.org/Pinhole/ Why so blurry? Shrinking the aperture : Shrinking the aperture Why not make the aperture as small as possible? Less light gets through Diffraction effects… Less light gets through Slide by Steve Seitz Shrinking the aperture : Shrinking the aperture The reason for lenses : The reason for lenses Slide by Steve Seitz Focus : Focus Focus and Defocus : Focus and Defocus 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 Changing the shape of the lens changes this distance Slide by Steve Seitz Thin lenses : Thin lenses Thin lens equation: Any object point satisfying this equation is in focus What is the shape of the focus region? How can we change the focus region? Thin lens applet: http://www.phy.ntnu.edu.tw/java/Lens/lens_e.html (by Fu-Kwun Hwang ) Slide by Steve Seitz Varying Focus : Varying Focus Ren Ng Depth Of Field : Depth Of Field Depth of Field : Depth of Field http://www.cambridgeincolour.com/tutorials/depth-of-field.htm Aperture controls Depth of Field : Aperture controls Depth of Field Changing the aperture size affects depth of field A smaller aperture increases the range in which the object is approximately in focus But small aperture reduces amount of light – need to increase exposure Varying the aperture : Varying the aperture Large apeture = small DOF Small apeture = large DOF Nice Depth of Field effect : Nice Depth of Field effect Field of View (Zoom) : Field of View (Zoom) Field of View (Zoom) : Field of View (Zoom) Field of View (Zoom) : Field of View (Zoom) FOV depends of Focal Length : f FOV depends of Focal Length Smaller FOV = larger Focal Length f Slide 35: From Zisserman & Hartley Field of View / Focal Length : Field of View / Focal Length Large FOV, small f Camera close to car Small FOV, large f Camera far from the car Fun with Focal Length (Jim Sherwood) : Fun with Focal Length (Jim Sherwood) http://www.hash.com/users/jsherwood/tutes/focal/Zoomin.mov Lens Flaws : Lens Flaws Lens Flaws: Chromatic Aberration : Lens Flaws: Chromatic Aberration Dispersion: wavelength-dependent refractive index (enables prism to spread white light beam into rainbow) Modifies ray-bending and lens focal length: f(?) color fringes near edges of image Corrections: add ‘doublet’ lens of flint glass, etc. Chromatic Aberration : Chromatic Aberration Near Lens Center Near Lens Outer Edge Radial Distortion (e.g. ‘Barrel’ and ‘pin-cushion’) : Radial Distortion (e.g. ‘Barrel’ and ‘pin-cushion’) straight lines curve around the image center Radial Distortion : Radial Distortion Radial distortion of the image Caused by imperfect lenses Deviations are most noticeable for rays that pass through the edge of the lens No distortion Pin cushion Barrel Radial Distortion : Radial Distortion You do not have the permission to view this presentation. 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