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Image formation Matlab tutorial Tuesday, Sept 2 Kristen Grauman
Image formation Matlab tutorial Tuesday, Sept 2 Kristen Grauman		 Image formation Matlab tutorial Tuesday, Sept 2 Kristen Grauman
Image formation Matlab tutorial Tuesday, Sept 2 Kristen Grauman		 Image formation
Image formation		 Pinhole camera
Pinhole camera		 Pinhole camera
Pinhole camera
Camera obscura
Camera obscura		 Camera obscura
Camera obscura
Camera obscura
Camera obscura		 Camera obscura
Camera obscura		 Camera obscura
Camera obscura		 Camera obscura at home
Camera obscura at home		 Camera obscura at home
Camera obscura at home
Perspective effects
Perspective effects		 Perspective effects
Perspective effects		 Perspective effects
Perspective effects		 Perspective effects
Perspective effects		 Perspective and art
Perspective and art
Perspective and art
Perspective and art		 Perspective projection equations
Perspective projection equations		 Perspective projection equations
Perspective projection equations		 Homogeneous coordinates
Homogeneous coordinates		 Homogeneous coordinates
Homogeneous coordinates
Homogeneous coordinates
Homogeneous coordinates		 Homogeneous coordinates
Homogeneous coordinates		 Weak perspective
Weak perspective		 Weak perspective
Weak perspective		 Weak perspective
Weak perspective
Orthographic projection
Orthographic projection		 Orthographic projection
Orthographic projection		 Orthographic projection
Orthographic projection		 Orthographic projection
Orthographic projection		 Orthographic projection
Orthographic projection
Pinhole size / aperture
Pinhole size / aperture		 Pinhole size / aperture
Pinhole size / aperture		 Adding a lens
Adding a lens		 Cameras with lenses
Cameras with lenses		 Human eye
Human eye
Thin lens
Thin lens		 Thin lens equation
Thin lens equation		 Focus and depth of field
Focus and depth of field		 Focus and depth of field
Focus and depth of field		 Focus and depth of field
Focus and depth of field
Focus and depth of field
Focus and depth of field		 Focus and depth of field
Focus and depth of field		 Focus and depth of field
Focus and depth of field		 Focus and depth of field
Focus and depth of field		 Focus and depth of field
Focus and depth of field
Depth from focus
Depth from focus		 Depth from focus
Depth from focus		 Field of view
Field of view		 Field of view depends on focal length
Field of view depends on focal length		 Field of view depends on focal length
Field of view depends on focal length
Field of view depends on focal length
Field of view depends on focal length		 Resolution
Resolution		 Digital images
Digital images		 Digital images
Digital images		 Color sensing in digital cameras
Color sensing in digital cameras
Color sensing in digital cameras
Color sensing in digital cameras		 Color images, RGB color space
Color images, RGB color space		 Color images, RGB color space
Color images, RGB color space		 Historical context
Historical context		 Historical context
Historical context
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Image formation Matlab tutorial Tuesday, Sept 2 Kristen Grauman UT-Austin

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1Image formation Matlab tutorial 24Adding a lens. A lens focuses light
Tuesday, Sept 2 Kristen Grauman UT-Austin. onto the film Rays passing through the
2Image formation. How are objects in center are not deviated All parallel rays
the world captured in an image? converge to one point on a plane located
3Physical parameters of image at the focal length f. f. focal point.
formation. Geometric Type of projection Slide by Steve Seitz.
Camera pose Optical Sensor’s lens type 25Pinhole vs. lens.
focal length, field of view, aperture 26Cameras with lenses. A lens focuses
Photometric Type, direction, intensity of parallel rays onto a single focal point
light reaching sensor Surfaces’ Gather more light, while keeping focus;
reflectance properties. make pinhole perspective projection
4Image formation. Let’s design a camera practical. F. focal point. optical center
Idea 1: put a piece of film in front of an (Center Of Projection).
object Do we get a reasonable image? Slide 27Human eye. Rough analogy with human
by Steve Seitz. visual system: Pupil/Iris – control amount
5Pinhole camera. Add a barrier to block of light passing through lens Retina -
off most of the rays This reduces blurring contains sensor cells, where image is
The opening is known as the aperture How formed Fovea – highest concentration of
does this transform the image? Slide by cones. Fig from Shapiro and Stockman.
Steve Seitz. 28Thin lens. Rays entering parallel on
6Pinhole camera. Pinhole camera is a one side go through focus on other, and
simple model to approximate imaging vice versa. In ideal case – all rays from
process, perspective projection. If we P imaged at P’. Thin lens. Left focus.
treat pinhole as a point, only one ray Right focus. Lens diameter d. Focal length
from any given point can enter the camera. f.
Image plane. Virtual image. pinhole. Fig 29Thin lens equation. Any object point
from Forsyth and Ponce. satisfying this equation is in focus.
7Camera obscura. In Latin, means ‘dark 30Focus and depth of field. Image
room’. "Reinerus Gemma-Frisius, credit: cambridgeincolour.com.
observed an eclipse of the sun at Louvain 31Focus and depth of field. Depth of
on January 24, 1544, and later he used field: distance between image planes where
this illustration of the event in his book blur is tolerable. Thin lens: scene points
De Radio Astronomica et Geometrica, 1545. at distinct depths come in focus at
It is thought to be the first published different image planes. (Real camera lens
illustration of a camera obscura..." systems have greater depth of field.).
Hammond, John H., The Camera Obscura, A “circles of confusion”. Shapiro and
Chronicle. Stockman.
http://www.acmi.net.au/AIC/CAMERA_OBSCURA. 32Focus and depth of field. How does the
tml. aperture affect the depth of field? A
8Camera obscura. An attraction in the smaller aperture increases the range in
late 19th century. Jetty at Margate which the object is approximately in
England, 1898. Around 1870s. focus. Slide from S. Seitz. Flower images
http://brightbytes.com/cosite/collection2. from Wikipedia
tml. Adapted from R. Duraiswami. http://en.wikipedia.org/wiki/Depth_of_fiel
9Camera obscura at home. .
http://blog.makezine.com/archive/2006/02/h 33Depth from focus. Images from same
w_to_room_sized_camera_obscu.html. Sketch point of view, different camera
from parameters. 3d shape / depth estimates.
http://www.funsci.com/fun3_en/sky/sky.htm. [figs from H. Jin and P. Favaro, 2002].
10Perspective effects. 34Field of view. Angular measure of
11Perspective effects. Far away objects portion of 3d space seen by the camera.
appear smaller. Forsyth and Ponce. Images from
12Perspective effects. http://en.wikipedia.org/wiki/Angle_of_view
13Perspective effects. Parallel lines in 35Field of view depends on focal length.
the scene intersect in the image Converge As f gets smaller, image becomes more wide
in image on horizon line. Image plane angle more world points project onto the
(virtual). pinhole. Scene. finite image plane As f gets larger, image
14Projection properties. Many-to-one: becomes more telescopic smaller part of
any points along same ray map to same the world projects onto the finite image
point in image Points ? points Lines ? plane. from R. Duraiswami.
lines (collinearity preserved) Distances 36Field of view depends on focal length.
and angles are not preserved Degenerate Smaller FOV = larger Focal Length. Slide
cases: – Line through focal point projects by A. Efros.
to a point. – Plane through focal point 37Resolution. sensor: size of real world
projects to line – Plane perpendicular to scene element a that images to a single
image plane projects to part of the image. pixel image: number of pixels Influences
15Perspective and art. Use of correct what analysis is feasible, affects best
perspective projection indicated in 1st representation choice. [fig from Mori et
century B.C. frescoes Skill resurfaces in al].
Renaissance: artists develop systematic 38Digital cameras. Film ? sensor array
methods to determine perspective Often an array of charge coupled devices
projection (around 1480-1515). Raphael. Each CCD is light sensitive diode that
Durer, 1525. converts photons (light energy) to
16Perspective projection equations. 3d electrons. camera. CCD array. frame
world mapped to 2d projection in image grabber. optics. computer.
plane. ‘ ’. ‘’. Image plane. Focal length. 39Digital images. Think of images as
Optical axis. Camera frame. Scene / world matrices taken from CCD array.
points. Forsyth and Ponce. 40Digital images. Intensity : [0,255].
17Homogeneous coordinates. Is this a 41Color sensing in digital cameras.
linear transformation? Trick: add one more Bayer grid. Estimate missing components
coordinate: Converting from homogeneous from neighboring values (demosaicing).
coordinates. no—division by z is Source: Steve Seitz.
nonlinear. homogeneous scene coordinates. 42Color images, RGB color space. B. R.
homogeneous image coordinates. Slide by G.
Steve Seitz. 43Historical context. Pinhole model:
18Perspective Projection Matrix. Mozi (470-390 BCE), Aristotle (384-322
Projection is a matrix multiplication BCE) Principles of optics (including
using homogeneous coordinates: Complete lenses): Alhacen (965-1039 CE) Camera
mapping from world points to image pixel obscura: Leonardo da Vinci (1452-1519),
positions? divide by the third coordinate Johann Zahn (1631-1707) First photo:
to convert back to non-homogeneous Joseph Nicephore Niepce (1822)
coordinates. Slide by Steve Seitz. Daguerr?otypes (1839) Photographic film
19Perspective projection & (Eastman, 1889) Cinema (Lumi?re Brothers,
calibration. Perspective equations so far 1895) Color Photography (Lumi?re Brothers,
in terms of camera’s reference frame…. 1908) Television (Baird, Farnsworth,
Camera’s intrinsic and extrinsic Zworykin, 1920s) First consumer camera
parameters needed to calibrate geometry. with CCD: Sony Mavica (1981) First fully
Camera frame. digital camera: Kodak DCS100 (1990).
20Perspective projection & Alhacen’s notes. Niepce, “La Table
calibration. Extrinsic: Camera frame Servie,” 1822. Slide credit: L. Lazebnik.
??World frame. Intrinsic: Image CCD chip.
coordinates relative to camera ?? Pixel 44Summary. Image formation affected by
coordinates. World frame. Camera frame. geometry, photometry, and optics.
21Weak perspective. Approximation: treat Projection equations express how world
magnification as constant Assumes scene points mapped to 2d image. Homogenous
depth << average distance to camera. coordinates allow linear system for
Image plane. World points: projection equations. Lenses make pinhole
22Orthographic projection. Given camera model practical. Parameters (focal length,
at constant distance from scene World aperture, lens diameter,…) affect image
points projected along rays parallel to obtained.
optical access. 45Next. Problem set 0 due Thursday
23Pinhole size / aperture. How does the turnin --submit harshd pset0
size of the aperture affect the image we’d <filename> Thursday: Color Read
get? Larger. Smaller. F&P Chapter 6.
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