Image formation Matlab tutorial Tuesday, Sept 2 Kristen Grauman UT-Austin |
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1 | Image formation Matlab tutorial | 24 | Adding a lens. A lens focuses light |
Tuesday, Sept 2 Kristen Grauman UT-Austin. | onto the film Rays passing through the | ||
2 | Image 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 | ||
3 | Physical 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 | 25 | Pinhole vs. lens. | |
focal length, field of view, aperture | 26 | Cameras 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 | ||
4 | Image 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 | 27 | Human eye. Rough analogy with human | |
by Steve Seitz. | visual system: Pupil/Iris – control amount | ||
5 | Pinhole 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. | 28 | Thin lens. Rays entering parallel on | |
6 | Pinhole 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 | 29 | Thin lens equation. Any object point | |
from Forsyth and Ponce. | satisfying this equation is in focus. | ||
7 | Camera obscura. In Latin, means ‘dark | 30 | Focus and depth of field. Image |
room’. "Reinerus Gemma-Frisius, | credit: cambridgeincolour.com. | ||
observed an eclipse of the sun at Louvain | 31 | Focus 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. | 32 | Focus and depth of field. How does the | |
tml. | aperture affect the depth of field? A | ||
8 | Camera 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 | ||
9 | Camera obscura at home. | . | |
http://blog.makezine.com/archive/2006/02/h | 33 | Depth 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]. | ||
10 | Perspective effects. | 34 | Field of view. Angular measure of |
11 | Perspective effects. Far away objects | portion of 3d space seen by the camera. | |
appear smaller. Forsyth and Ponce. | Images from | ||
12 | Perspective effects. | http://en.wikipedia.org/wiki/Angle_of_view | |
13 | Perspective effects. Parallel lines in | 35 | Field 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 | ||
14 | Projection 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 | 36 | Field 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 | 37 | Resolution. 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 | ||
15 | Perspective 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 | 38 | Digital 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 | ||
16 | Perspective projection equations. 3d | electrons. camera. CCD array. frame | |
world mapped to 2d projection in image | grabber. optics. computer. | ||
plane. ‘ ’. ‘’. Image plane. Focal length. | 39 | Digital images. Think of images as | |
Optical axis. Camera frame. Scene / world | matrices taken from CCD array. | ||
points. Forsyth and Ponce. | 40 | Digital images. Intensity : [0,255]. | |
17 | Homogeneous coordinates. Is this a | 41 | Color 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. | 42 | Color images, RGB color space. B. R. | |
homogeneous image coordinates. Slide by | G. | ||
Steve Seitz. | 43 | Historical context. Pinhole model: | |
18 | Perspective 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 | ||
19 | Perspective 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). | ||
20 | Perspective 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 | 44 | Summary. Image formation affected by | |
coordinates. World frame. Camera frame. | geometry, photometry, and optics. | ||
21 | Weak 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 | ||
22 | Orthographic 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. | 45 | Next. Problem set 0 due Thursday | |
23 | Pinhole 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. | ||
Image formation Matlab tutorial Tuesday, Sept 2 Kristen Grauman UT-Austin.ppt |
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