Без темы <<  Im nice Immigrants and Religious Conflict  >>
 Image formation Matlab tutorial Tuesday, Sept 2 Kristen Grauman Image formation Physical parameters of image formation Image formation Pinhole camera Pinhole camera Camera obscura Camera obscura Camera obscura at home Perspective effects Perspective effects Perspective effects Perspective effects Projection properties Perspective and art Perspective projection equations Homogeneous coordinates Perspective Projection Matrix Perspective projection & calibration Perspective projection & calibration Weak perspective Orthographic projection Pinhole size / aperture Adding a lens Pinhole vs Cameras with lenses Human eye Thin lens Thin lens equation Focus and depth of field Focus and depth of field Focus and depth of field Depth from focus Field of view Field of view depends on focal length Field of view depends on focal length Resolution Digital cameras Digital images Digital images Color sensing in digital cameras Color images, RGB color space Historical context Summary Next

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## Image formation Matlab tutorial Tuesday, Sept 2 Kristen Grauman UT-Austin

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UT-Austin

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### Image formation

How are objects in the world captured in an image?

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### Physical parameters of image formation

Geometric Type of projection Camera pose Optical Sensor’s lens type focal length, field of view, aperture Photometric Type, direction, intensity of light reaching sensor Surfaces’ reflectance properties

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### Image formation

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

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### Pinhole camera

Add a barrier to block off most of the rays This reduces blurring The opening is known as the aperture How does this transform the image?

Slide by Steve Seitz

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### Pinhole camera

Pinhole camera is a simple model to approximate imaging process, perspective projection.

If we treat pinhole as a point, only one ray from any given point can enter the camera.

Image plane

Virtual image

pinhole

Fig from Forsyth and Ponce

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### Camera obscura

In Latin, means ‘dark room’

"Reinerus Gemma-Frisius, observed an eclipse of the sun at Louvain on January 24, 1544, and later he used this illustration of the event in his book De Radio Astronomica et Geometrica, 1545. It is thought to be the first published illustration of a camera obscura..." Hammond, John H., The Camera Obscura, A Chronicle

http://www.acmi.net.au/AIC/CAMERA_OBSCURA.html

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### Camera obscura

An attraction in the late 19th century

Jetty at Margate England, 1898.

Around 1870s

http://brightbytes.com/cosite/collection2.html

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### Camera obscura at home

http://blog.makezine.com/archive/2006/02/how_to_room_sized_camera_obscu.html

Sketch from http://www.funsci.com/fun3_en/sky/sky.htm

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### Perspective effects

Far away objects appear smaller

Forsyth and Ponce

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### Perspective effects

Parallel lines in the scene intersect in the image Converge in image on horizon line

Image plane (virtual)

pinhole

Scene

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### Projection properties

Many-to-one: any points along same ray map to same point in image Points ? points Lines ? lines (collinearity preserved) Distances and angles are not preserved Degenerate cases: – Line through focal point projects to a point. – Plane through focal point projects to line – Plane perpendicular to image plane projects to part of the image.

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### Perspective and art

Use of correct perspective projection indicated in 1st century B.C. frescoes Skill resurfaces in Renaissance: artists develop systematic methods to determine perspective projection (around 1480-1515)

Raphael

Durer, 1525

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### Perspective projection equations

3d world mapped to 2d projection in image plane

‘ ’

‘’

Image plane

Focal length

Optical axis

Camera frame

Scene / world points

Forsyth and Ponce

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### Homogeneous coordinates

Is this a linear transformation?

Converting from homogeneous coordinates

no—division by z is nonlinear

homogeneous scene coordinates

homogeneous image coordinates

Slide by Steve Seitz

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### Perspective Projection Matrix

Projection is a matrix multiplication using homogeneous coordinates:

Complete mapping from world points to image pixel positions?

divide by the third coordinate to convert back to non-homogeneous coordinates

Slide by Steve Seitz

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### Perspective projection & calibration

Perspective equations so far in terms of camera’s reference frame…. Camera’s intrinsic and extrinsic parameters needed to calibrate geometry.

Camera frame

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### Perspective projection & calibration

Extrinsic: Camera frame ??World frame

Intrinsic: Image coordinates relative to camera ?? Pixel coordinates

World frame

Camera frame

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### Weak perspective

Approximation: treat magnification as constant Assumes scene depth << average distance to camera

Image plane

World points:

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### Orthographic projection

Given camera at constant distance from scene World points projected along rays parallel to optical access

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### Pinhole size / aperture

How does the size of the aperture affect the image we’d get?

Larger

Smaller

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A lens focuses light onto the film Rays passing through the center are not deviated All parallel rays converge to one point on a plane located at the focal length f

f

focal point

Slide by Steve Seitz

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lens

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### Cameras with lenses

A lens focuses parallel rays onto a single focal point Gather more light, while keeping focus; make pinhole perspective projection practical

F

focal point

optical center (Center Of Projection)

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### Human eye

Rough analogy with human visual system:

Pupil/Iris – control amount of light passing through lens Retina - contains sensor cells, where image is formed Fovea – highest concentration of cones

Fig from Shapiro and Stockman

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### Thin lens

Rays entering parallel on one side go through focus on other, and vice versa. In ideal case – all rays from P imaged at P’.

Thin lens

Left focus

Right focus

Lens diameter d

Focal length f

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### Thin lens equation

Any object point satisfying this equation is in focus

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### Focus and depth of field

Image credit: cambridgeincolour.com

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### Focus and depth of field

Depth of field: distance between image planes where blur is tolerable

Thin lens: scene points at distinct depths come in focus at different image planes. (Real camera lens systems have greater depth of field.)

“circles of confusion”

Shapiro and Stockman

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### Focus and depth of field

How does the aperture affect the depth of field?

A smaller aperture increases the range in which the object is approximately in focus

Slide from S. Seitz

Flower images from Wikipedia http://en.wikipedia.org/wiki/Depth_of_field

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### Depth from focus

Images from same point of view, different camera parameters

3d shape / depth estimates

[figs from H. Jin and P. Favaro, 2002]

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### Field of view

Angular measure of portion of 3d space seen by the camera

Images from http://en.wikipedia.org/wiki/Angle_of_view

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### Field of view depends on focal length

As f gets smaller, image becomes more wide angle more world points project onto the finite image plane As f gets larger, image becomes more telescopic smaller part of the world projects onto the finite image plane

from R. Duraiswami

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### Field of view depends on focal length

Smaller FOV = larger Focal Length

Slide by A. Efros

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### Resolution

sensor: size of real world scene element a that images to a single pixel image: number of pixels Influences what analysis is feasible, affects best representation choice.

[fig from Mori et al]

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### Digital cameras

Film ? sensor array Often an array of charge coupled devices Each CCD is light sensitive diode that converts photons (light energy) to electrons

camera

CCD array

frame grabber

optics

computer

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### Digital images

Think of images as matrices taken from CCD array.

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### Digital images

Intensity : [0,255]

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### Color sensing in digital cameras

Bayer grid

Estimate missing components from neighboring values (demosaicing)

Source: Steve Seitz

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B

R

G

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### Historical context

Pinhole model: Mozi (470-390 BCE), Aristotle (384-322 BCE) Principles of optics (including lenses): Alhacen (965-1039 CE) Camera obscura: Leonardo da Vinci (1452-1519), Johann Zahn (1631-1707) First photo: Joseph Nicephore Niepce (1822) Daguerr?otypes (1839) Photographic film (Eastman, 1889) Cinema (Lumi?re Brothers, 1895) Color Photography (Lumi?re Brothers, 1908) Television (Baird, Farnsworth, Zworykin, 1920s) First consumer camera with CCD: Sony Mavica (1981) First fully digital camera: Kodak DCS100 (1990)

Alhacen’s notes

Niepce, “La Table Servie,” 1822

Slide credit: L. Lazebnik

CCD chip

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### Summary

Image formation affected by geometry, photometry, and optics. Projection equations express how world points mapped to 2d image. Homogenous coordinates allow linear system for projection equations. Lenses make pinhole model practical. Parameters (focal length, aperture, lens diameter,…) affect image obtained.

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### Next

Problem set 0 due Thursday turnin --submit harshd pset0 <filename> Thursday: Color Read F&P Chapter 6

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