2-Camera-Properties.pdf

Camera properties
Panu Srestasathiern, PhD.
Researcher
Geo-Informatics and Space Technology Development Agency (Public Organization)
Camera properties

Image formation
Image formation -
- Recap
Recap
• The geometry of imaging system
pixel coordinate
system
x
world coordinate
system
camera coordinate
system
(R,T)
image coordinate
system
x1

Interior orientation
Interior orientation
• Interior orientation is the metric characteristics of cameras.
• It is used to convert pixel coordinates to coordinates in
camera space coordinate system.

Pinhole camera
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.

The reason for lenses
Lenses gather and
focus light, allowing
for brighter images.
for brighter images.

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

Camera Geometry
Camera Geometry
• The aperture allows light to enter the camera
• The image plane is where the image is formed
• The focal length is the distance between the aperture and the image
plane
• The optical axis passes through the center of the aperture and is
perpendicular to it.

Perspective projection equations
Perspective projection equations
• 3D world mapped to 2D projection in image plane
Image plane
Focal
length Scene / world points
Len
Forsyth and Ponce
Camera coordinate system
Optical axis

Image digitization
Image digitization
• Image sensor
– Complimentary Metal-Oxide Semiconductor (CMOS)
– Charge-Coupled Device (CCD)

Image digitization
Image digitization
• Sampling means measuring the value of an image at a finite
number of points.
• Quantization is the representation of the measured value at
the sampled point by an integer.

Digital images
Digital images
Think of images as matrices
taken from CCD array.

Digital images
Digital images width
520
j=1
i=1
Intensity : [0,255]
im[176][201] has
value 164
im[194][203] has
value 37
500
height

Exercise
Exercise
• An image’s dimension is 5184 [pixel] x 3888 [pixel]
• The sensor size is 6.17mm x 4.55 mm
• What is the pixel size in mm or micron

Exercise
Exercise
• What is the pixel size of the Sony Alpha NEX-5T at max
resolution
HINT: https://www.dpreview.com/
HINT: https://www.dpreview.com/

Focus and depth of field
• Depth of field: distance between image planes where blur is
tolerable
• How does the aperture affect the depth of field?
• A smaller aperture increases the range in which the object is
approximately in focus
approximately in focus

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

Smaller FOV = larger Focal Length

Imaging sensors: recording the image
Imaging sensors: recording the image
• Flash memory: fixed or removable solid state storage device
• Storage format:
– TIFF : uncompressed
– JPEG : compressed at various quality settings
Example
Example
TIFF JPEG JPEG
(Hi quality) (med quality)
640x280 pixels 1.0 MB 300 KB 90KB

Common Lens Related Issues
Common Lens Related Issues -
- Summary
Summary
Compound (Thick) Lens Vignetting
thickness
principal planes
nodal points
α
α
1
L
2
L
3
L
B
A
more light from A than B !
Chromatic Abberation Radial and Tangential Distortion
R
F
B
F G
F
Lens has different refractive indices
for different wavelengths.
image plane
ideal actual
ideal
actual

Lens Glare
Lens Glare
• Stray interreflections of light within the optical lens system.
• Happens when very bright sources are present in the scene.

Vignetting
Vignetting
• Vignetting is the result of light rays not making it through the
entire lens system to the sensor, due to being blocked by the
edges of individual lens elements or mechanical stops.
• Vignetting is most often seen at or in lower f/#s, short focal
length lenses, or lenses where higher resolutions need to be
length lenses, or lenses where higher resolutions need to be
achieved at a lower cost.

Vignetting
Vignetting
• light rays are clipped by the edges of the lens

Chromatic aberration
• As the refractive index of a transmittive medium is dependent
on the wavelenght of light, dispersion occurs, when white
light transmits such a medium.
• Refraction is stronger for light of short wavelengths, for
example blue, and less intensive for light of long wavelngths,
example blue, and less intensive for light of long wavelngths,
for example red.

• There are two main types of chromatic aberrations:
– The LATERAL (or transverse) chromatic aberration.
– The LONGITUDINAL chromatic aberration.

• LONGITUDINAL CHROMATIC ABERRATION
• There is longitudinal chromatic aberration, if a lens cannot
focus different colors in the same focal plane.
• It is caused by straight incident light.
• The foci of the different colors lie at different points in the
• The foci of the different colors lie at different points in the
longitudinal direction along the optical axis.

• LONGITUDINAL CHROMATIC ABERRATION
The longitidinal chromatic aberration leads to colored areas in
the images, that arise, because not all three colors can be
displayed in focus.
Longitudinal
chromatic aberration
is an error of focus

• LATERAL CHROMATIC ABERRATION
• Obliquely incident light leads to lateral chromatic aberration.
• In that case all colors are in focus in the same plane, but the
foci are not placed along the optical axis.
Lateral chromatic
aberration is an error
of magnification

• Comparison

Geometric Lens Distortions
• Ideally, a photograph should be a perfect pers-pective
mapping of the photographed scene.
• For example, the image of a straight line must be straight.

• Radial distortion
Radial lens distortion is the symmetric distortion caused by
the lens due to imperfections in curvature when the lens
was ground.
The distortion appear in radial direction.
The distortion appear in radial direction.
In other words, the image’s scale changes moving from the
center of the field to the edges, leading to straight lines
curving either towards the center or towards the edges.

Ideally, the image of circle is circle.

No Distortion Barrel Distortion Pincushion Distortion
(Positive distortion) (Negative distortion)

In barrel distortion, image magnification decreases with
distance from the optical axis.
In pincushion distortion, image magnification increases with
the distance from the optical axis.
the distance from the optical axis.
The wide-angle lenses (or rather zoom lenses when set to
short focal length) typically produce a pronounced barrel
distortion.

• Tangential distortion
Tangential distortion occurs when the lens and the image
plane are not parallel. The tangential distortion coefficients
model this type of distortion.

• Tangential distortion
Tangential distortion is perpendicular to radial direction.

Correcting radial distortion
Correcting radial distortion
from Helmut Dersch

Geometric lens distortions
Geometric lens distortions
• Mathematical model of radial and tangential distortion
• How to get these parameters? Camera calibration

Camera calibration
Camera calibration
• Simple method for off-the-shelf camera
– Use images of calibration pattern

• Spatial Resolution is the minimum distance between two
adjacent features or the minimum size of a feature, that can
be detected by a remote sensing system.
(www.geocomm.com)
• Spatial Resolution is not simply ground sample distance
What is Spatial Resolution?
What is Spatial Resolution?
• Spatial Resolution is not simply ground sample distance
– Also depends on how well a system is focused
• Point Spread Function (PSF)
43

Point Spread Function (PSF)
• Image of a point source

Image Formation Example I
Image Formation Example I

Image Formation Example II
Image Formation Example II

Relation between aperture size and Airy disk
• Diffraction Increases as the Imaging Lens Iris is Closed (f/A
Increases where A is the aperture size)

• Mathematical formula:

A real experiment
A real experiment
• Canon EOS Rebel 8 Megapixel Camera
Max resolution 3456 x 2304
CMOS Bayer Array
Manual mode
Raw data
Raw data
Pixel size 6.3 micron

High Spatial Resolution Data
High Spatial Resolution Data
Measured building
GSD = 1.2 cm
52

Image Variation with GSD
Image Variation with GSD
GSD = 4.8 cm GSD = 12 cm GSD = 18 cm

Image variation with aperture size
Image variation with aperture size
Increase aperture size
GSD = 4.8 cm

Optimal aperture size
• The diameter of Airy disk should less than the pixel size.
• That is, the main lobe of Airy disk should be in a single pixel.
Average visible wavelength is
approx. 540 micrometer.

• Exercise: …..

Radiometric characteristics
• Important preprocessing step for many vision and graphics
algorithms
• Use a color chart with precisely known reflectances.

• Use more camera exposures to fill up the curve.
• Method assumes constant lighting on all patches and works
best when source is far away (example sunlight).
• Unique inverse exists because g is monotonic and smooth for
all cameras.
all cameras.

2-Camera-Properties.pdf

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