COMP 9517 Computer Vision
Digital Images
7/31/2017
COMP 9517 S2, 2009
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Overview of Digital Images
• Humans derive a great deal of information about
the world through their visual sense – eyes.
• Three components for construction of images:
– A scene of objects
– Illumination of the objects
– Sensing the illumination
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COMP 9517 S2, 2009
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Overview of Digital Image
• 2D digital images is an array of intensity samples
reflected from or transmitted through objects
• Digital images contain fixed number of rows and
columns of Pixels
• Pixels (picture elements) are little tiles holding
quantised values (0-255) represent the
brightness at the points of the image
• Colour images have three values for each pixel
(for example, RGB)
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COMP 9517 S2, 2009
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Overview of Digital Image
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COMP 9517 S2, 2009
3 band for
colour image
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Digital Images - 2D Projection of 3D
• 3D world has color,
texture, surfaces,
volumes, light sources,
objects, motion,
connections, etc.
• 2D image is a projection
of a scene from a specific
viewpoint; many 3D
features are captured,
but some missed.
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COMP 9517 S2, 2009
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Image Receives Reflections
• Light reaches
surfaces of objects
• Surfaces reflect
• Camera receives light
energy
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COMP 9517 S2, 2009
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Radiation
• Different types of
electromagnetic radiation,
such as X-ray, infra-red
• Different wavelengths of
radiation have different
properties
• Different devices to detect
different radiation
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COMP 9517 S2, 2009
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Image Devices
• CCD (charge-coupled
device) cameras
• Lens collects light rays
• Cells (array of small
fixed elements) convert
light energy into
electrical charge
• Through frame grabber
or IEEE 1394 to PC
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COMP 9517 S2, 2009
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Computer Vision System
• Camera inputs to
frame buffer
• Program can
interpret data
• Program can add
graphics
• Program can add
imagery
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COMP 9517 S2, 2009
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Image Formation
• The geometry of image formation: the
projection of each point of the 3D scene
through the centre of projection (or lens centre)
onto the image plane
• Pinhole Camera
• Perspective projection
• Affine projection
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COMP 9517 S2, 2009
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Perspective Projection
• The apparent size of
object depends on
their distance: far
object appear smaller
• By similar triangles
x
y
( x ' , y ' , z ' )  ( f , f , f )
z
z
• Ignore the third
coordinate, and get
x
y
( x' , y ' )  ( f , f )
z
z
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COMP 9517 S2, 2009
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Affine Project
• Scene depth is small relative to the average
distance from the camera
• Let magnification m   f ' / z0 to be positive
constant, since z0 is negative, i.e. treat all points
in scene being at constant distance from camera
• Leads to weak perspective projection
( x' , y' )  (mx,my), m   f ' / z0
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COMP 9517 S2, 2009
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Affine Project
• The camera always remains at a roughly
constant distance from the scene
• Orthographic projection when normalise m to
be -1
( x' , y ' )  ( x, y ), m  1
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COMP 9517 S2, 2009
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Picture function
• A picture function is a mathematical
representation f(x,y) of a picture as a function
of two spatial variables x and y.
– x and y: real values defining points of the picture
– f(x,y): real value defining the intensity of point (x,y)
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COMP 9517 S2, 2009
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Picture Function and Digital Images
• Analog image: a 2D image F(x,y) has infinite
precision in both spatial parameters x, y and
intensity at each spatial point (x,y)
• Digital image: a 2D image I[r,c] by a discrete 2D
array of intensity samples with limited precision
– Can be stored in a 2D computer memory structure
– 2D array of discrete values. In C, char I[512][512]
– Intensity as an 8-bit number allows values of 0-255
– 3 such values for colour image.
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COMP 9517 S2, 2009
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Sampling and Quantisation
• Digitisation: convert analog image to digital
image
• Sampling: digitising the coordinate
– spatial discretisation of a picture function f (x,y)
– use a grid of sampling points, normally rectangular:
image sampled at points x = j Δx, y = k Δy, j = 1...M, k
= 1...N.
– Δx, Δy called the sampling interval.
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COMP 9517 S2, 2009
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Spatial Resolution
• Spatial Resolution:
pixels per unit of length
• Resolution decreases
by one half
• Human faces can be
recognized at 64 x 64
pixels per face
• Appropriate resolution is essential:
– too little resolution, poor recognition
– too much resolution,slow and wastes memory
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COMP 9517 S2, 2009
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Sampling and Quantisation
• Quantisation: digitising the amplitude
values
– called intensity or gray level quantisation
– Gray-level resolution:
• usually has 16, 32, 64, ...., 128, 256 levels
• number of levels should be high enough for
human perception of shading details - human
visual system requires about 100 levels for a
realistic image.
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COMP 9517 S2, 2009
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Image Coordinate System
• Raster oriented: down-leftward (a)
• Cartesian coordinate: up-leftward (b, c)
• Relationship btn pixel centre point to I[i,j]
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COMP 9517 S2, 2009
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Type of images
• Gray-scale image: a monochrome digital image
I[r,c] with one intensity value per pixel
• Multispectral image: a 2D image M[x,y] has a
vector of values at each pixel, colour image (r,g,b)
• Binary image: a digital image with all pixel values
0 or 1
• Labelled image: a digital image L[r,c] with pixel
values as symbols denoting the decisions made
for that pixel
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COMP 9517 S2, 2009
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Digital Image Format
• Image file header: non image information for
labelling and decoding data
• Image data
• Data Compression
– Lossless: can be recovered exactly
– Lossy: may lose quality
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COMP 9517 S2, 2009
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Common Image Format
• Run-Coded Binary Image:
an efficient coding scheme for binary or
labelled images
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COMP 9517 S2, 2009
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Common Image Format
• PGM(PBM/PGM, PPM): Portable gray map
One of the simplest file formats
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COMP 9517 S2, 2009
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Common Image Format
• Gif(GIF): Graphics Interchange Format, WWW, 8
bits – 256 colour levels, may be lossless
• Tiff(TIFF/TIF): Tag Image File Format, 1-24 bits,
lossy or lossless
• Jpeg(JFIF/JFI/JPG): Joint Photographic Experts
Group, up to 24 bits, recent standard,
independent of colour system, lossy or lossless
• PostScript(PDF/PDL/EPS): encoded by ASCII
• Mpeg(MPG/MPEG/MPEG-2): Motion Picture
Expert Group, stream-oriented encoding of video
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COMP 9517 S2, 2009
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References
• Driscoll, W. and Vaughan, W., eds (1978),
Handbook of Optics, McGrtaw-Hill.
• Boyle, W. and Smith, G. (1970), Charge coupled
semiconductor devices, Bell Syst. Tech. J. 49, 587593.
• Huang, T.S.(1965), PCM Picture Transmission.
IEEE Spectrum, vol. 2, no.12, pp.57-63.
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COMP 9517 S2, 2009
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Acknowledgement
• Some material, including images and tables,
were drawn from the textbook and Stockman’s
online resources.
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COMP 9517 S2, 2008
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